25:
93:
1593:. The length scale of these pairs is much larger than the wavelength of phonons, making it possible to neglect the dynamics of phonons and construct a theory in which two electrons effectively interact at a point. This theory has had remarkable success in describing and predicting the results of experiments on superconductivity.
1295:
short distance degrees of freedom is made systematic. Although this method is not sufficiently concrete to allow the actual construction of effective field theories, the gross understanding of their usefulness becomes clear through an RG analysis. This method also lends credence to the main technique
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or energy scale, while ignoring substructure and degrees of freedom at shorter distances (or, equivalently, at higher energies). Intuitively, one averages over the behavior of the underlying theory at shorter length scales to derive what is hoped to be a simplified model at longer length scales.
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Effective field theories typically work best when there is a large separation between length scale of interest and the length scale of the underlying dynamics. Effective field theories have found use in
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1676:. Due to the smaller separation of length scales here, this effective theory has some classificatory power, but not the spectacular success of the Fermi theory.
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Endlich, Solomon; Nicolis, Alberto; Porto, Rafael; Wang, Junpu (2013). "Dissipation in the effective field theory for hydrodynamics: First order effects".
342:
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1513:{\displaystyle {\begin{aligned}n&\to p+e^{-}+{\overline {\nu }}_{e}\\\mu ^{-}&\to e^{-}+{\overline {\nu }}_{e}+\nu _{\mu }.\end{aligned}}}
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1620:. Effective field theories have also been used to simplify problems in General Relativity, in particular in calculating the
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1708:
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2001:
2425:(Interactions, Symmetry Breaking and Effective Fields - from Quarks to Nuclei. an Internet Lecture by Jacek Dobaczewski)
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1202:
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68:
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1632:. Another common GR EFT is the Extreme Mass Ratio (EMR), which in the context of the inspiralling problem is called
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1561:. Such a separation of scales, by over 3 orders of magnitude, has not been met in any other situation as yet.
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required for an effective field theory means that they are generally not renormalizable in the same sense as
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Studies in
History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
1955:
Goldberger, Walter; Rothstein, Ira (2004). "An
Effective Field Theory of Gravity for Extended Objects".
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2706:
1815:
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214:
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Birnholtz, Ofek; Hadar, Shahar; Kol, Barak (2013). "Theory of post-Newtonian radiation and reaction".
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Birnholtz, Ofek; Hadar, Shahar; Kol, Barak (2014). "Radiation reaction at the level of the action".
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2823:
2539:
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Kol, Barak; Smolkin, Lee (2008). "Non-Relativistic
Gravitation: From Newton to Einstein and Back".
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consists of writing effective field theories for the particular property of matter being studied.
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1768:) particles, the interactions with low-energetic (soft) degrees of freedom are described by the
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A.A. Petrov and A. Blechman, ââEffective Field
Theories,ââ Singapore: World Scientific (2016).
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Porto, Rafael A (2006). "Post-Newtonian corrections to the motion of spinning bodies in NRGR".
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C.P. Burgess, ââIntroduction to
Effective Field Theory,ââ Cambridge University Press (2020).
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of particle physics. In this more fundamental theory, the interactions are mediated by a
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1332:. Since effective field theories are not valid at small length scales, they need not be
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are treated as a field theory, which should be derivable from the underlying theory of
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containing two heavy quarks, an effective field theory which expands in powers of the
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1974:
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itself is expected to be the low energy effective field theory of a full theory of
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signature of inspiralling finite-sized objects. The most common EFT in GR is "
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2502:
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Birnholtz, Ofek; Hadar, Shahar; Kol, Barak (1998). "Effective Field Theory".
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1753:(NRQCD), has been found useful, especially when used in conjunctions with
1312:. The construction of an effective field theory accurate to some power of
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3092:
2180:
Leutwyler, H (1994). "On the
Foundations of Chiral Perturbation Theory".
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requires a new set of free parameters at each order of the expansion in
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Presently, effective field theories are discussed in the context of the
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theory, then the effective field theory can be seen as an expansion in
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129:
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The
Unreasonable Effectiveness of Mathematics in the Natural Sciences
2475:
1765:
1644:
Presently, effective field theories are written for many situations.
