Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action with a Scalar Dilation Field

ABSTRACT

Recently we have studied the instant-form quantization (IFQ) of the conformally gauge-fixed Polyakov D1 brane action with and without a scalar dilaton field using the Hamiltonian and path integral formulations in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ^{0}=τ=constant . The light-front quantization (LFQ) of this theory without a scalar dilaton field has also been studied by us recently. In the present work we study the LFQ of this theory in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time σ^{+}=τ+σ=constant , using the Hamiltonian and path integral formulations. The light-front theory is seen to be a constrained system in the sense of Dirac. The light-front theory is seen to possess a set of twenty seven primary second-class contraints. In the present work Hamiltonian and path integral quantizations of this theory are studied on the light-front.

Recently we have studied the instant-form quantization (IFQ) of the conformally gauge-fixed Polyakov D1 brane action with and without a scalar dilaton field using the Hamiltonian and path integral formulations in the equal world-sheet time framework on the hyperplanes defined by the world- sheet time σ

KEYWORDS

Light-Front Quantization, Hamiltonian Quantization, Path Integral Quantization, Constrained Dynamics, Constraint Quantization, Gauge Symmetry, String Gauge Symmetry, String Theory, D-brane Actions, Polyakov Action, Light-Cone Quantization

Light-Front Quantization, Hamiltonian Quantization, Path Integral Quantization, Constrained Dynamics, Constraint Quantization, Gauge Symmetry, String Gauge Symmetry, String Theory, D-brane Actions, Polyakov Action, Light-Cone Quantization

Cite this paper

nullU. Kulshreshtha and D. Kulshreshtha, "Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action with a Scalar Dilation Field,"*Journal of Modern Physics*, Vol. 2 No. 8, 2011, pp. 826-833. doi: 10.4236/jmp.2011.28097.

nullU. Kulshreshtha and D. Kulshreshtha, "Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action with a Scalar Dilation Field,"

References

[1] D. Luest and S. Theisen, “Lectures in String Theory,” Lecture Notes in Physics, Springer Verlag, Berlin, Vol. 346, 1989.

[2] L. Brink and M. Henneaux, “Principles of String Theory,” Plenum Press, New York, 1988.

[3] C. V. Johnson, “D-Brane Primer,” hep-th/0007170.

[4] M. Aganagic, J. Park, C. Popescu and J. Schwarz, “Dual D-Brane Actions,” Nuclear Physics B, Vol. 496, No. 1-2, 1997, pp. 215-230. doi:10.1016/S0550-3213(97)00257-5

[5] M. Abou Zeid and C. M. Hull, “Intrinsic Geometry of D-Branes,” Physics Letters B, Vol. 404, No. 3-4, 199, pp. 7264-270.

[6] C. Schmidhuber, “D-Brane Actions,” Nuclear Physics B, Vol. 467, No. 1-2, 1996, pp. 146-158. doi:10.1016/0550-3213(96)00092-2

[7] S. P. de Alwis, K. Sato, “D-Strings and F-Strings from String Loops,” Physical Review D, Vol. 53, No. 12, 1996, pp. 7187-7196. doi:10.1103/PhysRevD.53.7187

[8] A. A. Tseytlin, “Self Duality of Born-Infeld Action and Dirichlet Three-Brane of Type IIB Super String Theory,” Nuclear Physics B, Vol. 469, No. 1-2, 1996, pp. 51-67. doi:10.1016/0550-3213(96)00173-3

[9] Usha 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,” Phy- sics Letters B, Vol. 555, No. 3-4, 2003, pp. 255-263.

[10] D.S. Kulshreshtha, “Polyakov D1 Brane Action on the Light-Front,” Invited Talk at the Light-Cone 2008: Relativistic Nuclear and Particle Physics (2008), Mulhouse, 7-11 July, 2008, Published in PoS LC2008: 007, 2008, hep-th/0809.1038.

[11] Usha Kulshreshtha and D. S. Kulshreshtha, “Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action,” Journal of Modern Physics, Vol. 2, No. 5, 2011, pp. 335-340 (in Press).

