31:
2312:
2918:
2818:
1226:), while the gluon fields are defined on the links connecting neighboring sites. This approximation approaches continuum QCD as the spacing between lattice sites is reduced to zero. Because the computational cost of numerical simulations can increase dramatically as the lattice spacing decreases, results are often
1388:
The lattice discretization means approximating continuous and infinite space-time by a finite lattice spacing and size. The smaller the lattice, and the bigger the gap between nodes, the bigger the error. Limited resources commonly force the use of smaller physical lattices and larger lattice spacing
1979:
Bennett, Ed; Lucini, Biagio; Del Debbio, Luigi; Jordan, Kirk; Patella, Agostino; Pica, Claudio; Rago, Antonio; Trottier, H. D.; Wingate, M.; Aubin, C.; Bernard, C.; Burch, T.; DeTar, C.; Gottlieb, Steven; Gregory, E. B.; Heller, U. M.; Hetrick, J. E.; Osborn, J.; Sugar, R.; Toussaint, D.; Di Pierro,
1436:
as a framework for studying strongly coupled theories non-perturbatively. However, it was found to be a regularization suitable also for perturbative calculations. Perturbation theory involves an expansion in the coupling constant, and is well-justified in high-energy QCD where the coupling constant
1383:
Lattice QCD is a way to solve the theory exactly from first principles, without any assumptions, to the desired precision. However, in practice the calculation power is limited, which requires a smart use of the available resources. One needs to choose an action which gives the best physical
1392:
The quark masses are also approximated. Quark masses are larger than experimentally measured. These have been steadily approaching their physical values, and within the past few years a few collaborations have used nearly physical values to extrapolate down to physical
1437:
is small, while it fails completely when the coupling is large and higher order corrections are larger than lower orders in the perturbative series. In this region non-perturbative methods, such as Monte-Carlo sampling of the correlation function, are necessary.
1253:
can be used, in which the quark fields are treated as non-dynamic "frozen" variables. While this was common in early lattice QCD calculations, "dynamical" fermions are now standard. These simulations typically utilize algorithms based upon
1448:. In this case the lattice spacing is a real physical value, and not an artifact of the calculation which has to be removed (a UV regulator), and a quantum field theory can be formulated and solved on the physical lattice.
1384:
description of the system, with minimum errors, using the available computational power. The limited computer resources force one to use approximate physical constants which are different from their true physical values:
1210:
is the lattice spacing, which regularizes the theory. As a result, lattice QCD is mathematically well-defined. Most importantly, lattice QCD provides a framework for investigation of non-perturbative phenomena such as
1980:
M.; El-Khadra, A.; Kronfeld, A. S.; Mackenzie, P. B.; Menscher, D.; Simone, J. (2016). "BSMBench: A flexible and scalable HPC benchmark from beyond the standard model physics".
1421:
Lattice QCD Monte-Carlo calculations. In perturbative calculations both the operators of the action and the propagators are calculated on the lattice and expanded in powers of
1187:
of points in space and time. When the size of the lattice is taken infinitely large and its sites infinitesimally close to each other, the continuum QCD is recovered.
2562:
1472:
Currently there is no formulation of lattice QCD that allows us to simulate the real-time dynamics of a quark-gluon system such as quarkâgluon plasma.
280:
2211:
2084:
1429:, otherwise the results cannot be compared. The expansion has to be carried out to the same order in the continuum scheme and the lattice one.
1147:
1456:
The U(1), SU(2), and SU(3) lattice gauge theories can be reformulated into a form that can be simulated using "spin qubit manipulations" on a
1202:
at low energies. This formulation of QCD in discrete rather than continuous spacetime naturally introduces a momentum cut-off at the order 1/
1349:
1309:
Lattice QCD has also been used as a benchmark for high-performance computing, an approach originally developed in the context of the IBM
1284:
has been determined theoretically with an error of less than 2 percent. Lattice QCD predicts that the transition from confined quarks to
200:
2855:
1425:. When renormalizing a calculation, the coefficients of the expansion need to be matched with a common continuum scheme, such as the
240:
1368:
interaction part of the action to calculate the gauge configurations, and then uses the simulated gauge configurations to calculate
2418:
1397:
In order to compensate for the errors one improves the lattice action in various ways, to minimize mainly finite spacing errors.
1164:
1596:; Trottier, H. D.; Wingate, M.; Aubin, C.; Bernard, C.; et al. (2004). "High-Precision Lattice QCD Confronts Experiment".
2007:
1005:
2686:
2204:
1140:
2681:
770:
3365:
3122:
1670:
A. Bazavov; et al. (2010). "Nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks".
1357:
43:
2031:
Byrnes, Tim; Yamamoto, Yoshihisa (17 February 2006). "Simulating lattice gauge theories on a quantum computer".
1199:
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117:
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875:
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147:
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250:
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Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly
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2451:
1457:
152:
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2651:
2441:
2351:
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303:
245:
1814:
S. DĂŒrr; Z. Fodor; J. Frison; et al. (2008). "Ab Initio
Determination of Light Hadron Masses".