1361:. This theory was developed during the early study of weak decays of
1276:
2334:"Effective Field Theories, Reductionism and Scientific Explanation"
1691:
has had better success. This theory deals with the interactions of
1578:
1336:. Indeed, the ever expanding number of parameters at each order in
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767:
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2043:
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of constructing effective field theories, through the analysis of
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European
Community on Computational Methods in Applied Sciences
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1668:, similarly to quantum chromodynamics being the theory of the
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This theory posited a pointlike interaction between the four
3210:
International
Council for Industrial and Applied Mathematics
1712:
1700:
1696:
1357:
The best-known example of an effective field theory is the
1344:
which requires only the renormalization of two parameters.
1242:
model. An effective field theory includes the appropriate
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1554:
1533:
success and was eventually understood to arise from the
2232:
1347:
2458:
2000:
Porto, Rafael A.; Rothstein, Ira; Goldberger, Walter.
1596:
16:
Type of approximation to an underlying physical theory
2829:
Numerical methods for ordinary differential equations
1388:
1271:. They simplify calculations, and allow treatment of
1246:
to describe physical phenomena occurring at a chosen
3205:
Société de Mathématiques
Appliquées et Industrielles
3198:
Japan Society for Industrial and Applied Mathematics
2834:
Numerical methods for partial differential equations
2548:
1999:
1672:
and quantum electrodynamics being the theory of the
1324:
or other processes where the maximum momentum scale
3021:
2368:Birnholtz, Ofek; Hadar, Shahar; Kol, Barak (1997).
1954:
1785:can also be treated using Effective Field Theories
1564:
1529:involved in these reactions. The theory had great
1512:
2367:
2316:
2126:
1901:
3255:
1837:"Classical Mechanics of Nonconservative Systems"
1234:, for an underlying physical theory, such as a
3193:Society for Industrial and Applied Mathematics
1577:. Here the underlying theory is the theory of
1373:undergoing weak decay were known. The typical
2444:
2375:Annual Review of Nuclear and Particle Science
1664:. Quantum hadrodynamics is the theory of the
1352:
1203:
3011:Supersymmetric theory of stochastic dynamics
1282:
1585:interacting with lattice vibrations called
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91:
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1968:
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1904:International Journal of Modern Physics A
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1852:
69:Learn how and when to remove this message
2331:
32:This article includes a list of general
3256:
1834:
2432:
2081:
1709:spontaneous chiral symmetry breaking
1348:Examples of effective field theories
18:
1626:Non-Relativistic General Relativity
1597:Effective field theories in gravity
13:
2460:Industrial and applied mathematics
1796:Form factor (quantum field theory)
1628:" (NRGR), which is similar to the
1300:. If there is a single mass scale
38:it lacks sufficient corresponding
14:
3300:
2690:Stochastic differential equations
2310:
1711:. The expansion parameter is the
1639:
3006:Supersymmetric quantum mechanics
1764:reactions with light energetic (
23:
2888:Stochastic variational calculus
2680:Ordinary differential equations
2370:"Aspects of Heavy Quark Theory"
1770:soft-collinear effective theory
1565:BCS theory of superconductivity
1320:. This technique is useful for
1230:is a type of approximation, or
2685:Partial differential equations
2558:Arbitrary-precision arithmetic
2226:
2173:
2120:
2075:
2061:10.1088/0264-9381/25/14/145011
2022:
1993:
1948:
1895:
1872:10.1103/PhysRevLett.110.174301
1828:
1738:(HQET), has been found useful.
1683:the effective field theory of
1569:Another famous example is the
1457:
1400:
391:Renormalization group equation
1:
2573:Interactive geometry software
2407:10.1146/annurev.nucl.47.1.591
2361:10.1016/S1355-2198(01)00005-3
2031:Classical and Quantum Gravity
1821:
1616:. The expansion scale is the
220:Spontaneous symmetry breaking
180:Symmetry in quantum mechanics
1749:of the heavy quarks, called
1736:heavy quark effective theory
1656:, where the interactions of
1541:, which forms a part of the
1479:
1428:
7:
2625:Computational number theory
2588:Numerical-analysis software
1789:
10:
3305:
2332:Hartmann, Stephan (2001).
2265:10.1103/PhysRevD.88.105001
2159:10.1103/PhysRevD.88.104037
2106:10.1103/PhysRevD.73.104031
1979:10.1103/PhysRevD.73.104029
1689:chiral perturbation theory
1359:Fermi theory of beta decay
1353:Fermi theory of beta decay
1291:(RG) where the process of
215:Explicit symmetry breaking
3223:
3185:
3169:
3131:
3083:
3031:Algebra of physical space
2896:
2854:
2648:
2610:
2498:Automated theorem proving
2466:
1934:10.1142/S0217751X14501322
1283:The renormalization group
381:BargmannâWigner equations
308:Path Integral Formulation
3289:Condensed matter physics
2824:Numerical linear algebra
2283:
1835:Galley, Chad R. (2013).
