New semiclassical approach in charged scalar QED
This thesis proposes a new semiclassical approach for calculating charged-scalar closed-loop quantities in scalar Quantum Electrodynamics. This is carried through by the replacement of field degrees of freedom with particle coordinates through the introduction of Feynman path integrals. The canonical formalism for charged-scalar QED, with all Green's functions written in terms of functional integrals, is converted into a loopwise expansion of the theory, obtained via the path integral formulation. The connection of Schwinger-Dyson equations and Ward-Takahashi identities to the particle coordinate equations of motion is explored. The one charged-scalar closed-loop contribution to the photon propagator in two dimensional scalar QED is calculated using the path integral formulation. The semiclassical approximation developed gives the asymptotic behavior of the large order terms in the perturbation series expansion of the one loop contribution to the photon self-energy. This is performed via the expansion in collective coordinates about classical particle trajectories that dominate the large order behavior. The expansion in collective coordinates is worked out exactly for the calculation of this Green's function. The Borel sum of the one loop contribution to the photon self-energy indicates that for massless scalar QED in two dimensions the photon acquires a mass through a dynamical mechanism as in the Schwinger model. This is not seen at any finite order of perturbation theory, and so the semiclassical approach is essential to observe this effect. The semiclassical approximation is extended to four dimensional scalar QED, and classical particle trajectories are analyzed for both the charged-scalar propagator and closed-loop quantities. All four dimensional results are expressed in terms of their cutoff dependence, and renormalization difficulties are discussed.
- Research Organization:
- Brown Univ., Providence, RI (USA)
- OSTI ID:
- 5283000
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ASYMPTOTIC SOLUTIONS
ELECTRODYNAMICS
FEYNMAN PATH INTEGRAL
FIELD THEORIES
FUNCTIONS
GREEN FUNCTION
INTEGRALS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
RENORMALIZATION
SCALARS
SEMICLASSICAL APPROXIMATION
SERIES EXPANSION
WARD IDENTITY