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Simplicial gauge theory and quantum gauge theory simulation. (English) Zbl 1229.81182
Summary: We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionally, we perform simplicial Monte Carlo quantum gauge field simulations involving measurements of the action as well as differently sized Wilson loops as functions of β.
MSC:
81T13Yang-Mills and other gauge theories
81T25Quantum field theory on lattices
81V05Strong interaction, including quantum chromodynamics
35Q40PDEs in connection with quantum mechanics
65C05Monte Carlo methods
References:
[1]Yang, C. -N.; Mills, R. L.: Conservation of isotopic spin and isotopic gauge invariance, Phys. rev. 96, 191-195 (1954)
[2]Weinberg, S.: The quantum theory of fields, vol. 1: foundations, (1995)
[3]Weinberg, S.: The quantum theory of fields, vol. 2: modern applications, (1996)
[4]Peskin, M. E.; Schroeder, D. V.: An introduction to quantum field theory, (1995)
[5]Wilson, K. G.: Confinement of quarks, Phys. rev. D 10, No. 8, 2445-2459 (1974)
[6]Creutz, M.: Quarks, gluons and lattices, Cambridge monographs on mathematical physics (1986)
[7]Christ, N. H.; Friedberg, R.; Lee, T. D.: Weights of links and plaquettes in a random lattice, Nucl. phys. B 210, 337 (1982)
[8]Christ, N. H.; Friedberg, R.; Lee, T. D.: Gauge theory on a random lattice, Nucl. phys. B 210, 310 (1982)
[9]Christ, N. H.; Friedberg, R.; Lee, T. D.: Random lattice field theory: general formulation, Nucl. phys. B 202, 89 (1982)
[10]Drouffe, J. M.; Moriarty, K. J. M.; Mouhas, C. N.: Monte Carlo simulation of pure U(N) and SU(N) gauge theories on a simplicial lattice, Comput. phys. Commun. 30, 249 (1983)
[11]Drouffe, J. M.; Moriarty, K. J. M.; Mouhas, C. N.: U(1) four-dimensional gauge theory on a simplicial lattice, J. phys. G 10, 115 (1984)
[12]Drouffe, J. M.; Moriarty, K. J. M.: Gauge theories on a simplicial lattice, Nucl. phys. B 220, 253-268 (1983)
[13]Drouffe, J. M.; Moriarty, K. J. M.: U(2) four-dimensional simplicial lattice gauge theory, Z. phys. C 24, 395 (1984)
[14]Cahill, K. E.; Reeder, R.: Comparison of the simplicial method with Wilson’s lattice gauge theory for U(1) in three-dimensions, Phys. lett. B 168, 381 (1986)
[15]URL http://stacks.iop.org/0305-4616/10/i=10/a=001.
[16]Ardill, R. W. B.; Clarke, J. P.; Drouffe, J. M.; Moriarty, K. J. M.: Quantum chromodynamics on a simplicial lattice, Phys. lett. B 128, 203 (1983)
[17]Ciarlet, P. G.: The finite element method for elliptic problems, Studies in mathematics and its applications 4 (1978) · Zbl 0383.65058
[18]Monk, P.: Finite element methods for Maxwell’s equations, (2006)
[19]Nédélec, J. -C.: Mixed finite elements in R3, Num. math. 35, 315-341 (1980) · Zbl 0419.65069 · doi:10.1007/BF01396415
[20]Whitney, H.: Geometric integration theory, (1957) · Zbl 0083.28204
[21]Hiptmair, R.: Finite elements in computational electromagnetism, Acta numerica 11, 237-339 (2002) · Zbl 1123.78320 · doi:10.1017/S0962492902000041
[22]Bender, C. M.; Milton, K. A.: Approximate determination of the mass gap in quantum field theory using the method of finite elements, Phys. rev. D 34, No. 10, 3149-3155 (1986)
[23]Bender, C. M.; Milton, K. A.; Sharp, D. H.: Gauge invariance and the finite-element solution of the Schwinger model, Phys. rev. D 31, No. 2, 383-388 (1985)
[24]Halvorsen, T. G.; Sorensen, T. M.: Simplicial gauge theory on spacetime
[25]Flyvbjerg, H.; Petersen, H. G.: Error estimates on averages of correlated data, Journal of chemical physics 91, No. 1, 461-466 (1989)
[26]Creutz, M.: Monte Carlo study of quantized SU(2) gauge theory, Phys. rev. D 21, 2308-2315 (1980)
[27]Christiansen, S. H.; Munthe-Kaas, H. Z.; Owren, B.: Topics in structure-preserving discretization, Acta numerica 20, 1-119 (2011) · Zbl 1233.65087 · doi:10.1017/S096249291100002X
[28]MPICH2, URL http://www.mcs.anl.gov/mpi/mpich2.
[29]H. Bauke, TINA pseudo-RNG library, URL http://trng.berlios.de.