Thermofield Dynamics and Path-Integral Formalism

Abstract

Thermofield Dynamics (TFD), a real time formalism for thermal quantum field theory, is formulated in terms of a path-integral approach following the Weinberg procedure. In order to assure precise rules for the development, we use a representation of Lie-algebras such that the TFD algebraic ingredients are derived, including the tilde conjugation rules. The association with the canonical formalism is obtained, and for the case of bosons, we introduce the Feynman diagrams and derive the n-point functions.

Noncommutative Thermofield Dynamics

“…In order for a quantum field theory in the doubled Hilbert space H T to be constructed, we consider initially a free boson system, and apply the tilde conjugation rules to introduce, up to normalization factors, the following generating functional [44,45] …”

“…Here we consider the thermal field quantization by using a doubled path-integral formalism [41,44,45], but extended to non-commutative spaces. Although we concentrate on the λφ 4 theory, our procedure can be generalized to other interacting non-commutative fields.…”