Propagator, sewing rules, and vacuum amplitude for the Polyakov point particles with ghosts

Journal Article · Sat Dec 31 23:00:00 EST 1988 · Int. J. Theor. Phys.; (United States)

DOI:https://doi.org/10.1007/BF00670368· OSTI ID:5810170

Giannakis, I; Ordonez, C R; Rubin, M A; Zucchini, R

The authors apply techniques developed for strings to the case of the spinless point particle. The Polyakov path integral with ghosts is used to obtain the propagator and one-loop vacuum amplitude. The propagator is shown to correspond to the Green's function for the BRST field theory in Siegel gauge. The reparametrization invariance of the Polyakov path integral is shown to lead automatically to the correct trace log result for the one-loop diagram, despite the fact that naive sewing of the ends of a propagator would give an incorrect answer. This type of failure of naive sewing is identical to that found in the string case. The present treatment provides, in the simplified context of the point particle, a pedagogical introduction to Polyakov path integral methods with and without ghosts.

• Research Organization: Rockefeller Univ., New York, NY (USA)
• OSTI ID: 5810170
• Journal Information: Int. J. Theor. Phys.; (United States), Journal Name: Int. J. Theor. Phys.; (United States) Vol. 28:1; ISSN IJTPB
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
COMPOSITE MODELS
COORDINATES
DELTA FUNCTION
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
EQUATIONS
EQUATIONS OF MOTION
EXTENDED PARTICLE MODEL
FEYNMAN PATH INTEGRAL
FIELD THEORIES
FUNCTIONS
GAUGE INVARIANCE
GEODESICS
GREEN FUNCTION
HAMILTONIANS
INTEGRALS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE MODELS
PROPAGATOR
QUANTIZATION
QUANTUM FIELD THEORY
QUANTUM OPERATORS
QUARK MODEL
STRING MODELS
TENSORS
VACUUM STATES