Poincar'e–Lie algebra and relativistic phase space

Abstract

In this work we investigate representations of the Poincar´e group taking as the representation space the Hilbert space of thermofield dynamics, a real-time formalism developed in quantum field theory at finite temperature. We concentrate our study on those representations that give rise to the notion of phase space, with direct application in kinetic theory. As a result, we show an alternative way to derive a relativistic Boltzmann equation, based on the notion of a propagator defined in phase space. The quantum counterpart of the approach is discussed through the notion of the Wigner function.