1777:condensed matter physics
1630:post-Newtonian expansion
1539:electroweak interactions
1328:satisfies the condition
1261:condensed matter physics
386:Schwinger-Dyson equation
2563:Finite element analysis
2513:Constraint satisfaction
1910:(24): 1450132â1450190.
1841:Physical Review Letters
1342:quantum electrodynamics
416:Electroweak interaction
411:Quantum electrodynamics
376:WheelerâDeWitt equation
253:Background field method
53:more precise citations.
3118:Mathematical economics
2792:Multivariable calculus
2675:Differential equations
2518:Constraint programming
2508:Computational geometry
2423:Effective field theory
2212:10.1006/aphy.1994.1094
1816:GinzburgâLandau theory
1662:quantum chromodynamics
1514:
1228:effective field theory
421:Quantum chromodynamics
278:Effective field theory
3274:Renormalization group
3269:Statistical mechanics
3071:Supersymmetry algebra
3056:Representation theory
3051:Renormalization group
2697:Differential geometry
2578:Optimization software
2550:Mathematical software
1801:Renormalization group
1722:containing one heavy
1674:electromagnetic force
1654:quantum hadrodynamics
1515:
1289:renormalization group
1257:statistical mechanics
1240:statistical mechanics
366:KleinâGordon equation
298:LSZ reduction formula
3264:Quantum field theory
3123:Mathematical finance
3108:Social choice theory
3023:Algebraic structures
2972:in quantum mechanics
2908:Analytical mechanics
2874:Stochastic processes
2846:Variational calculus
2658:Approximation theory
2583:Statistical software
2009:online.kitp.ucsb.edu
1806:Quantum field theory
1751:non-relativistic QCD
1648:One major branch of
1614:Loop Quantum Gravity
1386:
1236:quantum field theory
459:Theory of everything
293:Lattice field theory
263:Correlation function
85:Quantum field theory
3098:Operations research
2967:Perturbation theory
2765:Multilinear algebra
2736:Functional analysis
2593:Numerical libraries
2525:Computational logic
2398:1997ARNPS..47..591B
2353:2001SHPMP..32..267H
2257:2013PhRvD..88j5001E
2204:1994AnPhy.235..165L
2151:2013PhRvD..88j4037B
2053:2008CQGra..25n5011K
1926:2014IJMPA..2950132B
1863:2013PhRvL.110q4301G
438:Incomplete theories
3235:Mathematics portal
3132:Other applications
2856:Probability theory
2839:Validated numerics
2819:Numerical analysis
2712:Geometric analysis
2702:Differential forms
2535:Information theory
2090:(104031): 104031.
1811:Quantum triviality
1670:strong interaction
1622:gravitational wave
1602:General relativity
1510:
1508:
1265:general relativity
1244:degrees of freedom
303:Partition function
230:Topological charge
150:General relativity
145:Special relativity
3251:
3250:
3085:Decision sciences
3079:
3078:
3061:Spacetime algebra
2753:Harmonic analysis
2719:Dynamical systems
2663:Clifford analysis
2640:Discrete geometry
2606:
2605:
2305:978-052-1195-47-8
2295:978-981-4434-92-8
2235:Physical Review D
2182:Annals of Physics
2129:Physical Review D
2084:Physical Review D
1957:Physical Review D
1747:relative velocity
1575:superconductivity
1482:
1431:
1220:
1219:
283:Expectation value
258:BRST quantization
205:Poincaré symmetry
160:YangâMills theory
140:Quantum mechanics
79:
78:
71:
3296:
3279:Chemical physics
3036:Feynman integral
3019:
3018:
2979:Potential theory
2868:random variables
2758:Fourier analysis
2741:Operator algebra
2668:Clifford algebra
2620:Computer algebra
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1705:Goldstone bosons
1703:, which are the
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273:Effective action
200:Lorentz symmetry
125:Electromagnetism
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40:inline citations
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328:Renormalization
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2733:
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2731:
2729:Control theory
2726:
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2704:
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2456:
2455:
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2441:
2433:
2427:
2426:
2420:
2389:hep-ph/9703290
2365:
2347:(2): 267â304.
