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Aplication of the CTP formalism in an action with pseudo-differential operator

Abstract

The CTP (closed time path) formalism is a mathematical tool for calculating Green functions in physical systems. The main advantage of this technique is that, unlike the Feynman's formalism, the CTP formalism can be applied in nonequilibrium systems. On the other hand, in condensed material physics, some nonlocal models in the spacetime and of low dimensionality have been widely discussed in the scientific literature, in particular, in the description of two-dimensional materials. Among these, we highlight the Pseudo quantum electrodynamics that has been successfully applied to describe electronic interactions in graphene and transition metal dichalcogenides. In this work, we introduce the CTP formalism, using a discussion aimed at calculating physical observables. We highlight the fact that this formalism is very useful when the vacuum in the distant past is different from the vacuum in the distant future. Following this brief review, we made an original application of CTP formalism in the action of the Proca-Pseudo quantum electrodynamics theory in (0+1) dimensions, calculating several relevant Green functions, including: Feynman's Green function; Dyson's Green Function; Green function of positive frequency and; Green function of negative frequency.

Keywords:
Path Integral; Feynman Diagrams; Nonlocal models

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