Variations of QED in three dimensions

Journal Article · Fri Feb 15 00:00:00 EST 1991 · Annals of Physics (New York); (United States)

DOI:https://doi.org/10.1016/0003-4916(91)90219-X· OSTI ID:5672155

Fronsdal, C ^[1]

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1. Univ. of California, Los Angeles (United States)

The quantization of three-dimensional electrodynamics in 2 + 2 De Sitter space is carried out in detail. In three dimensions the author finds completely different types of quantum electrodynamics. The most interesting versions have spins +1 and/or {minus}1. When both spins are combined as modes of a single vector potential with definite parity, then the field strength vanishes; nevertheless the theory has an infinite space of propagating physical modes. This version of three-dimensional QED is equivalent to three-dimensional singleton theory. The requirements of gauge invariance prohibit local interactions, in the classical theory and within the framework of canonical quantization, and interactions are thus limited to the boundary at spatial infinity, a torus. There are also two chiral theories, in which the physical modes have spin +1 only, or {minus}1 only; here the field strength is not identically zero, though it vanishes on the physical subspace. The chiral theories do not have smooth limits as the curvature tends to zero. All these versions of electrodynamics are smooth limits as the curvature tends to zero. All these versions of electrodynamics are smooth limits of massive vector theories, and all can be regarded as quantized counterparts of classical Chern-Simons theory. The most standard form of three-dimensional QED has physical modes with spin zero; it is in a sense a limit of a massive theory with spin zero. In two dimensions the only physical degree of freedom is an excitation with vanishing energy and momentum, a topological mode.

• OSTI ID: 5672155
• Journal Information: Annals of Physics (New York); (United States), Vol. 206:1; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
QUANTUM ELECTRODYNAMICS
VARIATIONS
BOUNDARY CONDITIONS
CHIRAL SYMMETRY
DIMENSIONS
GAUGE INVARIANCE
LORENTZ INVARIANCE
PARITY
QUANTIZATION
SPIN
SYMMETRY
SYMMETRY GROUPS
ANGULAR MOMENTUM
ELECTRODYNAMICS
FIELD THEORIES
INVARIANCE PRINCIPLES
PARTICLE PROPERTIES
QUANTUM FIELD THEORY
662220* - Quantum Electrodynamics- (1992-)