2329:
2324:hep-ph/9806303
2312:
2311:External links
2309:
2308:
2307:
2297:
2285:
2282:
2279:
2278:
2241:(10): 105001.
2225:
2195:hep-ph/9311274
2188:(1): 165â203.
2172:
2135:(10): 104037.
2119:
2074:
2037:(14): 145011.
2021:
2002:"EFT meets GR"
1992:
1970:hep-th/0409156
1963:(10): 104029.
1947:
1894:
1847:(17): 174301.
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1640:Other examples
1638:
1598:
1595:
1566:
1563:
1543:standard model
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1399:
1397:
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1392:
1391:
1377:studied were:
1365:when only the
1354:
1351:
1349:
1346:
1334:renormalizable
1284:
1281:
1218:
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404:Standard Model
402:
401:
398:
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388:
383:
378:
373:
368:
363:
361:Dirac equation
357:
354:
353:
350:
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346:
345:
340:
338:Wick's theorem
335:
330:
325:
323:Regularization
320:
315:
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225:Noether charge
222:
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210:Gauge symmetry
207:
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176:
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96:
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31:
29:
22:
15:
9:
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4:
3:
2:
3301:
3290:
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3208:
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3188:
3186:Organizations
3184:
3178:
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3168:
3161:
3157:
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3150:
3147:
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3082:
3072:
3069:
3067:
3064:
3062:
3059:
3057:
3054:
3052:
3049:
3047:
3046:Quantum group
3044:
3042:
3039:
3037:
3034:
3032:
3029:
3028:
3026:
3024:
3020:
3012:
3009:
3007:
3004:
3003:
3002:
3001:Supersymmetry
2999:
2995:
2992:
2990:
2987:
2986:
2985:
2984:String theory
2982:
2980:
2977:
2973:
2970:
2969:
2968:
2965:
2961:
2958:
2956:
2953:
2951:
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2911:
2910:
2909:
2906:
2905:
2903:
2901:
2895:
2889:
2886:
2884:
2883:Path integral
2881:
2879:
2875:
2872:
2869:
2865:
2864:Distributions
2862:
2861:
2859:
2857:
2853:
2847:
2844:
2840:
2837:
2835:
2832:
2830:
2827:
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2817:
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2808:
2805:
2803:
2800:
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2790:
2786:
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2778:
2776:
2773:
2771:
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2759:
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2755:
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2727:
2725:
2722:
2721:
2720:
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2700:
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2698:
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2691:
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2673:
2669:
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2659:
2656:
2655:
2653:
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2647:
2641:
2638:
2636:
2633:
2631:
2630:Combinatorics
2628:
2626:
2623:
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2618:
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2615:
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2531:
2528:
2526:
2523:
2519:
2516:
2515:
2514:
2511:
2509:
2506:
2504:
2503:Coding theory
2501:
2499:
2496:
2494:
2491:
2487:
2484:
2482:
2479:
2478:
2477:
2474:
2473:
2471:
2469:
2468:Computational
2465:
2461:
2454:
2449:
2447:
2442:
2440:
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2240:
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2209:
2205:
2201:
2196:
2191:
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2156:
2152:
2148:
2143:
2138:
2134:
2130:
2123:
2115:
2111:
2107:
2103:
2098:
2097:gr-qc/0511061
2093:
2089:
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2010:
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1971:
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1962:
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1797:
1794:
1793:
1784:
1783:Hydrodynamics
1781:
1778:
1774:
1771:
1767:
1763:
1759:
1756:
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1748:
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1726:(such as the
1725:
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1698:
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1682:
1678:
1675:
1671:
1667:
1666:nuclear force
1663:
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1647:
1646:
1645:
1637:
1635:
