Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing

ABSTRACT

The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.

The Chern-Simons theory in two-space one-time dimensions is quantized on the light-front under appropriate gauge-fixing conditions using the Hamiltonian, path integral and BRST formulations.

KEYWORDS

Hamiltonian Quantization, Path Integral Quantization, BRST Quantization, Chern-Simons Theories, Light-Cone Quantization, Light-Front Quantization, Constrained Dynamics, Quantum Electrodynamics Models in Lower Dimensions, Light-Cone Quantization

Hamiltonian Quantization, Path Integral Quantization, BRST Quantization, Chern-Simons Theories, Light-Cone Quantization, Light-Front Quantization, Constrained Dynamics, Quantum Electrodynamics Models in Lower Dimensions, Light-Cone Quantization

Cite this paper

nullU. Kulshreshtha, D. Kulshreshtha and J. Vary, "Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,"*Journal of Modern Physics*, Vol. 1 No. 6, 2010, pp. 385-392. doi: 10.4236/jmp.2010.16055.

nullU. Kulshreshtha, D. Kulshreshtha and J. Vary, "Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,"

References

[1] G. V. Dunne, “Aspects of Chern-Simons Theories,” hep-th/9902115, and references therein.

[2] A. Smirnov, “Notes on Chern-Simons Theory in the Temporal Gauge”, arXiv: hep-th/09105011.

[3] E. J. Ferrer, R. Hurka and V. D. L. Incera, “High Tem-perature Anyon Superconductivity,” Modern Physics Letters B, Vol. 11, No.1, 1997, pp. 1-8.

[4] R. B. Laughlin, “Nobel Lecture: Fractional Quantiza-tion,” Reviews of Modern Physics, Vol. 71 No. 4, 1999, pp. 863-874.

[5] F. Wilczek, “Quantum Mechanics of Fractional Spin Particles,” Physical Review Letters, Vol. 49, No. 14, 1982, pp. 957-959.

[6] D. Boyanovsky, “Chern-Simons with Matter Fields”, Phyical Review, Vol. 42, No. 4, 1990, pp. 1179-1183.

[7] D. Boyanovsky, E. T. Newman and C. Rovelli, “On the Quantization of Dynamical Systems with Chern-Simons Terms,” Physical Review, D45, 1992, pp. 1210-1216.

[8] U. Kulshreshtha and D. S. Kulshreshtha, “Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,” Canadian Journal of Physics, Vol. 86, No. 2, 2008, pp. 401-407.

[9] U. Kulshreshtha, D. S. Kulshreshtha, H. J. W. Muel-ler-Kirsten and J. P. Vary, “Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Higgs Theory under Appropriate Gauge-Fixing,” Physica Scripta, Vol. 79, No. 4, 2009, pp. 045001.

[10] U. Kulshreshtha, “Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Higgs Theory in the Broken Symmetry Phase,” Physica Scripta, Vol. 75, No. 6, 2007, pp. 795-802.

[11] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST For-mulations of the Chern-Simons Higgs Theory under Ap-propriate Gauge-Fixing,” Physica Scripta, 82:055101, 2010.

[12] P. A. M. Dirac, “Generalized Hamiltonian Dynamics,” Canadian Journal of Mathematics, Vol. 2, 1950, pp. 129-148.

[13] M. Henneaux and C. Teitelboim, “Quantization of Gauge Systems,” Princeton University Press, New Jersey, 1992.

[14] U. Kulshreshtha and D. S. Kulshreshtha, “Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a 2-Form Gauge Field: The Instant-Form and Front- Form Hamiltonian and Path Integral Formulations,” Physics Letters B, Vol. 555, No. 3-4, 2003, pp. 255-263.

[15] U. kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Dirac-Born-Infeld Nambu-Goto D1 Brane Action with and without a Dila-ton Field under Gauge-Fixing,” The European Physical Journal C, Vol. 29, No. 3, 2003, pp. 453-461.

