Euclidean Path-Integral Representation of the Vector Field. II : The Gauge Field

概要

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Euclidean path-integral formula of the abelian gauge field is constructed from a quantum theory defined by an axial gauge Hamiltonian. It is shown that to make the theory well-defined the ordinary periodic boundary condition is not sufficient and that a new boundary condition with a single parameter b, called "b"-boundary condition, should be introduced. Any infrared divergence, which inevitably arises even in a finite volume under the periodic boundary condition, can be removed with this boundary condition without introducing a mass term, i.e., without destroying a gauge invariance. In this formalism, the covariant, Coulomb and A_0=0 gauge path-integral representations can be obtained by a c-number gauge transformation. It is also shown that, in the covariant gauge case, the propagator is indeed covariant, causal and independent of the parameter b.
理論物理学刊行会の論文
1982-06-25