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**Instant-Form and Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an U(1) Gauge Field** ()

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world-sheet time *σ*^{0}=*τ*=constant and the LFQ 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. The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field *B** _{αβ}*(

*σ*,

*τ*)

*or in the presence of*

*U*(1) gauge field

*A*

*(*

_{α}*σ*,

*τ*)

*and the constant scalar axion field*

*C*(

*σ*,

*τ*), then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino or Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

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*U*(1) Gauge Field,"

*Journal of Modern Physics*, Vol. 4 No. 4A, 2013, pp. 57-69. doi: 10.4236/jmp.2013.44A009.

Conflicts of Interest

The authors declare no conflicts of interest.

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