Fermion fields in eta - xi spacetime.

Abstract

Fermion fields in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime are discussed. By the path-integral formulation of quantum field theory, we show that the (zero-temperature) Green's functions for Dirac fields on the Euclidean section in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime are equal to the imaginary-time thermal Green's functions in Minkowski spacetime, and that the (zero-temperature) Green's functions on the Lorentzian section in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime correspond to the real-time thermal Green's functions in Minkowski spacetime. The antiperiodicity of fermion fields in $\ensuremath{\eta}\ensuremath{-}\ensuremath{\xi}$ spacetime originates from Lorentz transformation properties of the fields.