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3238:
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technique used to select the gauge configurations in the Monte-Carlo simulation imposes the use of
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Lattice QCD has already successfully agreed with many experiments. For example, the mass of the
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are free from the sign problem when applied to the case of QCD with gauge group SU(2) (QC
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In lattice QCD, fields representing quarks are defined at lattice sites (which leads to
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2013:
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can be extremely computationally intensive, requiring the use of the largest available
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2016 International
Conference on High Performance Computing & Simulation (HPCS)
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It provides reliable predictions only for hadrons containing heavy quarks, such as
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2085:"ALICE collaboration opens avenue for high-precision studies of the strong force"
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At present, lattice QCD is primarily applicable at low densities where the
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92:
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2163:
Chandrasekharan, Wiese - An
Introduction to Chiral Symmetry on the Lattice
1360:, which depends on the action and the fields. Usually one starts with the
3243:
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3049:
2622:
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2525:
2311:
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3054:
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2802:
2761:
2741:
2736:
2552:
2461:
2346:
1764:
1730:(1982). "Microcanonical Ensemble Formulation of Lattice Gauge Theory".
1722:
1515:
1372:
745:
655:
520:
460:
132:
67:
1329:
is a method to pseudo-randomly sample a large space of variables. The
1219:
formation, which are intractable by means of analytic field theories.
2782:
2535:
2456:
2428:
2341:
1342:
1310:
1191:
2917:
3319:
3147:
2600:
2595:
2513:
1946:
705:
1990:
1889:
1828:
1684:
3279:
3167:
3102:
3019:
3014:
2590:
1483:
1445:
1365:
2888:
2585:
2508:
2503:
2466:
1475:
It is computationally intensive, with the bottleneck not being
1369:
1356:, using field configurations which are chosen according to the
1302:
1281:
1592:; Follana, E.; Gray, A.; Lepage, G. P.; Mason, Q.; Nobes, M.;
2897:
2883:
1978:
1476:
1444:
theory. One can use the lattice to represent the real atomic
1176:
1172:
1875:
P. Petreczky (2012). "Lattice QCD at non-zero temperature".
2331:
2231:
1348:
In lattice Monte-Carlo simulations the aim is to calculate
2817:
2893:
1440:
Lattice perturbation theory can also provide results for
2158:
Lombardo - Lattice QCD at Finite
Temperature and Density
1813:
2184:
1588:
1432:
The lattice regularization was initially introduced by
1234:
by repeated calculations at different lattice spacings
2172:
1774:"Lattice gauge theory in the microcanonical ensemble"
1249:. To reduce the computational burden, the so-called
1389:than wanted, leading to larger errors than wanted.
1306:), within the range of experimental measurements.
3352:
1582:
2030:
1400:
2849:
2205:
2173:The FermiQCD Library for Lattice Field theory
1352:. This is done by explicitly calculating the
1141:
2168:Kuti, Julius - Lattice QCD and String Theory
1874:
2863:
2119:Introduction to Quantum Fields on a Lattice
1468:The method suffers from a few limitations:
2856:
2842:
2212:
2198:
2133:Lattice Methods for Quantum Chromodynamics
1669:
1378:
1321:
1148:
1134:
29:
2219:
2044:
1989:
1963:
1945:
1888:
1827:
1683:
1665:
1663:
1611:
1241:Numerical lattice QCD calculations using
1927:
2126:Lattice Gauge Theories, An Introduction
1238:that are large enough to be tractable.
3353:
1660:
1548:
1269:does not interfere with calculations.
2837:
2637:Inverse beta decay (electron capture)
2193:
2140:Quantum Chromodynamics on the Lattice
1542:
1451:
1417:. The results are used primarily to
2153:Gupta - Introduction to Lattice QCD
1928:Rafelski, Johann (September 2015).
1479:but the bandwidth of memory access.
1405:In lattice perturbation theory the
16:Quantum chromodynamics on a lattice
13:
2121:, Cambridge University Press 2002.
2111:, Cambridge University Press 1997.
2104:, Cambridge University Press 1985.
2094:
1413:in powers of the lattice spacing,
14:
3377:
2146:
1930:"Melting hadrons, boiling quarks"
1552:(1974). "Confinement of quarks".
2916:
2816:
2419:TolmanâOppenheimerâVolkoff limit
2310:
2185:Flavour Lattice Averaging Group
2077:
2024:
1934:The European Physical Journal A
1288:occurs around a temperature of
2138:C. Gattringer and C. B. Lang,
1972:
1921:
1868:
1807:
1758:
1716:
1463:
329:Renormalization group equation
1:
3305:Macroscopic quantum phenomena
1907:10.1088/0954-3899/39/9/093002
1630:10.1103/PhysRevLett.92.022001
1536:
1521:SU(2) color superconductivity
1316:
158:Spontaneous symmetry breaking
118:Symmetry in quantum mechanics
3315:Order and disorder (physics)
2704:Quantum chromodynamics (QCD)
2647:Electron degeneracy pressure
7:
2109:Quantum Fields on a Lattice
2107:I. Montvay and G. MĂŒnster,
2102:Quarks, gluons and lattices
2000:10.1109/HPCSim.2016.7568421
1494:
1401:Lattice perturbation theory
1375:and correlation functions.