[16] D. Nemeschansky, C. Preitschopf and M. Weinstein, “A BRST Primer,” Annals of Physics, Vol. 183, No. 2, 1988, pp. 226-268.

[17] P. A. M. Dirac, “Forms of Relativistic Dynamics,” Re-views of Modern Physics, Vol. 21, No. 3, 1949, pp. 392-399.

[18] S. J. Brodsky, H. C. Pauli and S. S. Pinsky, “Quantum Chromodynamics and other Field Theories on the Light-Cone”, Physics Reports, Vol. 301, No. 4-6, 1998, pp. 299-486.

[1] G. V. Dunne, “Aspects of Chern-Simons Theories,” hep-th/9902115, and references therein.

[2] A. Smirnov, “Notes on Chern-Simons Theory in the Temporal Gauge”, arXiv: hep-th/09105011.

[3] E. J. Ferrer, R. Hurka and V. D. L. Incera, “High Tem-perature Anyon Superconductivity,” Modern Physics Letters B, Vol. 11, No.1, 1997, pp. 1-8.

[4] R. B. Laughlin, “Nobel Lecture: Fractional Quantiza-tion,” Reviews of Modern Physics, Vol. 71 No. 4, 1999, pp. 863-874.

[5] F. Wilczek, “Quantum Mechanics of Fractional Spin Particles,” Physical Review Letters, Vol. 49, No. 14, 1982, pp. 957-959.

[6] D. Boyanovsky, “Chern-Simons with Matter Fields”, Phyical Review, Vol. 42, No. 4, 1990, pp. 1179-1183.

[7] D. Boyanovsky, E. T. Newman and C. Rovelli, “On the Quantization of Dynamical Systems with Chern-Simons Terms,” Physical Review, D45, 1992, pp. 1210-1216.

[8] U. Kulshreshtha and D. S. Kulshreshtha, “Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,” Canadian Journal of Physics, Vol. 86, No. 2, 2008, pp. 401-407.

[9] U. Kulshreshtha, D. S. Kulshreshtha, H. J. W. Muel-ler-Kirsten and J. P. Vary, “Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Higgs Theory under Appropriate Gauge-Fixing,” Physica Scripta, Vol. 79, No. 4, 2009, pp. 045001.

[10] U. Kulshreshtha, “Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Higgs Theory in the Broken Symmetry Phase,” Physica Scripta, Vol. 75, No. 6, 2007, pp. 795-802.

[11] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST For-mulations of the Chern-Simons Higgs Theory under Ap-propriate Gauge-Fixing,” Physica Scripta, 82:055101, 2010.

[12] P. A. M. Dirac, “Generalized Hamiltonian Dynamics,” Canadian Journal of Mathematics, Vol. 2, 1950, pp. 129-148.

[13] M. Henneaux and C. Teitelboim, “Quantization of Gauge Systems,” Princeton University Press, New Jersey, 1992.

[14] U. Kulshreshtha and D. S. Kulshreshtha, “Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a 2-Form Gauge Field: The Instant-Form and Front- Form Hamiltonian and Path Integral Formulations,” Physics Letters B, Vol. 555, No. 3-4, 2003, pp. 255-263.

[15] U. kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Dirac-Born-Infeld Nambu-Goto D1 Brane Action with and without a Dila-ton Field under Gauge-Fixing,” The European Physical Journal C, Vol. 29, No. 3, 2003, pp. 453-461.

[16] D. Nemeschansky, C. Preitschopf and M. Weinstein, “A BRST Primer,” Annals of Physics, Vol. 183, No. 2, 1988, pp. 226-268.

[17] P. A. M. Dirac, “Forms of Relativistic Dynamics,” Re-views of Modern Physics, Vol. 21, No. 3, 1949, pp. 392-399.

[18] S. J. Brodsky, H. C. Pauli and S. S. Pinsky, “Quantum Chromodynamics and other Field Theories on the Light-Cone”, Physics Reports, Vol. 301, No. 4-6, 1998, pp. 299-486.