[12] Usha Kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Quantization of the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilation Field,” International Journal of Theoretical Physics, Vol. 48, No. 4, 2009, pp. 937-944. doi:10.1007/s10773-008-9866-z

[13] D. S. Kulshreshtha, “Light-Front Quantization of the Polyakov D1 Brane Action with a Scalar Dilaton Field,” Invited Talk at the Light-Cone 2007: Relativistic Hadronic and Nuclear Physics (LC2007), Columbus, 14-18 May 2007, hep-th/0711.1342.

[14] D. S. Kulshreshtha, “String gauge Symmetries in the Light-Front Polyakov D1 Brane Action,” Invited Talk at the International Conference Light-Cone 2010: Relativistic Hadronic and Particle Physics (LC2010), Valencia, 14-18 June 2010, Published in PoS LC2010: 006, 2010, SISSA, Trieste, Italy.

[15] Usha kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Dirac-Born-Infeld- Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” European Physical Jour- nal, Vol. C29, No. 3, 2003, pp. 453-461.

[16] Usha kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Nambu-Goto D1 Brane Action With and Without a Dilaton Field under Gauge-Fixing,” International Journal of Theoretical Physics, Vol. 43, No. 12, 2004, pp. 2355-2369. doi:10.1007/s10773-004-7704-5

[17] Usha kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Born-Infeld- Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” International Journal of Theoretical Physics, Vol. 44, No. 5, 2005, pp. 587-603. doi:10.1007/s10773-005-3985-6

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

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

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

[21] Usha 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

[22] Usha Kulshreshtha and D. S. Kulshreshtha, “Gauge-Invariant Reformulation of the Vector Schwinger Model with a Photon Mass Term and Its Hamiltonian, Path Integral and BRST Formulations,” International Journal of Modern Physics, Vol. A22, No. 32, 2007, pp. 6183-6201.

[23] P. A. M. Dirac, “Forms of Relativistic Dynamics,” Reviews of 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,” Vol. 301, No. 4-6, 1998, pp. 299-486.

[25] Usha Kulshreshtha, “Hamiltonian and BRST Formulations of the Nelsen-Olesen Model,” International Journal of Theoretical Physics, Vol. 41, No. 2, 2002, pp. 273-291. doi:10.1023/A:1014058806710

[26] Usha Kulshreshtha, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Nelsen-Olsen (Bogomol'nyi) Model in the Light-Cone Gauges,” International Journal of Theoretical Physics, Vol. 46, No. 10, 2007, pp. 2516-2530. doi:10.1007/s10773-007-9367-5

[27] Usha 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,” Physics Scripta, Vol. 82, No. 5, 2010, 055101.

[28] Usha 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, No. 6, 2010, pp. 385-392.

[29] J. Maharana, “Quantization of Nonlinear Sigma Model in Constrained Hamiltonian Formalism,” Physics Letters B, Vol. 128, No. 6, 1983, pp. 411-414. doi:10.1016/0370-2693(83)90928-0

[30] M. M. Sheikh-Jabbari and A. Shirzad; “Boundary conditions as Dirac constraints,” European Physical Journal C, Vol. 19, No. 2, 2001, pp. 383-390. doi:10.1007/s100520100590

[1] D. Luest and S. Theisen, “Lectures in String Theory,” Lecture Notes in Physics, Springer Verlag, Berlin, Vol. 346, 1989.

[2] L. Brink and M. Henneaux, “Principles of String Theory,” Plenum Press, New York, 1988.

[3] C. V. Johnson, “D-Brane Primer,” hep-th/0007170.

[4] M. Aganagic, J. Park, C. Popescu and J. Schwarz, “Dual D-Brane Actions,” Nuclear Physics B, Vol. 496, No. 1-2, 1997, pp. 215-230. doi:10.1016/S0550-3213(97)00257-5

[5] M. Abou Zeid and C. M. Hull, “Intrinsic Geometry of D-Branes,” Physics Letters B, Vol. 404, No. 3-4, 199, pp. 7264-270.

[6] C. Schmidhuber, “D-Brane Actions,” Nuclear Physics B, Vol. 467, No. 1-2, 1996, pp. 146-158. doi:10.1016/0550-3213(96)00092-2

[7] S. P. de Alwis, K. Sato, “D-Strings and F-Strings from String Loops,” Physical Review D, Vol. 53, No. 12, 1996, pp. 7187-7196. doi:10.1103/PhysRevD.53.7187

[8] A. A. Tseytlin, “Self Duality of Born-Infeld Action and Dirichlet Three-Brane of Type IIB Super String Theory,” Nuclear Physics B, Vol. 469, No. 1-2, 1996, pp. 51-67. doi:10.1016/0550-3213(96)00173-3

[9] Usha 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,” Phy- sics Letters B, Vol. 555, No. 3-4, 2003, pp. 255-263.

