Hamiltonian and Path Integral Quantization of the Conformally Gauge-Fixed Polyakov D1 Brane Action in the Presence of a Scalar Dilation Field

Abstract

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.

Light-Front Quantization of Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an U(1) Gauge Field

“…The axion field C and the U (1) gauge field A α , are seen to behave like the Wess-Zumino (WZ) fields and the term involving these fields is seen to behave like a WZ term for this action.The Polyakov action is one of the most widely studied topics in string theory [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. Recently we have studied [9][10][11][12][13][14][15][16] the Hamiltonian [17] and path integral [9,[12][13][14][15][16] formulations of the conformally gauge-fixed Polyakov D1 brane action (CGFPD1BA) with and without a scalar dilaton field in the instant-form (IF) quantization (IFQ) [12,18,19] as well as in the light-front (LF) quantization (LFQ) [9,[13][14][15][16]18,19] (using the IF of dynamics [18,19] on the hyperplanes defined by the World-Sheet (WS) time σ 0 = τ = constant for IFQ [18,19] and using the light-front (LF) dynamics on the hyperplanes of the LF defined by the light-cone (LC) ...…”

“…Recently we have studied [9][10][11][12][13][14][15][16] the Hamiltonian [17] and path integral [9,[12][13][14][15][16] formulations of the conformally gauge-fixed Polyakov D1 brane action (CGFPD1BA) with and without a scalar dilaton field in the instant-form (IF) quantization (IFQ) [12,18,19] as well as in the light-front (LF) quantization (LFQ) [9,[13][14][15][16]18,19] (using the IF of dynamics [18,19] on the hyperplanes defined by the World-Sheet (WS) time σ 0 = τ = constant for IFQ [18,19] and using the light-front (LF) dynamics on the hyperplanes of the LF defined by the light-cone (LC) time: σ + = (τ + σ ) = constant) [18,19]. In both the above cases the theory is seen to be gauge-non-invariant(GNI) [9], [12][13][14][15][16], possessing a set of second-class constraints, owing to the conformal gauge-fixing of the theory. This GNI theory has been studied by us in Ref.…”

“…Now the actionS in the so called conformal-gauge in both the instant-and front-forms of dynamics finally reads [1][2][3][4][5]9,[12][13][14][15][16]:…”

“…This action is seen to lack the local gauge symmetries. This theory in the IFQ is seen to be an unconstrained theory [12] and in the LFQ it is seen to possess a set of 26 second-class constraints [13][14][15][16]. The Hamiltonian and path integral formulations of this CGFPD1BA in the IFQ have been studied by us in Ref.…”

“…The Hamiltonian and path integral formulations of this CGFPD1BA in the IFQ have been studied by us in Ref. [12] and this action in the presence of a 2-form gauge field has been studied by us in Ref. [9].…”