1631:
1627:
1623:
1619:
1615:
1611:
1610:string theory
1607:
1603:
1594:
1592:
1588:
1584:
1580:
1576:
1572:
1562:
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1556:
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1315:
1311:
1307:
1303:
1299:
1294:
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1274:
1270:
1269:hydrodynamics
1266:
1262:
1258:
1254:
1249:
1245:
1241:
1237:
1233:
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1213:
1208:
1206:
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1199:
1194:
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1184:
1179:
1176:
1174:
1171:
1169:
1166:
1164:
1161:
1159:
1156:
1154:
1153:Zamolodchikov
1151:
1149:
1148:Zamolodchikov
1146:
1144:
1141:
1139:
1136:
1134:
1131:
1129:
1126:
1124:
1121:
1119:
1116:
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1111:
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1101:
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1091:
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1079:
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1026:
1024:
1021:
1019:
1016:
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1009:
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1004:
1001:
999:
996:
994:
991:
989:
986:
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966:
964:
961:
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956:
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561:
559:
556:
554:
551:
549:
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541:
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531:
529:
526:
524:
521:
519:
516:
514:
511:
509:
506:
504:
501:
499:
496:
494:
491:
489:
486:
484:
481:
480:
473:
472:
465:
462:
460:
457:
455:
452:
450:
449:Supersymmetry
447:
445:
444:String theory
442:
441:
435:
434:
427:
424:
422:
419:
417:
414:
412:
409:
408:
405:
400:
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62:
52:
48:
42:
41:
35:
30:
21:
20:
3241: /
3237: /
3227:
3103:Optimization
3066:Superalgebra
2939:
2925:Field theory
2898:Mathematical
2876: /
2724:Chaos theory
2707:Gauge theory
2635:Graph theory
2530:Cryptography
2379:
2373:
2344:
2340:
2238:
2234:
2228:
2185:
2181:
2175:
2132:
2128:
2122:
2087:
2083:
2077:
2034:
2030:
2024:
2012:. Retrieved
2008:
1995:
1960:
1956:
1950:
1907:
1903:
1897:
1844:
1840:
1830:
1643:
1600:
1591:Cooper pairs
1568:
1535:gauge theory
1524:
1356:
1337:
1329:
1325:
1317:
1313:
1309:
1305:
1301:
1292:
1286:
1248:length scale
1227:
1221:
1182:
1028:Stueckelberg
758:Jona-Lasinio
333:Vacuum state
318:Quantization
277:
155:Gauge theory
135:Strong force
120:Field theory
65:
56:
37:
3243:topics list
3177:Mathematics
3093:Game theory
2994:Topological
2960:Topological
2955:Statistical
2918:Hamiltonian
2382:: 591â661.
1755:lattice QCD
1618:Planck mass
1551:gauge boson
1306:microscopic
1273:dissipation
1168:Zinn-Justin
1018:Sommerfield
943:Pomeranchuk
908:Osterwalder
903:Oppenheimer
833:ĆopuszaĆski
653:Fredenhagen
454:Technicolor
51:introducing
3258:Categories
3149:Psychology
3113:Statistics
2913:Lagrangian
2540:Statistics
2476:Algorithms
2014:3 November
1822:References
1608:, such as
1571:BCS theory
1549:-changing
1322:scattering
1298:symmetries
1163:Zimmermann
1058:Vainshtein
933:Polchinski
793:Kontsevich
738:Iliopoulos
713:Heisenberg
538:Bogoliubov
476:Scientists
313:Propagator
195:T-symmetry
190:P-symmetry
185:C-symmetry
173:Symmetries
130:Weak force
114:Background
34:references
3154:Sociology
3144:Chemistry
2940:Effective
2935:Conformal
2930:Classical
2802:Geometric
2775:Geometric
2273:118441607
2248:1211.6461
2167:119170985
2142:1305.6930
2114:119377563
2069:119216835
2044:0712.4116
1942:118541484
1917:1402.2610
1854:1210.2745
1766:collinear
1579:electrons
1499:μ
1495:ν
1480:¯
1477:ν
1466:−
1458:→
1449:−
1445:μ
1429:¯
1426:ν
1415:−
1401:→
1375:reactions
1279:effects.
1277:radiation
1098:Wetterich
1083:Weisskopf
1033:Sudarshan
983:Schwinger
893:Nishijima
858:Maldacena
823:Leutwyler
783:Kinoshita
683:Goldstone
673:Gell-Mann
588:Doplicher
355:Equations
3229:Category
2878:analysis
2797:Exterior
2770:Exterior
2650:Analysis
2612:Discrete
2486:analysis
2416:13843227
2220:16739698
1987:54188791
1889:14591873
1881:23679733
1790:See also
1775:Much of
1527:fermions
1113:Wightman
1078:Weinberg
1068:Virasoro
1048:Tomonaga
1043:Thirring
1038:Symanzik
998:Semenoff
973:Schrader
938:Polyakov
853:Majorana
788:Klebanov
743:Ivanenko
733:'t Hooft
703:Guralnik
648:Fröhlich
643:Fritzsch
638:Frampton
553:Buchholz
498:Bargmann
488:Anderson
268:Crossing
59:May 2013
3239:outline
3170:Related
3139:Biology
2989:Bosonic
2950:Quantum
2900:physics
2866: (
2598:Solvers
2394:Bibcode
2349:Bibcode
2253:Bibcode
2200:Bibcode
2147:Bibcode
2049:Bibcode
1922:Bibcode
1859:Bibcode
1772:(SCET).