10:
3382:
2063:10.1103/PhysRevA.73.022328
1965:10.1140/epja/i2015-15114-0
1752:10.1103/PhysRevLett.49.613
1702:10.1103/RevModPhys.82.1349
1458:universal quantum computer
1163:is a well-established non-
153:Explicit symmetry breaking
3267:
3221:
3093:
3007:
2981:
2925:
2914:
2876:
2811:
2775:
2727:
2667:
2652:Pauli exclusion principle
2571:
2487:
2427:
2401:
2352:Supernova nucleosynthesis
2319:
2308:
2285:Cataclysmic variable star
2230:
2131:T. DeGrand and C. DeTar,
1672:Reviews of Modern Physics
1486:, which have one or more
319:BargmannâWigner equations
246:Path Integral Formulation
3340:Thermo-dielectric effect
3239:Enthalpy of vaporization
2933:BoseâEinstein condensate
2608:Fundamental interactions
2135:, World Scientific 2006.
2128:, World Scientific 2005.
1801:10.1103/PhysRevD.28.1506
1576:10.1103/PhysRevD.10.2445
1183:formulated on a grid or
1167:approach to solving the
324:Schwinger-Dyson equation
3234:Enthalpy of sublimation
2694:Quantum electrodynamics
2300:Super soft X-ray source
1846:10.1126/science.1163233
1732:Physical Review Letters
1599:Physical Review Letters
1501:Lattice model (physics)
1379:Fermions on the lattice
1322:Monte-Carlo simulations
1260:microcanonical ensemble
354:Electroweak interaction
349:Quantum electrodynamics
314:WheelerâDeWitt equation
191:Background field method
3366:Quantum chromodynamics
3249:Latent internal energy
2999:Color-glass condensate
2803:Physics of shock waves
2563:Observational timeline
2409:Gravitational collapse
1267:numerical sign problem
1251:quenched approximation
1169:quantum chromodynamics
359:Quantum chromodynamics
216:Effective field theory
3059:Magnetically ordered
2699:Quantum hydrodynamics
1358:distribution function
1350:correlation functions
304:KleinâGordon equation
236:LSZ reduction formula
3361:Lattice field theory
2938:Fermionic condensate
2793:Nuclear astrophysics
2581:Elementary particles
1984:. pp. 834â839.
1766:David J. E. Callaway
1724:David J. E. Callaway
1511:Lattice gauge theory
1506:Lattice field theory
1181:lattice gauge theory
397:Theory of everything
231:Lattice field theory
201:Correlation function
23:Quantum field theory
3153:Chemical ionization
3045:Programmable matter
3035:Quantum spin liquid
2903:Supercritical fluid
2642:Degeneracy pressure
2572:Particles, forces,
2414:Chandrasekhar limit
2055:2006PhRvA..73b2328B
1956:2015EPJA...51..114R
1899:2012JPhG...39i3002P
1838:2008Sci...322.1224D
1793:1983PhRvD..28.1506C
1744:1982PhRvL..49..613C
1694:2010RvMP...82.1349B
1622:2004PhRvL..92b2001D
1568:1974PhRvD..10.2445W
1331:importance sampling
1271:Monte Carlo methods
1243:Monte Carlo methods
376:Incomplete theories
3300:Leidenfrost effect
3229:Enthalpy of fusion
2994:Quarkâgluon plasma
2798:Physical cosmology
2752:Quarkâgluon plasma
2613:Strong interaction
2178:2015-02-03 at the
1286:quarkâgluon plasma
1256:molecular dynamics
1217:quarkâgluon plasma
241:Partition function
168:Topological charge
88:General relativity
83:Special relativity
3348:
3347:
3330:Superheated vapor
3325:Superconductivity
3295:Equation of state
3143:Flash evaporation
3095:Phase transitions
3080:String-net liquid
2973:Photonic molecule
2943:Degenerate matter
2831:
2830:
2729:Degenerate matter
2714:Color confinement
2677:Quantum mechanics
2374:Carbon detonation
2320:Stellar processes
2033:Physical Review A
2009:978-1-5090-2088-1
1555:Physical Review D
1452:Quantum computing
1407:scattering matrix
1200:coupling constant
1158:
1157:
221:Expectation value
196:BRST quantization
143:Poincaré symmetry
98:YangâMills theory
78:Quantum mechanics
3373:
3285:Compressed fluid
2920:
2865:States of matter
2858:
2851:
2844:
2835:
2834:
2823:Stars portal
2821:
2820:
2618:Weak interaction
2574:and interactions
2558:Electroweak star
2452:Pair instability
2369:Electron capture
2314:
2214:
2207:
2200:
2191:
2190:
2142:, Springer 2010.
2089:
2088:
2081:
2075:
2074:
2048:
2046:quant-ph/0510027
2028:
2022:
2021:
1993:
1976:
1970:
1969:
1967:
1949:
1925:
1919:
1918:
1892:
1872:
1866:
1865:
1831:
1822:(5905): 1224â7.
1811:
1805:
1804:
1787:(6): 1506â1514.
1778:
1762:
1756:
1755:
1720:
1714:
1713:
1687:
1678:(2): 1349â1417.
1667:
1658:
1657:
1615:
1590:Davies, C. T. H.
