New approach to the path integral representation for the Dirac particle propagator

Journal Article · Tue Nov 15 04:00:00 EST 1994 · Physical Review, D (Particles Fields); (United States)

DOI:https://doi.org/10.1103/PhysRevD.50.6594· OSTI ID:7123109

Aliev, T M; Fainberg, V Y; Pak, N K ^[1]

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1. Physics Department, Middle East Technical University, 06531 Ankara (Turkey)

The path integral representation for the propagator of a spinning particle in an external electromagnetic field is derived using the functional derivative formalism with the help of a Weyl symbol representation. The proposed method essentially simplifies the proof of the path integral representation starting from the equation for the Green function and automatically leads to a precise and unambiguous form of the boundary conditions for the Grassmann variables and puts a strong restriction on the choice of the gauge condition. The path integral representation as in the canonical case has been obtained from the general quantization method of Batalin, Fradkin, and Vilkovisky employing a Weyl symbol representation; being the nontrivial first class constraint algebra for a Dirac particle plays an important role in this derivation. This algebra is the limiting case of the superconformal algebra for a Ramond-type open string when the width of one goes to zero.

• OSTI ID: 7123109
• Journal Information: Physical Review, D (Particles Fields); (United States), Journal Name: Physical Review, D (Particles Fields); (United States) Vol. 50:10; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

661100 -- Classical & Quantum Mechanics-- (1992-)
662110* -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
BOUNDARY CONDITIONS
CONFORMAL GROUPS
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
ELECTROMAGNETIC FIELDS
EQUATIONS
FEYNMAN PATH INTEGRAL
FUNCTIONS
GREEN FUNCTION
INTEGRALS
LIE GROUPS
MATHEMATICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLES
PROPAGATOR
QUANTIZATION
SYMMETRY GROUPS
WAVE EQUATIONS