Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase

Affiliation(s)

Department of Physics, Kirori Mal College, University of Delhi, Delhi, India.

Department of Physics and Astrophysics, University of Delhi, Delhi, India.

Department of Physics and Astronomy, Iowa State University, Ames, USA.

Department of Physics, Kirori Mal College, University of Delhi, Delhi, India.

Department of Physics and Astrophysics, University of Delhi, Delhi, India.

Department of Physics and Astronomy, Iowa State University, Ames, USA.

ABSTRACT

In the present work we study the Hamiltonian, path integral and BRST formulations of the Chern-Simons-Higgs theory in two-space one-time dimensions, in the so-called broken symmetry phase of the Higgs potential (where the phase *φ*(*x** ^{μ}*) of the complex matter field Φ(

Cite this paper

U. Kulshreshtha, D. Kulshreshtha and J. Vary, "Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase,"*Journal of Modern Physics*, Vol. 4 No. 4, 2013, pp. 38-48. doi: 10.4236/jmp.2013.44A007.

U. Kulshreshtha, D. Kulshreshtha and J. Vary, "Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase,"

References

[1] G. V. Dunne, “Aspects of Chern-Simons Theories,” Lectures Given at Les Houches Summer School in Theoretical Physics, Session 69: Topological Aspects of Low- Dimensional Systems, Les Houches, 7-31 July 1998. arXiv: hep-th/9902115

[2] F. Wilczek, “Quantum Mechanics of Fractional Spin Particles,” Physical Review Letters, Vol. 49, No. 14, 1982, pp. 957-959. doi:10.1103/PhysRevLett.49.957

[3] D. Boyanovsky, E. T. Newman and C. Rovelli, “On the Quantization of Dynamical Systems with Chern-Simons Terms,” Physical Review D, Vol. 45, No. 4, 199, pp. 1210-1216. doi:10.1103/PhysRevD.45.1210

[4] E. J. Ferrer, R. Hurka and V. de la Incera, “High Temperature Anyon Superconductivity,” Modern Physics Letters B, Vol. 11, No. 1, 1997, pp. 1-8. doi:10.1142/S0217984997000025

[5] R. B. Laughlin, “Nobel Lecture: Fractional Quantization,” Reviews Modern Physics, Vol. 71, No. 4, 1999, pp. 863-874. doi:10.1103/RevModPhys.71.863

[6] A. Smirnov, “Notes on Csern-Simons Theory in the Temporal Gauge,” International School of Subnuclear Physics (ISSP 2009): 47th Course: The Most Unexpected at LHC and the Status of High Energy Frontier, 29 August-7 September, 2009, Sicily, pp. 489-498. arXiv:0910.5011[hep-th]

[7] 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. doi:10.1139/P07-176

[8] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,” Journal of Modern Physics, Vol. 1, 2010, pp. 385-392. doi:10.4236/jmp.2010.16055

[9] U. Kulshreshtha, D. S. Kulshreshtha, H. J. W. Mueller-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, Article ID: 045001. doi:10.1088/0031-8949/79/04/045001

[10] U. Kulshreshtha, “Light-Front Quantization of the Chern-Simons Higgs Theory,” Invited Contributed Talk at the International Light-Cone Conference (LC2010) on Relativistic Hadronic and Particle Physics, Valencia, 18-22 May 2010.

[11] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Higgs Theory under Appropriate Gauge-Fixing,” Physica Scripta, Vol. 82, No. 5, 2010, Article ID: 055101. doi:10.1088/0031-8949/82/05/055101

[12] 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. doi:10.1088/0031-8949/75/6/009

[13] U. Kulshreshtha, “Light-Front Quantization of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase,” Invited Contributed Talk at the International Light-Cone Conference: LC2011, Dallas, 22-27 June 2011, pp. 457-461.

[14] U. Kulshreshtha and D. S. Kulshreshtha, “The Front-Form Hamiltonian and BRST Formulations of the Nielsen-Olesen Model in The Broken Symmetry Phase,” Canadian Journal of Physics, Vol. 82, 2004, pp. 569-583.

[15] D. Boyanovsky, “Chern-Simons with Matter Fields: Broken Symmetry Phase,” Physical Review D, Vol. 42, No. 4, 1990, pp. 1179-1183. doi:10.1103/PhysRevD.42.1179

[16] P. A. M. Dirac, “Generalized Hamiltonian Dynamics,” Canadian Journal of Mathematics, Vol. 2, 1950, pp. 129-148. doi:10.4153/CJM-1950-012-1

[17] P. Senjanovic, “Path Integral Quantization of Field Theories with Second Class Constraints,” Annals of Physics, Vol. 100, No. 1-2, 1976, pp. 227-261.

[18] 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,” Physical Letters B, Vol. 555, No. 3-4, 2003, pp. 255-263.

[19] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian and Path Integral Formulations of Large N Scalar QCD2,” Physics Letters B, Vol. 708, No. 1-2, 2012, pp. 195-198. doi:10.1016/j.physletb.2012.01.034

[20] C. Becchi, A. Rouet and A. Stora, “The Abelian Higgs-Kibble Model. Unitarity of the S-Operator,” Physics Letters B, Vol. 52, No. 3, 1974, pp. 344-346. doi:10.1016/0370-2693(74)90058-6

[21] V. Tyutin, “Lebedev Report No. FIAN-39,” (unpublished).