1586:
1580:
1579:
1546:
1442:condensed matter
1305:
1300:
1294:
1224:fermion doubling
1171:(QCD) theory of
1150:
1143:
1136:
211:Effective action
138:Lorentz symmetry
63:Electromagnetism
33:
19:
18:
3381:
3380:
3376:
3375:
3374:
3372:
3371:
3370:
3351:
3350:
3349:
3344:
3275:Baryonic matter
3263:
3217:
3188:Saturated fluid
3128:Crystallization
3089:
3063:Antiferromagnet
3003:
2977:
2921:
2912:
2872:
2862:
2832:
2827:
2815:
2807:
2771:
2723:
2663:
2632:Pair production
2573:
2567:
2541:Shell collapsar
2490:
2483:
2423:
2397:
2383:Gamma-ray burst
2363:Bondi accretion
2337:Nucleosynthesis
2315:
2306:
2265:Stellar physics
2226:
2218:
2180:Wayback Machine
2149:
2097:
2095:Further reading
2092:
2083:
2082:
2078:
2029:
2025:
2010:
1977:
1973:
1926:
1922:
1873:
1869:
1812:
1808:
1781:Physical Review
1776:
1763:
1759:
1721:
1717:
1668:
1661:
1613:hep-lat/0304004
1587:
1583:
1547:
1543:
1539:
1497:
1466:
1454:
1403:
1381:
1364:part and gauge-
1324:
1319:
1313:supercomputer.
1298:
1296:
1289:
1276:
1154:
1125:
1124:
1123:
1121:
415:
407:
406:
402:Quantum gravity
377:
369:
368:
364:Higgs mechanism
344:
334:
333:
309:Proca equations
294:
286:
285:
281:Wightman Axioms
266:Renormalization
226:Feynman diagram
181:
173:
172:
113:
103:
102:
53:
38:
36:Feynman diagram
17:
12:
11:
5:
3379:
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3332:
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3302:
3297:
3292:
3287:
3282:
3277:
3271:
3269:
3265:
3264:
3262:
3261:
3256:
3254:Trouton's rule
3251:
3246:
3241:
3236:
3231:
3225:
3223:
3219:
3218:
3216:
3215:
3210:
3205:
3200:
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3165:
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3145:
3140:
3135:
3130:
3125:
3123:Critical point
3120:
3115:
3110:
3105:
3099:
3097:
3091:
3090:
3088:
3087:
3082:
3077:
3076:
3075:
3070:
3065:
3057:
3052:
3047:
3042:
3037:
3032:
3027:
3025:Liquid crystal
3022:
3017:
3011:
3009:
3005:
3004:
3002:
3001:
2996:
2991:
2985:
2983:
2979:
2978:
2976:
2975:
2970:
2965:
2960:
2958:Strange matter
2955:
2953:Rydberg matter
2950:
2945:
2940:
2935:
2929:
2927:
2923:
2922:
2915:
2913:
2911:
2910:
2905:
2900:
2891:
2886:
2880:
2878:
2874:
2873:
2861:
2860:
2853:
2846:
2838:
2829:
2828:
2826:
2825:
2812:
2809:
2808:
2806:
2805:
2800:
2795:
2790:
2785:
2779:
2777:
2776:Related topics
2773:
2772:
2770:
2769:
2767:Strange matter
2764:
2759:
2754:
2749:
2744:
2739:
2737:Neutron matter
2733:
2731:
2725:
2724:
2722:
2721:
2716:
2711:
2706:
2701:
2696:
2691:
2690:
2689:
2687:Basic concepts
2684:
2673:
2671:
2669:Quantum theory
2665:
2664:
2662:
2661:
2654:
2649:
2644:
2639:
2634:
2628:
2627:
2626:
2625:
2620:
2615:
2605:
2604:
2603:
2598:
2593:
2588:
2577:
2575:
2569:
2568:
2566:
2565:
2560:
2555:
2550:
2545:
2544:
2543:
2533:
2528:
2523:
2522:
2521:
2516:
2511:
2506:
2495:
2493:
2491:exotic objects
2485:
2484:
2482:
2481:
2474:
2469:
2464:
2459:
2454:
2449:
2444:
2442:Type Ib and Ic
2439:
2433:
2431:
2425:
2424:
2422:
2421:
2416:
2411:
2405:
2403:
2399:
2398:
2396:
2395:
2390:
2385:
2380:
2371:
2366:
2356:
2355:
2354:
2349:
2344:
2334:
2332:Surface fusion
2329:
2327:Nuclear fusion
2323:
2321:
2317:
2316:
2309:
2307:
2305:
2304:
2303:
2302:
2297:
2287:
2282:
2277:
2272:
2270:Stellar plasma
2267:
2262:
2257:
2252:
2247:
2242:
2236:
2234:
2228:
2227:
2217:
2216:
2209:
2202:
2194:
2188:
2187:
2182:
2170:
2165:
2160:
2155:
2148:
2147:External links
2145:
2144:
2143:
2136:
2129:
2122:
2112:
2105:
2096:
2093:
2091:
2090:
2076:
2023:
2008:
1971:
1920:
1867:
1806:
1770:Aneesur Rahman
1757:
1738:(9): 613â616.
1728:Aneesur Rahman
1715:
1659:
1594:Shigemitsu, J.