1743:hadrons
1720:hadrons
1693:hadrons
1687:called
1658:hadrons
1587:phonons
1547:flavour
1371:leptons
1367:hadrons
1304:in the
1224:physics
1123:Wilczek
1088:Wentzel
1063:Veltman
1008:Shirkov
1003:Shifman
993:Seiberg
978:Schwarz
958:Rubakov
878:Naimark
828:Lipatov
818:Lehmann
798:Kreimer
778:Kendall
668:Gelfand
663:Glashow
623:Feynman
603:Faddeev
598:Englert
568:Coleman
558:Cachazo
543:Brodsky
528:Bjorken
518:Berezin
508:Belavin
248:Anomaly
106:History
47:improve
2812:Vector
2807:Tensor
2785:Vector
2780:Tensor
2481:design
2414:
2303:
2293:
2271:
2218:
2165:
2112:
2067:
1985:
1940:
1887:
1879:
1762:hadron
1728:bottom
1363:nuclei
1267:, and
1178:Zumino
1143:Yukawa
1133:Witten
1128:Wilson
1118:Wigner
1053:Tyutin
1013:Skyrme
963:Ruelle
928:Plefka
923:Peskin
913:Parisi
873:MĂžller
863:Migdal
848:Maiani
843:LĂŒders
808:Landau
803:Kuraev
773:KÀllén
763:Jordan
748:Jackiw
688:Gribov
578:DeWitt
573:Dashen
563:Callan
533:Bleuer
503:Becchi
493:Anselm
36:, but
2945:Gauge
2412:S2CID
2384:arXiv
2337:(PDF)
2319:arXiv
2284:Books
2269:S2CID
2243:arXiv
2216:S2CID
2190:arXiv
2163:S2CID
2137:arXiv
2110:S2CID
2092:arXiv
2065:S2CID
2039:arXiv
2005:(PDF)
1983:S2CID
1965:arXiv
1938:S2CID
1912:arXiv
1885:S2CID
1849:arXiv
1732:charm
1724:quark
1701:kaons
1697:pions
1695:with
1583:metal
1581:in a
1330:k/MâȘ1
1238:or a
1226:, an
1173:Zuber
1023:Stora
988:Segal
968:Salam
953:Proca
948:Popov
918:Pauli
898:Oehme
888:Neveu
883:Nambu
868:Mills
753:Jaffe
728:Hagen
723:Higgs
698:Gupta
693:Gross
678:Glimm
658:Furry
628:Fierz
618:Fermi
613:Fayet
608:Fadin
593:Dyson
583:Dirac
548:Brout
523:Bethe
483:Adler
242:Tools
2301:ISBN
2291:ISBN
2016:2023
1877:PMID
1760:For
1741:For
1718:For
1713:pion
1634:EMRI
1369:and
1275:and
1138:Yang
1108:Wick
1103:Weyl
1093:Wess
1073:Ward
768:Jost
718:Hepp
708:Haag
633:Fock
513:Bell
2402:doi
2357:doi
2261:doi
2208:doi
2186:235
2155:doi
2102:doi
2057:doi
1975:doi
1930:doi
1867:doi
1845:110
1730:or
1707:of
1699:or
1685:QCD
1679:In
1652:is
1612:or
1573:of
1559:MeV
1555:GeV
1537:of
1338:1/M
1318:1/M
1314:1/M
1310:1/M
1222:In
1158:Zee
838:Low
813:Lee
3260::
2410:.
2400:.
2392:.
2380:47
2378:.
2372:.
2355:.
2345:32
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2339:.
2267:.
2259:.
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2237:.
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2206:.
2198:.
2184:.
2161:.
2153:.
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2133:88
2131:.
2108:.
2100:.
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2086:.
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2033:.
2007:.
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1959:.
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1928:.
1920:.
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1906:.
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1875:.
1865:.
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1636:.
1263:,
1259:,
1255:,
3162:"
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2452:e
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1491:+
1486:e
1471:+
1462:e
1435:e
1420:+
1411:e
1407:+
1404:p
1394:n
1326:k
1302:M
1211:e
1204:t
1197:v
72:)
66:(
61:)
57:(
43:.
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