Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1 Brane Action

ABSTRACT

In a recent paper we have studied the Hamiltonian and path integral quantizations of the conformally gauge-fixed Polyakov D1 brane action in the instant-form of dynamics using the equal world-sheet time framework on the hyperplanes defined by the world- sheet time . In the present work we quantize the same 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 , using the standard constraint quantization techniques in the Hamiltonian and path integral formulations. The light-front theory is seen to be a constrained system in the sense of Dirac, which is in contrast to the corresponding case of the instant-form theory, where the theory remains unconstrained in the sense of Dirac. The light-front theory is seen to possess a set of twenty six primary second-class contraints. In the present work Hamiltonian and path integral quantizations of this theory are studied on the light-front.

In a recent paper we have studied the Hamiltonian and path integral quantizations of the conformally gauge-fixed Polyakov D1 brane action in the instant-form of dynamics using the equal world-sheet time framework on the hyperplanes defined by the world- sheet time . In the present work we quantize the same 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 , using the standard constraint quantization techniques in the Hamiltonian and path integral formulations. The light-front theory is seen to be a constrained system in the sense of Dirac, which is in contrast to the corresponding case of the instant-form theory, where the theory remains unconstrained in the sense of Dirac. The light-front theory is seen to possess a set of twenty six primary second-class contraints. In the present work Hamiltonian and path integral quantizations of this theory are studied on the light-front.

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,"*Journal of Modern Physics*, Vol. 2 No. 5, 2011, pp. 335-340. doi: 10.4236/jmp.2011.25041.

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

References

[1] D. Luest and S. Theisen, “Lectures on String Theory,” Lecture Notes in Physics, Vol. 346, Springer Verlag, Berlin, 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. A. Zeid and C. M. Hull, “Intrinsic Geometry of D-Branes,” Physics Letters B, Vol. 404, No. 3-4, 1997, pp. 264-270. doi:10.1016/S0370-2693(97)00570-4

[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 and 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] 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. doi:10.1016/S0370-2693(03)00056-X

[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] U. 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

[12] D. S. Kulshreshtha, “Light-Front Quantization of the Pol- yakov 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.

[13] 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 Dilaton Field under Gauge-Fixing,” European Physical Journal C, Vol. 29, No.3, 2003, pp. 453-461. doi:10.1140/epjc/s2003-01239-8

[14] U. 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

[15] U. 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

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

[18] P. Senjanovic, “Path Integral Quantization of Field Theories with Second-Class Constraints,” Annals of Physics, Vol. 100, No. 1-2, 1976, pp. 227-261. Erratum: Annals of Physics, Vol. 209, No. 1, 1991, p. 248.

[19] 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

[20] U. Kulshreshtha, “Vector Scwinger Model with a Photon Mass Term: Gauge-Invariant Reformulation, Operator Solutions and Hamiltonian and Path Integral Formulations,” Modern Physics Letters A, Vol. 22, No. 39, 2007, pp. 2993-3001. doi:10.1142/S0217732307023663

[21] U. 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 A, Vol. 22, No. 32, 2007, pp. 6183-6201. doi:10.1142/S0217751X07038049

[22] 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

[23] 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

[24] U. 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

[25] U. 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

[26] 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,” Physics Scripta, Vol. 82, No. 5, 2010, p. 055101. doi:10.1088/0031-8949/82/05/055101

[27] 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, No. 6, 2010, pp. 385-392. doi:10.4236/jmp.2010.16055

[28] 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

[29] 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 on String Theory,” Lecture Notes in Physics, Vol. 346, Springer Verlag, Berlin, 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. A. Zeid and C. M. Hull, “Intrinsic Geometry of D-Branes,” Physics Letters B, Vol. 404, No. 3-4, 1997, pp. 264-270. doi:10.1016/S0370-2693(97)00570-4

[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 and 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] 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. doi:10.1016/S0370-2693(03)00056-X

[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] U. 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

[12] D. S. Kulshreshtha, “Light-Front Quantization of the Pol- yakov 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.

[13] 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 Dilaton Field under Gauge-Fixing,” European Physical Journal C, Vol. 29, No.3, 2003, pp. 453-461. doi:10.1140/epjc/s2003-01239-8

[14] U. 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

[15] U. 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

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

[18] P. Senjanovic, “Path Integral Quantization of Field Theories with Second-Class Constraints,” Annals of Physics, Vol. 100, No. 1-2, 1976, pp. 227-261. Erratum: Annals of Physics, Vol. 209, No. 1, 1991, p. 248.

[19] 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

[20] U. Kulshreshtha, “Vector Scwinger Model with a Photon Mass Term: Gauge-Invariant Reformulation, Operator Solutions and Hamiltonian and Path Integral Formulations,” Modern Physics Letters A, Vol. 22, No. 39, 2007, pp. 2993-3001. doi:10.1142/S0217732307023663

[21] U. 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 A, Vol. 22, No. 32, 2007, pp. 6183-6201. doi:10.1142/S0217751X07038049

[22] 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

[23] 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

[24] U. 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

[25] U. 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

[26] 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,” Physics Scripta, Vol. 82, No. 5, 2010, p. 055101. doi:10.1088/0031-8949/82/05/055101

[27] 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, No. 6, 2010, pp. 385-392. doi:10.4236/jmp.2010.16055

[28] 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

[29] 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