Spin in the worldline path integral in 2 + 1 dimensions |
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Authors: | C.D. Fosco,R.A. Vá zquez |
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Affiliation: | a Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica, 8400 Bariloche, Argentina b Departamento de Física de Partículas, Facultad de Física and Instituto Galego de Física de Altas Energías, Universidad de Santiago, E-15782 Santiago de Compostela, Spain |
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Abstract: | We present a constructive derivation of a worldline path integral for the effective action and the propagator of a Dirac field in 2 + 1 dimensions, in terms of spacetime and SU(2) paths. After studying some general properties of this representation, we show that the auxiliary gauge-group variable can be integrated, deriving a worldline action depending only on x(τ), the spacetime paths. We then show that the functional integral automatically imposes the constraint , while there is a spin action, which agrees with the one one should expect for a spin- field. |
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Keywords: | Worldline Path integral |
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