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

Usha Kulshreshtha, Daya Shankar Kulshreshtha

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**DOI: **10.4236/jmp.2011.28097
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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.

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

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U. 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.

Conflicts of Interest

The authors declare no conflicts of interest.

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