Gauge transformations, path-space formulae, supersymmetry and geometry in constructive quantum electrodynamics
The traditional approaches to quantizing Maxwell's equations and the Euclidean formulation of quantum gauge field theory is summarized in the first chapter of this work. Elements of a class of inequivalent representations of the canonical commutation relations, the so-called Rideau gauges, are shown to be related via unbounded Krein-unitary similarity transformations. Then the Feynman-Kac formula and the Krein-essential-selfadjointness property for the quantum electrodynamics (QED) Hamiltonian in Feynman gauge is extended to a rage of covariant gauges, including Landau gauge. A martingale decomposition for the free field in a covariant gauge is given. In Chapter Three the discussion turns to non-covariantly-quantized QED and supersymmetry. A path-space formula for a Coulomb gauge supersymmetric model with maximal cutoffs is given (in imaginary time) and its integrability is proven. Finally, in Chapter Four relevant features of A. Connes' theory of non-commutative geometry are presented and an example of an unbounded Fredholm module is constructed from the two-dimensional supersymmetric Sine-Gordon model. Its index is shown to be that of the free theory. The connection of this model is two-dimensional electrodynamics is discussed.
- Research Organization:
- Indiana Univ., Bloomington, IN (United States)
- OSTI ID:
- 5193293
- Country of Publication:
- United States
- Language:
- English
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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMMUTATION RELATIONS
CONSTRUCTIVE FIELD THEORY
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GAUGE INVARIANCE
GEOMETRY
HAMILTONIANS
INVARIANCE PRINCIPLES
MATHEMATICAL OPERATORS
MATHEMATICS
MAXWELL EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTIZATION
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
QUANTUM OPERATORS
SINE-GORDON EQUATION
SUPERSYMMETRY
SYMMETRY