[10] D.S. Kulshreshtha, “Polyakov D1 Brane Action on the Light-Front,” Invited Talk at the Light-Cone 2008: Relativistic Nuclear and Particle Physics (2008), Mulhouse, 7-11 July, 2008, Published in PoS LC2008: 007, 2008, hep-th/0809.1038.

[11] Usha Kulshreshtha and D. S. Kulshreshtha, “Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action,” Journal of Modern Physics, Vol. 2, No. 5, 2011, pp. 335-340 (in Press).

[12] Usha Kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Quantization of the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilation Field,” International Journal of Theoretical Physics, Vol. 48, No. 4, 2009, pp. 937-944. doi:10.1007/s10773-008-9866-z

[13] D. S. Kulshreshtha, “Light-Front Quantization of the Polyakov D1 Brane Action with a Scalar Dilaton Field,” Invited Talk at the Light-Cone 2007: Relativistic Hadronic and Nuclear Physics (LC2007), Columbus, 14-18 May 2007, hep-th/0711.1342.

[14] D. S. Kulshreshtha, “String gauge Symmetries in the Light-Front Polyakov D1 Brane Action,” Invited Talk at the International Conference Light-Cone 2010: Relativistic Hadronic and Particle Physics (LC2010), Valencia, 14-18 June 2010, Published in PoS LC2010: 006, 2010, SISSA, Trieste, Italy.

[15] Usha kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Dirac-Born-Infeld- Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” European Physical Jour- nal, Vol. C29, No. 3, 2003, pp. 453-461.

[16] Usha kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Nambu-Goto D1 Brane Action With and Without a Dilaton Field under Gauge-Fixing,” International Journal of Theoretical Physics, Vol. 43, No. 12, 2004, pp. 2355-2369. doi:10.1007/s10773-004-7704-5

[17] Usha kulshreshtha and D. S. Kulshreshtha, “Hamiltonian and Path Integral Formulations of the Born-Infeld- Nambu-Goto D1 Brane Action with and without a Dilaton Field under Gauge-Fixing,” International Journal of Theoretical Physics, Vol. 44, No. 5, 2005, pp. 587-603. doi:10.1007/s10773-005-3985-6

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

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

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

[21] Usha 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

[22] Usha Kulshreshtha and D. S. Kulshreshtha, “Gauge-Invariant Reformulation of the Vector Schwinger Model with a Photon Mass Term and Its Hamiltonian, Path Integral and BRST Formulations,” International Journal of Modern Physics, Vol. A22, No. 32, 2007, pp. 6183-6201.

[23] P. A. M. Dirac, “Forms of Relativistic Dynamics,” Reviews of 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,” Vol. 301, No. 4-6, 1998, pp. 299-486.

[25] Usha Kulshreshtha, “Hamiltonian and BRST Formulations of the Nelsen-Olesen Model,” International Journal of Theoretical Physics, Vol. 41, No. 2, 2002, pp. 273-291. doi:10.1023/A:1014058806710

[26] Usha Kulshreshtha, “Light-Front Hamiltonian, Path Integral and BRST Formulations of the Nelsen-Olsen (Bogomol'nyi) Model in the Light-Cone Gauges,” International Journal of Theoretical Physics, Vol. 46, No. 10, 2007, pp. 2516-2530. doi:10.1007/s10773-007-9367-5

[27] Usha 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,” Physics Scripta, Vol. 82, No. 5, 2010, 055101.

[28] Usha 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, No. 6, 2010, pp. 385-392.

[29] J. Maharana, “Quantization of Nonlinear Sigma Model in Constrained Hamiltonian Formalism,” Physics Letters B, Vol. 128, No. 6, 1983, pp. 411-414. doi:10.1016/0370-2693(83)90928-0

[30] M. M. Sheikh-Jabbari and A. Shirzad; “Boundary conditions as Dirac constraints,” European Physical Journal C, Vol. 19, No. 2, 2001, pp. 383-390. doi:10.1007/s100520100590