[22] D. Nemeschansky, C. Preitschopf and M. Weinstein, “A BRST Primer,” Annals of Physics, Vol. 183, No. 2, 1988, pp. 226-268. doi:10.1016/0003-4916(88)90233-3

[23] P. A. M. Dirac, “Forms of Relativistic Dynamics,” Reviews Modern Physics, Vol. 21, No. 3, 1949, pp. 392-399. doi:10.1103/RevModPhys.21.392

[24] 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. doi:10.1016/S0370-1573(97)00089-6

[1] G. V. Dunne, “Aspects of Chern-Simons Theories,” Lectures Given at Les Houches Summer School in Theoretical Physics, Session 69: Topological Aspects of Low- Dimensional Systems, Les Houches, 7-31 July 1998. arXiv: hep-th/9902115

[2] F. Wilczek, “Quantum Mechanics of Fractional Spin Particles,” Physical Review Letters, Vol. 49, No. 14, 1982, pp. 957-959. doi:10.1103/PhysRevLett.49.957

[3] D. Boyanovsky, E. T. Newman and C. Rovelli, “On the Quantization of Dynamical Systems with Chern-Simons Terms,” Physical Review D, Vol. 45, No. 4, 199, pp. 1210-1216. doi:10.1103/PhysRevD.45.1210

[4] E. J. Ferrer, R. Hurka and V. de la Incera, “High Temperature Anyon Superconductivity,” Modern Physics Letters B, Vol. 11, No. 1, 1997, pp. 1-8. doi:10.1142/S0217984997000025

[5] R. B. Laughlin, “Nobel Lecture: Fractional Quantization,” Reviews Modern Physics, Vol. 71, No. 4, 1999, pp. 863-874. doi:10.1103/RevModPhys.71.863

[6] A. Smirnov, “Notes on Csern-Simons Theory in the Temporal Gauge,” International School of Subnuclear Physics (ISSP 2009): 47th Course: The Most Unexpected at LHC and the Status of High Energy Frontier, 29 August-7 September, 2009, Sicily, pp. 489-498. arXiv:0910.5011[hep-th]

[7] 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. doi:10.1139/P07-176

[8] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Theory under Appropriate Gauge-Fixing,” Journal of Modern Physics, Vol. 1, 2010, pp. 385-392. doi:10.4236/jmp.2010.16055

[9] U. Kulshreshtha, D. S. Kulshreshtha, H. J. W. Mueller-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, Article ID: 045001. doi:10.1088/0031-8949/79/04/045001

[10] U. Kulshreshtha, “Light-Front Quantization of the Chern-Simons Higgs Theory,” Invited Contributed Talk at the International Light-Cone Conference (LC2010) on Relativistic Hadronic and Particle Physics, Valencia, 18-22 May 2010.

[11] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Chern-Simons Higgs Theory under Appropriate Gauge-Fixing,” Physica Scripta, Vol. 82, No. 5, 2010, Article ID: 055101. doi:10.1088/0031-8949/82/05/055101

[12] 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. doi:10.1088/0031-8949/75/6/009

[13] U. Kulshreshtha, “Light-Front Quantization of the Chern-Simons-Higgs Theory in the Broken Symmetry Phase,” Invited Contributed Talk at the International Light-Cone Conference: LC2011, Dallas, 22-27 June 2011, pp. 457-461.

[14] U. Kulshreshtha and D. S. Kulshreshtha, “The Front-Form Hamiltonian and BRST Formulations of the Nielsen-Olesen Model in The Broken Symmetry Phase,” Canadian Journal of Physics, Vol. 82, 2004, pp. 569-583.

[15] D. Boyanovsky, “Chern-Simons with Matter Fields: Broken Symmetry Phase,” Physical Review D, Vol. 42, No. 4, 1990, pp. 1179-1183. doi:10.1103/PhysRevD.42.1179

[16] P. A. M. Dirac, “Generalized Hamiltonian Dynamics,” Canadian Journal of Mathematics, Vol. 2, 1950, pp. 129-148. doi:10.4153/CJM-1950-012-1

[17] P. Senjanovic, “Path Integral Quantization of Field Theories with Second Class Constraints,” Annals of Physics, Vol. 100, No. 1-2, 1976, pp. 227-261.

[18] 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,” Physical Letters B, Vol. 555, No. 3-4, 2003, pp. 255-263.

[19] U. Kulshreshtha, D. S. Kulshreshtha and J. P. Vary, “Light-Front Hamiltonian and Path Integral Formulations of Large N Scalar QCD2,” Physics Letters B, Vol. 708, No. 1-2, 2012, pp. 195-198. doi:10.1016/j.physletb.2012.01.034

[20] C. Becchi, A. Rouet and A. Stora, “The Abelian Higgs-Kibble Model. Unitarity of the S-Operator,” Physics Letters B, Vol. 52, No. 3, 1974, pp. 344-346. doi:10.1016/0370-2693(74)90058-6

[21] V. Tyutin, “Lebedev Report No. FIAN-39,” (unpublished).

[22] D. Nemeschansky, C. Preitschopf and M. Weinstein, “A BRST Primer,” Annals of Physics, Vol. 183, No. 2, 1988, pp. 226-268. doi:10.1016/0003-4916(88)90233-3

[23] P. A. M. Dirac, “Forms of Relativistic Dynamics,” Reviews Modern Physics, Vol. 21, No. 3, 1949, pp. 392-399. doi:10.1103/RevModPhys.21.392

[24] 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. doi:10.1016/S0370-1573(97)00089-6