1581:
1540:
1538:
1535:
1534:
1533:
1528:
1523:
1518:
1513:
1508:
1503:
1496:
1493:
1492:
1491:
1488:strange quarks
1480:
1473:
1465:
1462:
1453:
1450:
1402:
1399:
1395:
1394:
1390:
1380:
1377:
1335:Euclidean time
1323:
1320:
1318:
1315:
1274:
1247:supercomputers
1198:and the large
1194:nature of the
1156:
1155:
1153:
1152:
1145:
1138:
1130:
1127:
1126:
1119:
1118:
1113:
1108:
1103:
1098:
1093:
1088:
1083:
1078:
1073:
1068:
1063:
1058:
1053:
1048:
1043:
1038:
1033:
1028:
1023:
1018:
1013:
1008:
1003:
998:
993:
988:
983:
978:
973:
968:
963:
958:
953:
948:
943:
938:
933:
928:
923:
918:
913:
908:
903:
898:
893:
888:
883:
878:
873:
868:
863:
858:
853:
848:
843:
838:
833:
828:
823:
818:
813:
808:
803:
798:
793:
788:
783:
778:
773:
768:
763:
758:
753:
748:
743:
738:
733:
728:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
673:
668:
663:
658:
653:
648:
643:
638:
633:
628:
623:
618:
613:
608:
603:
598:
593:
588:
583:
578:
573:
568:
563:
558:
553:
548:
543:
538:
533:
528:
523:
518:
513:
508:
503:
498:
493:
488:
483:
478:
473:
468:
463:
458:
453:
448:
443:
438:
433:
428:
423:
417:
416:
413:
412:
409:
408:
405:
404:
399:
394:
389:
384:
378:
375:
374:
371:
370:
367:
366:
361:
356:
351:
345:
342:Standard Model
340:
339:
336:
335:
332:
331:
326:
321:
316:
311:
306:
301:
299:Dirac equation
295:
292:
291:
288:
287:
284:
283:
278:
276:Wick's theorem
273:
268:
263:
261:Regularization
258:
253:
248:
243:
238:
233:
228:
223:
218:
213:
208:
203:
198:
193:
188:
182:
179:
178:
175:
174:
171:
170:
165:
163:Noether charge
160:
155:
150:
148:Gauge symmetry
145:
140:
135:
130:
125:
120:
114:
109:
108:
105:
104:
101:
100:
95:
90:
85:
80:
75:
70:
65:
60:
54:
51:
50:
47:
46:
40:
39:
34:
26:
25:
15:
9:
6:
4:
3:
2:
3378:
3367:
3364:
3362:
3359:
3358:
3356:
3341:
3338:
3336:
3333:
3331:
3328:
3326:
3323:
3321:
3318:
3316:
3313:
3311:
3310:Mpemba effect
3308:
3306:
3303:
3301:
3298:
3296:
3293:
3291:
3290:Cooling curve
3288:
3286:
3283:
3281:
3278:
3276:
3273:
3272:
3270:
3266:
3260:
3257:
3255:
3252:
3250:
3247:
3245:
3242:
3240:
3237:
3235:
3232:
3230:
3227:
3226:
3224:
3220:
3214:
3213:Vitrification
3211:
3209:
3206:
3204:
3201:
3199:
3196:
3194:
3191:
3189:
3186:
3184:
3181:
3179:
3178:Recombination
3176:
3174:
3173:Melting point
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3149:
3146:
3144:
3141:
3139:
3136:
3134:
3131:
3129:
3126:
3124:
3121:
3119:
3118:Critical line
3116:
3114:
3111:
3109:
3108:Boiling point
3106:
3104:
3101:
3100:
3098:
3096:
3092:
3086:
3083:
3081:
3078:
3074:
3071:
3069:
3066:
3064:
3061:
3060:
3058:
3056:
3053:
3051:
3048:
3046:
3043:
3041:
3040:Exotic matter
3038:
3036:
3033:
3031:
3028:
3026:
3023:
3021:
3018:
3016:
3013:
3012:
3010:
3006:
3000:
2997:
2995:
2992:
2990:
2987:
2986:
2984:
2980:
2974:
2971:
2969:
2966:
2964:
2961:
2959:
2956:
2954:
2951:
2949:
2946:
2944:
2941:
2939:
2936:
2934:
2931:
2930:
2928:
2924:
2919:
2909:
2906:
2904:
2901:
2899:
2895:
2892:
2890:
2887:
2885:
2882:
2881:
2879:
2875:
2870:
2866:
2859:
2854:
2852:
2847:
2845:
2840:
2839:
2836:
2824:
2819:
2814:
2813:
2810:
2804:
2801:
2799:
2796:
2794:
2791:
2789:
2786:
2784:
2781:
2780:
2778:
2774:
2768:
2765:
2763:
2760:
2758:
2755:
2753:
2750:
2748:
2745:
2743:
2740:
2738:
2735:
2734:
2732:
2730:
2726:
2720:
2719:Deconfinement
2717:
2715:
2712:
2710:
2707:
2705:
2702:
2700:
2697:
2695:
2692:
2688:
2685:
2683:
2680:
2679:
2678:
2675:
2674:
2672:
2670:
2666:
2660:
2659:
2655:
2653:
2650:
2648:
2645:
2643:
2640:
2638:
2635:
2633:
2630:
2629:
2624:
2621:
2619:
2616:
2614:
2611:
2610:
2609:
2606:
2602:
2599:
2597:
2594:
2592:
2589:
2587:
2584:
2583:
2582:
2579:
2578:
2576:
2570:
2564:
2561:
2559:
2556:
2554:
2551:
2549:
2546:
2542:
2539:
2538:
2537:
2534:
2532:
2529:
2527:
2524:
2520:
2517:
2515:
2512:
2510:
2507:
2505:
2502:
2501:
2500:
2497:
2496:
2494:
2492:
2486:
2480:
2479:
2475:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2455:
2453:
2450:
2448:
2445:
2443:
2440:
2438:
2435:
2434:
2432:
2430:
2426:
2420:
2417:
2415:
2412:
2410:
2407:
2406:
2404:
2400:
2394:
2393:Orbital decay
2391:
2389:
2386:
2384:
2381:
2379:
2375:
2372:
2370:
2367:
2364:
2360:
2357:
2353:
2350:
2348:
2345:
2343:
2340:
2339:
2338:
2335:
2333:
2330:
2328:
2325:
2324:
2322:
2318:
2313:
2301:
2298:
2296:
2293:
2292:
2291:
2288:
2286:
2283:
2281:
2280:Variable star
2278:
2276:
2273:
2271:
2268:
2266:
2263:
2261:
2258:
2256:
2253:
2251:
2248:
2246:
2243:
2241:
2238:
2237:
2235:
2233:
2229:
2225:
2222:
2215:
2210:
2208:
2203:
2201:
2196:
2195:
2192:
2186:
2183:
2181:
2177:
2174:
2171:
2169:
2166:
2164:
2161:
2159:
2156:
2154:
2151:
2150:
2141:
2137:
2134:
2130:
2127:
2123:
2120:
2116:
2113:
2110:
2106:
2103:
2099:
2098:
2087:. 2020-12-09.
