A Mass Term for Three-Dimensional Gauge Fields
Dec, 198015 pages
Published in:
- Nucl.Phys.B 185 (1981) 157-171
- Published: 1981
Report number:
- FERMILAB-PUB-80-103-THY,
- FERMILAB-PUB-80-103-T
Citations per year
Abstract: (Elsevier)
We propose the interaction L ξ ≡ 1 2 ξϵ μνλ Tr A μ [∂ ν A λ − 2 3 igA ν A λ ] as a mass term for gauge fields in three-dimensional spacetime. The A μ belong to a Lie algebra (represented here in terms of matrices), ε μνλ is the completely antisymmetric symbol, the coupling g has units [ mass ] 1 2 , and the parameter ξ has units [mass]. L ξ , related to the instanton current of four dimensions, is gauge invariant up to a total divergence and a topological density. (There is a supersymmetric extension with the same property.) When technical complications can be ignored, L ξ provides gauge particles with mass without breaking local symmetry and without introducing auxiliary fields. Perturbative analysis of models involving L ξ (collectively called “ξ theories”) is complicated by gauge-non-invariant infrared singularities in gauge-field propagators. Nevertheless, quantized abelian ξ-theories (collectively called “ξ QED”) do define gauge-invariant and infrared-finite scattering in perturbation theory. The consistency of non-abelian ξ theories is not yet established. The physics of non-relativistic charges ξ QED is, in its gross features, the same as that of the Aharanov-Bohm effect - the static field of a point charge is a non-trivial pure gauge at large distances. (We argue that in spite of the long-range fields, propagation of charges at large times is free; so that in ξ QED there should be no unexpected subtleties in the axiomatic definition of scattering amplitudes.) Compatibility of gauge invariance and mass in three dimensions is related to the existence of massive spinning representations of the Poincaré algebra with only one polarization per momentum. The massive spin-one photon of ξ QED is such a particle. (There is in fact a massive unitary representation of the three-dimensional Poincaré algebra with only one polarization for spin equal to any real number, integral multiple of one-half or otherwise. It is possible that particles with such an anomalous spin are present in some field theories.) L ξ is invariant under the discrete transformation C but not under T , nor under any reflection P in a single spatial axis. L ξ is invariant under PCT .- GAUGE FIELD THEORY: THREE-DIMENSIONAL
- GAUGE BOSON: MASS
- MASS: GAUGE BOSON
- CHARGE: TOPOLOGICAL
- INVARIANCE: GAUGE
- FIELD EQUATIONS: INSTANTON
- PHOTON: PROPAGATOR
- GAUGE FIELD THEORY: COULOMB GAUGE
- GAUGE FIELD THEORY: LANDAU GAUGE
- FIELD THEORY: INFRARED PROBLEM
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