Using the Stueckelberg formalism, we construct a gauge-invariant version of the vector Schwinger model (VSM) with a photon mass term studied by one of us recently. This model describes two-dimensional massive electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings. This model describing the 2D massive electrodynamics becomes gaugenoninvariant (GNI). This is in contrast to the case of the massless VSM which is a gauge-invariant (GI) theory (as a consequence of demanding the regularization for the theory to be GI). In this work we first construct a GI theory corresponding to this model describing the 2D massive electrodynamics, using the Stueckelberg formalism and then we recover the physical contents of the original GNI theory studied earlier, under some special gauge choice. We then study the Hamiltonian, path integral and BRST formulations of this GI theory under appropriate gauge-fixing. The theory presents a new class of models in the 2D quantum electrodynamics with massless fermions but with a photon mass term.
The conformally gauge-fixed Polyakov D1 brane action in the presence of a scalar dilaton field is seen to be a constrained system in the sense of Dirac. In the present work we study its Hamiltonian and path integral quantization in the instant-form of dynamics using the equal world-sheet time framework.
The front-form Hamiltonian and BRST formulations of the NielsenOlesen model are investigated in two-space one-time dimension in the broken (frozen) symmetry phase, where the phase ϕ(xμ) of the complex matter field Φ(xμ) carries the charge degree of freedom of the complex matter field and is, in fact, akin to the Goldstone Boson.PACS No.: 11.15.q
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