Light-Front BRST Quantization of the Vector Schwinger Model with a Photon Mass Term

Hamiltonian, Path Integral and BRST Formulations of the Vector Schwinger Model with a Photon Mass Term with Faddeevian Regularization

“…This modified model is seen to be a gauge-non-invariant (GNI) theory [13][14][15][16][17] in the IFQ [27][28][29][30][31]. This happens, as expected, because of the presence of a mass term for the vector gauge field and a corresponding presence of a set of second-class constraints in the theory [13][14][15][16][17].…”

“…Recently, in a series of papers [10][11][12][13][14][15][16][17], we have studied the VSM with a photon mass term (PMT) describing 2D electrodynamics with mass-less fermions but with a massive photon, in the so-called standard regularization (SR) [10][11][12][13][14][15][16][17].…”

“…In the above work, we have studied [10][11][12][13][14][15][16][17] this model with a mass term for the U(1) gauge field [14][15][16][17]. We have also studied [13,14] its Hamiltonian [27] and path integral [28][29][30][31] formulations as well as its operator solutions [13][14][15][16][17] in the usual instant-form (IF) of dynamics (on the hyperplanes defined by the IF time: t (:= x 0 ) = constant, called the IF quantization (IFQ) [27], as well as in the light-front (LF) quantization (LFQ) (on the hyperplanes defined by the LF time: τ (:= (x 0 + x 1 )/ √ 2) = constant [15][16][17][29][30][31][32][33].…”

“…We have also studied [13,14] its Hamiltonian [27] and path integral [28][29][30][31] formulations as well as its operator solutions [13][14][15][16][17] in the usual instant-form (IF) of dynamics (on the hyperplanes defined by the IF time: t (:= x 0 ) = constant, called the IF quantization (IFQ) [27], as well as in the light-front (LF) quantization (LFQ) (on the hyperplanes defined by the LF time: τ (:= (x 0 + x 1 )/ √ 2) = constant [15][16][17][29][30][31][32][33]. It is important to emphasize here that although this model, has been studied in the literature rather widely but without a photon mass term (which was a consequence of demanding the regularization for the VSM to be gauge-invariant (GI)) [1][2][3][4][6][7][8][9][10][11][12][13][14][15][16][17].…”

“…The theory with a mass term for the U(1) gauge field [13][14][15][16][17] represents a new class of models in the 2D quantum electrodynamics with mass-less fermions (but with a photon mass term [13][14][15][16][17]). …”