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

Usha Kulshreshtha, Daya Shankar Kulshreshtha

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DOI: 10.4236/jmp.2011.25041                

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.

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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