Maxwell-Chern-Simons-Higgs theory
DOI:
https://doi.org/10.14311/AP.2022.62.0085Keywords:
electrodynamics, Higgs theories, Chern-Simons-Higgs theories, Hamiltonian formulations, gauge-theoriesAbstract
We consider the three dimensional electrodynamics described by a complex scalar field coupled with the U(1) gauge field in the presence of a Maxwell term, a Chern-Simons term and the Higgs potential. The Chern-Simons term provides a velocity dependent gauge potential and the presence of the Maxwell term makes the U(1) gauge field dynamical. We study the Hamiltonian formulation of this Maxwell-Chern-Simons-Higgs theory under the appropriate gauge fixing conditions.
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P. A. M. Dirac. Generalized Hamiltonian dynamics. Canadian Journal of Mathematics 2:129–148, 1950. https://doi.org/10.4153/cjm-1950-012-1.
V. L. Ginzburg, L. D. Landau. On the theory of superconductivity (in Russian). Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki 20:1064–1082, 1950.
A. A. Abrikosov. On the magnetic properties of superconductors of the second group. Soviet Physics JETP 5:1174–1182, 1957.
H. B. Nielson, P. Olsen. Vortex line models for dual strings. Nuclear Physics B 61:45–61, 1973.
C. Becchi, A. Rouet, R. Stora. The abelian Higgs Kibble model, unitarity of the S-operator. Physics Letters B 52(3):344–346, 1974. https://doi.org/10.1016/0370-2693(74)90058-6.
E. B. Bogomolnyi. The stability of classical solutions. Soviet Journal of Nuclear Physics 24(4):449–458, 1976.
S. Deser, R. Jackiw, S. Templeton. Three-dimensional massive gauge theories. Physical Review Letters 48:975–978, 1982. Annals of Physics, 140:372, 1982, https://doi.org/10.1103/PhysRevLett.48.975.
F. Wilczek. Quantum mechanics of fractional-spin particles. Physical Review Letters 49:957–959, 1982. https://doi.org/10.1103/PhysRevLett.49.957.
A. J. Niemi, G. W. Semenoff. Axial-anomaly-induced fermion fractionization and effective gauge-theory actions in odd-dimensional space-times. Physical Review Letters 51:2077–2080, 1983. https://doi.org/10.1103/PhysRevLett.51.2077.
A. N. Redlich. Gauge noninvariance and parity nonconservation of three-dimensional fermions. Physical Review Letters 52:18–21, 1984. https://doi.org/10.1103/PhysRevLett.52.18.
K. Ishikawa. Chiral anomaly and quantized Hall effect. Physical Review Letters 53:1615–1618, 1984. https://doi.org/10.1103/PhysRevLett.53.1615.
G. W. Semenoff, P. Sodano. Non-Abelian adiabatic phases and the fractional quantum Hall effect. Physical Review Letters 57:1195–1198, 1986. https://doi.org/10.1103/PhysRevLett.57.1195.
L. Jacobs, C. Rebbi. Interaction energy of superconducting vortices. Physical Review B 19:4486–4494, 1979. https://doi.org/10.1103/PhysRevB.19.4486.
I. V. Krive, A. S. Rozhavski˘ı. Fractional charge in quantum field theory and solid-state physics. Soviet Physics Uspekhi 30(5):370, 1987. https://doi.org/10.1070/PU1987v030n05ABEH002884.
A. L. Fetter, C. B. Hanna, R. B. Laughlin. Random-phase approximation in the fractional-statistics gas. Physical Review B 39:9679–9681, 1989. https://doi.org/10.1103/PhysRevB.39.9679.
T. Banks, J. D. Lykken. Landau-Ginzburg description of anyonic superconductors. Nuclear Physics B 336(3):500–516, 1990. https://doi.org/10.1016/0550-3213(90)90439-K.
G. V. Dunne, C. A. Trugenberger. Self-duality and nonrelativistic Maxwell-Chern-Simons solitons. Physical Review D 43:1323–1331, 1991. https://doi.org/10.1103/PhysRevD.43.1323.
S. Forte. Quantum mechanics and field theory with fractional spin and statistics. Reviews of Modern Physics 64:193–236, 1992. https://doi.org/10.1103/RevModPhys.64.193.
U. Kulshreshtha. Hamiltonian and BRST formulations of the two-dimensional Abelian Higgs model. Canadian Journal of Physics 78(1):21–31, 2000. https://doi.org/10.1139/p00-002.
U. Kulshreshtha. Hamiltonian and BRST formulations of the Nielsen-Olesen model. International Journal of Theoretical Physics 41(2):273–291, 2002. https://doi.org/10.1023/A:1014058806710.
U. Kulshreshtha, D. S. Kulshreshtha. Hamiltonian, path integral, and BRST formulations of the Chern–Simons theory under appropriate gauge-fixing. Canadian Journal of Physics 86(2):401–407, 2008. https://doi.org/10.1139/p07-176.
U. Kulshreshtha, D. S. Kulshreshtha, H. J. W. Mueller-Kirsten, J. P. Vary. Hamiltonian, path integral and BRST formulations of the Chern–Simons–Higgs theory under appropriate gauge fixing. Physica Scripta 79(4):045001, 2009. https://doi.org/10.1088/0031-8949/79/04/045001.
H. J. W. Mueller-Kirsten. Introduction to Quantum Mechanics: Schrödinger Equation and Path Integral. World Scientific, Singapore, 2006. ISBN 9789814397735.
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