2086:
2080:
2072:
2068:
2064:
2060:
2056:
2052:
2047:
2042:
2039:(2): 022328.
2038:
2034:
2027:
2019:
2015:
2011:
2005:
2001:
1997:
1992:
1987:
1983:
1975:
1966:
1961:
1957:
1953:
1948:
1943:
1939:
1935:
1931:
1924:
1916:
1912:
1908:
1904:
1900:
1896:
1891:
1886:
1883:(9): 093002.
1882:
1878:
1871:
1863:
1859:
1855:
1851:
1847:
1843:
1839:
1835:
1830:
1825:
1821:
1817:
1810:
1802:
1798:
1794:
1790:
1786:
1782:
1775:
1771:
1767:
1761:
1753:
1749:
1745:
1741:
1737:
1733:
1729:
1725:
1719:
1711:
1707:
1703:
1699:
1695:
1691:
1686:
1681:
1677:
1673:
1666:
1664:
1655:
1651:
1647:
1643:
1639:
1635:
1631:
1627:
1623:
1619:
1614:
1609:
1606:(2): 022001.
1605:
1601:
1600:
1595:
1591:
1585:
1577:
1573:
1569:
1565:
1561:
1557:
1556:
1551:
1545:
1541:
1532:
1531:Wilson action
1529:
1527:
1526:QCD sum rules
1524:
1522:
1519:
1517:
1514:
1512:
1509:
1507:
1504:
1502:
1499:
1498:
1489:
1485:
1481:
1478:
1474:
1471:
1470:
1469:
1461:
1459:
1449:
1447:
1443:
1438:
1435:
1430:
1428:
1427:MS-bar scheme
1424:
1420:
1416:
1412:
1408:
1398:
1391:
1387:
1386:
1385:
1376:
1374:
1371:
1367:
1363:
1359:
1355:
1351:
1346:
1344:
1340:
1339:Wick rotation
1336:
1332:
1328:
1314:
1312:
1307:
1304:
1293:
1287:
1283:
1278:
1272:
1268:
1263:
1261:
1257:
1252:
1248:
1244:
1239:
1237:
1233:
1229:
1225:
1220:
1218:
1214:
1209:
1205:
1201:
1197:
1193:
1188:
1186:
1182:
1178:
1174:
1170:
1166:
1162:
1151:
1146:
1144:
1139:
1137:
1132:
1131:
1129:
1128:
1122:
1117:
1114:
1112:
1109:
1107:
1104:
1102:
1099:
1097:
1094:
1092:
1091:Zamolodchikov
1089:
1087:
1086:Zamolodchikov
1084:
1082:
1079:
1077:
1074:
1072:
1069:
1067:
1064:
1062:
1059:
1057:
1054:
1052:
1049:
1047:
1044:
1042:
1039:
1037:
1034:
1032:
1029:
1027:
1024:
1022:
1019:
1017:
1014:
1012:
1009:
1007:
1004:
1002:
999:
997:
994:
992:
989:
987:
984:
982:
979:
977:
974:
972:
969:
967:
964:
962:
959:
957:
954:
952:
949:
947:
944:
942:
939:
937:
934:
932:
929:
927:
924:
922:
919:
917:
914:
912:
909:
907:
904:
902:
899:
897:
894:
892:
889:
887:
884:
882:
879:
877:
874:
872:
869:
867:
864:
862:
859:
857:
854:
852:
849:
847:
844:
842:
839:
837:
834:
832:
829:
827:
824:
822:
819:
817:
814:
812:
809:
807:
804:
802:
799:
797:
794:
792:
789:
787:
784:
782:
779:
777:
774:
772:
769:
767:
764:
762:
759:
757:
754:
752:
749:
747:
744:
742:
739:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
692:
689:
687:
684:
682:
679:
677:
674:
672:
669:
667:
664:
662:
659:
657:
654:
652:
649:
647:
644:
642:
639:
637:
634:
632:
629:
627:
624:
622:
619:
617:
614:
612:
609:
607:
604:
602:
599:
597:
594:
592:
589:
587:
584:
582:
579:
577:
574:
572:
569:
567:
564:
562:
559:
557:
554:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
527:
524:
522:
519:
517:
514:
512:
509:
507:
504:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
474:
472:
469:
467:
464:
462:
459:
457:
454:
452:
449:
447:
444:
442:
439:
437:
434:
432:
429:
427:
424:
422:
419:
418:
411:
410:
403:
400:
398:
395:
393:
390:
388:
387:Supersymmetry
385:
383:
382:String theory
380:
379:
373:
372:
365:
362:
360:
357:
355:
352:
350:
347:
346:
343:
338:
337:
330:
327:
325:
322:
320:
317:
315:
312:
310:
307:
305:
302:
300:
297:
296:
290:
289:
282:
279:
277:
274:
272:
