PROBLEMS WITH THE PATH-INTEGRAL DESCRIPTION OF THE TEMPORAL, LIGHT-CONE AND FOCK-SCHWINGER GAUGES

1992 ◽  
Vol 07 (03) ◽  
pp. 219-224 ◽  
Author(s):  
MARTIN LAVELLE ◽  
DAVID McMULLAN
Keyword(s):  
Phase Space ◽  
Path Integral ◽  
Light Cone ◽  
Space Formalism

Simple arguments are presented to show that the standard Faddeev-Popov formulations of the temporal, light-cone and Fock-Schwinger gauges are not unitary. We also demonstrate that the phase space formalism of these theories provide three counterexamples to the Fradkin-Vilkovisky theorem.

LIGHT-FRONT HAMILTONIAN AND PATH INTEGRAL QUANTIZATION OF VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM

2012 ◽  
Vol 27 (27) ◽  
pp. 1250157 ◽  
Author(s):  
USHA KULSHRESHTHA
Keyword(s):  
Path Integral ◽  
Light Cone ◽  
Mass Term ◽  
Light Front ◽  
Light Cone Gauge ◽  
Schwinger Model ◽  
Path Integral Quantization ◽  
New Class ◽  
Gauge Fixing ◽  
Form Theory

Vector Schwinger model with a mass term for the photon, describing 2D electrodynamics with massless fermions, studied by us recently [U. Kulshreshtha, Mod. Phys. Lett. A22, 2993 (2007); U. Kulshreshtha and D. S. Kulshreshtha, Int. J. Mod. Phys. A22, 6183 (2007); U. Kulshreshtha, PoS LC2008, 008 (2008)], represents a new class of models. This theory becomes gauge-invariant when studied on the light-front. This is in contrast to the instant-form theory which is gauge-non-invariant. In this work, we study the light-front Hamiltonian and path integral quantization of this theory under appropriate light-cone gauge-fixing. The discretized light-cone quantization of the theory where we wish to make contact with the experimentally observational aspects of the theory would be presented in a separate paper.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

2010 ◽  
Vol 25 (02) ◽  
pp. 135-141
Author(s):  
H. A. ELEGLA ◽  
N. I. FARAHAT
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Path Integral ◽  
Equations Of Motion ◽  
Singular System ◽  
Constrained Systems ◽  
Classical Structure ◽  
Path Integral Quantization ◽  
Total Differential

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

scholarly journals Superfield formulation of the phase space path integral

1999 ◽  
Vol 446 (2) ◽  
pp. 175-178 ◽  
Author(s):  
I.A. Batalin ◽  
K. Bering ◽  
P.H. Damgaard
Keyword(s):  
Phase Space ◽  
Path Integral

scholarly journals PATH INTEGRATION IN RELATIVISTIC QUANTUM MECHANICS

1993 ◽  
Vol 08 (09) ◽  
pp. 1629-1635 ◽  
Author(s):  
IAN H. REDMOUNT ◽  
WAI-MO SUEN
Keyword(s):  
Path Integral ◽  
Light Cone ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Free Particle ◽  
Wkb Approximation ◽  
Relativistic Quantum Mechanics ◽  
Path Integral Formulation ◽  
Quantum Theories ◽  
Short Time

The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple relativistic action proportional to its proper time. This propagator is nonvanishing outside the light cone, implying that spacelike trajectories must be included in the path integral. The propagator matches the WKB approximation to the corresponding configuration-space path integral far from the light cone; outside the light cone that approximation consists of the contribution from a single spacelike geodesic. This propagator also has the unusual property that its short-time limit does not coincide with the WKB approximation, making the construction of a concrete skeletonized version of the path integral more complicated than in nonrelativistic theory.

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