269:
267:
264:
262:
259:
257:
254:
252:
249:
247:
244:
242:
239:
237:
234:
232:
229:
227:
224:
222:
219:
217:
214:
212:
209:
207:
204:
202:
199:
197:
194:
192:
189:
187:
184:
183:
177:
176:
169:
166:
164:
161:
159:
156:
154:
151:
149:
146:
144:
141:
139:
136:
134:
131:
129:
126:
124:
121:
119:
116:
115:
112:
107:
106:
99:
96:
94:
91:
89:
86:
84:
81:
79:
76:
74:
71:
69:
66:
64:
61:
59:
56:
55:
49:
48:
45:
42:
41:
37:
32:
28:
27:
24:
21:
20:
3335:Superheating
3208:Vaporization
3203:Triple point
3198:Supercooling
3163:Lambda point
3113:Condensation
3030:Time crystal
3008:Other states
2948:Quantum Hall
2788:Astrophysics
2757:Preon matter
2747:Quark matter
2708:
2682:Introduction
2656:
2499:Neutron star
2489:Compact and
2476:
2388:Helium flash
2378:deflagration
2295:X-ray binary
2221:Stellar core
2139:
2132:
2125:
2118:
2108:
2101:
2079:
2036:
2032:
2026:
1981:
1974:
1937:
1933:
1923:
1880:
1876:
1870:
1819:
1815:
1809:
1784:
1780:
1760:
1735:
1731:
1718:
1675:
1671:
1603:
1597:
1584:
1559:
1553:
1544:
1467:
1455:
1439:
1431:
1422:
1414:
1404:
1396:
1382:
1362:gauge bosons
1347:
1325:
1308:
1279:
1264:
1262:algorithms.
1240:
1235:
1231:
1228:extrapolated
1221:
1207:
1203:
1196:strong force
1189:
1165:perturbative
1160:
1159:
1120:
966:Stueckelberg
696:Jona-Lasinio
271:Vacuum state
256:Quantization
93:Gauge theory
73:Strong force
58:Field theory
3244:Latent heat
3193:Sublimation
3138:Evaporation
3073:Ferromagnet
3068:Ferrimagnet
3050:Dark matter
2982:High energy
2709:Lattice QCD
2623:Gravitation
2548:Exotic star
2526:White dwarf
2519:Radio-quiet
2290:Binary star
2260:Metallicity
2100:M. Creutz,
1562:(8): 2445.
1464:Limitations
1419:renormalize
1373:propagators
1327:Monte-Carlo
1213:confinement
1161:Lattice QCD
1106:Zinn-Justin
956:Sommerfield
881:Pomeranchuk
846:Osterwalder
841:Oppenheimer
771:ĆopuszaĆski
591:Fredenhagen
392:Technicolor
3355:Categories
3259:Volatility
3222:Quantities
3183:Regelation
3158:Ionization
3133:Deposition
3085:Superglass
3055:Antimatter
2989:QCD matter
2968:Supersolid
2963:Superfluid
2926:Low energy
2762:Strangelet
2742:QCD matter
2553:Quark star
2531:Black hole
2462:Quark-nova
2429:Supernovae
2347:RP-process
2275:Supergiant
2124:H. Rothe,
1947:1508.03260
1940:(9): 114.
1877:J. Phys. G
1550:Wilson, K.
1537:References
1516:QCD matter
1317:Techniques
1179:. It is a
1101:Zimmermann
996:Vainshtein
871:Polchinski
731:Kontsevich
676:Iliopoulos
651:Heisenberg
476:Bogoliubov
414:Scientists
251:Propagator
133:T-symmetry
128:P-symmetry
123:C-symmetry
111:Symmetries
68:Weak force
52:Background
2783:Astronomy
2536:Collapsar
2457:Hypernova
2359:Accretion
2342:R-process
2250:Structure
2245:Evolution
2240:Formation
2018:115229961
1991:1401.3733
1915:119193093
1890:1203.5320
1829:0906.3599
1710:119259340
1685:0903.3598
1638:0031-9007
1343:spacetime
1311:Blue Gene
1290:150
1192:nonlinear
1036:Wetterich
1021:Weisskopf
971:Sudarshan
921:Schwinger
831:Nishijima
796:Maldacena
761:Leutwyler
721:Kinoshita
621:Goldstone
611:Gell-Mann
526:Doplicher
293:Equations
3320:Spinodal
3268:Concepts
3148:Freezing
2601:Neutrino
2596:Electron
2514:Magnetar
2402:Collapse
2224:collapse
2176:Archived
1862:14225402
1854:19023076
1772:(1983).
1654:16205350
1646:14753930
1495:See also
1484:hyperons
1411:expanded
1370:hadronic
1301:10
1206:, where
1051:Wightman
1016:Weinberg
1006:Virasoro
986:Tomonaga
981:Thirring
976:Symanzik
936:Semenoff
911:Schrader
876:Polyakov
791:Majorana
726:Klebanov
681:Ivanenko
671:'t Hooft
641:Guralnik
586:Fröhlich
581:Fritzsch
576:Frampton
491:Buchholz
436:Bargmann
426:Anderson
206:Crossing
3280:Binodal
3168:Melting
3103:Boiling
3020:Crystal
3015:Colloid
2658:More...
2591:Neutron
2478:More...
2472:Remnant
2447:Type II
2437:Type Ia
2115:J. Smit
2071:6105195
2051:Bibcode
1952:Bibcode
1895:Bibcode
1834:Bibcode
1816:Science
1789:Bibcode
1740:Bibcode
1690:Bibcode
1618:Bibcode
1564:Bibcode
1446:crystal
1393:values.
1366:fermion
1337:, by a
1185:lattice
1061:Wilczek
1026:Wentzel
1001:Veltman
946:Shirkov
941:Shifman
931:Seiberg
916:Schwarz
896:Rubakov
816:Naimark
766:Lipatov
756:Lehmann
736:Kreimer
716:Kendall
606:Gelfand
601:Glashow
561:Feynman
541:Faddeev
536:Englert
506:Coleman
496:Cachazo
481:Brodsky
466:Bjorken
456:Berezin
446:Belavin
186:Anomaly
44:History
2908:Plasma
2889:Liquid
2586:Proton
2509:Quasar
2504:Pulsar
2467:Nebula
2069:
2016:
2006:
1913:
1860:
1852:
1708:
1652:
1644:
1636:
1434:Wilson
1354:action
1282:proton
1177:gluons
1173:quarks
1116:Zumino
1081:Yukawa
1071:Witten
1066:Wilson
1056:Wigner
991:Tyutin
951:Skyrme
901:Ruelle
866:Plefka
861:Peskin
851:Parisi
811:MĂžller
801:Migdal
786:Maiani
781:LĂŒders
746:Landau
741:Kuraev
711:KÀllén
701:Jordan
686:Jackiw
626:Gribov
516:DeWitt
511:Dashen
501:Callan
471:Bleuer
441:Becchi
431:Anselm
2898:Vapor
2884:Solid
2877:State
2232:Stars
2067:S2CID
2041:arXiv
2014:S2CID
1986:arXiv
1942:arXiv
1911:S2CID
1885:arXiv
1858:S2CID
1824:arXiv
1777:(PDF)
1706:S2CID
1680:arXiv
1650:S2CID
1608:arXiv
1477:flops
1232:a = 0
1111:Zuber
961:Stora
926:Segal
906:Salam
891:Proca
886:Popov
856:Pauli
836:Oehme
826:Neveu
821:Nambu
806:Mills
691:Jaffe
666:Hagen
661:Higgs
636:Gupta
631:Gross
616:Glimm
596:Furry
566:Fierz
556:Fermi
551:Fayet
546:Fadin
531:Dyson
521:Dirac
486:Brout
461:Bethe
421:Adler
180:Tools
2869:list
2255:Core
2004:ISBN
1850:PMID
1768:and
1726:and
1642:PMID
1634:ISSN
1277:D).
1215:and
1175:and
1076:Yang
1046:Wick
1041:Weyl
1031:Wess
1011:Ward
706:Jost
656:Hepp
646:Haag
571:Fock
451:Bell
2894:Gas
2059:doi
1996:doi
1960:doi
1903:doi
1842:doi
1820:322
1797:doi
1785:D28
1748:doi
1698:doi
1626:doi
1572:doi
1409:is
1341:of
1297:1.7
1292:MeV
1258:or
1230:to
1096:Zee
776:Low
751:Lee
3357::
2896:/
2376:/
2117:,
2065:.
2057:.
2049:.
2037:73
2035:.
2012:.
2002:.
1994:.
1958:.
1950:.
1938:51
1936:.
1932:.
1909:.
1901:.
1893:.
1881:39
1879:.
1856:.
1848:.
1840:.
1832:.
1818:.
1795:.
1783:.
1779:.
1746:.
1736:49
1734:.
1704:.
1696:.
1688:.
1676:82
1674:.
1662:^
1648:.
1640:.
1632:.
1624:.
1616:.
1604:92
1602:.
1570:.
1560:10
1558:.
1460:.
1345:.
2871:)
2867:(
2857:e
2850:t
2843:v
2365:)
2361:(
2213:e
2206:t
2199:v
2073:.
2061::
2053::
2043::
2020:.
1998::
1988::
1968:.
1962::
1954::
1944::
1917:.
1905::
1897::
1887::
1864:.
1844::
1836::
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1799::
1791::
1754:.
1750::
1742::
1712:.
1700::
1692::
1682::
1656:.
1628::
1620::
1610::
1578:.
1574::
1566::
1490:.
1423:a
1415:a
1303:K
1299:Ă
1295:(
1275:2
1236:a
1208:a
1204:a
1149:e
1142:t
1135:v
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