Functional Quantum Field Theory in Phase Space
Jos\'e A. R. Cembranos, Marcos Skowronek
TL;DR
This paper explores the phase space representation of quantum field theories by deriving the Wigner functional for free fields, comparing it with other formulations, and extending Jackiw's functional approach using Moyal's equation.
Contribution
It introduces a method to formulate quantum free field theories in phase space, extending Jackiw's representation with Moyal's equation for better analysis.
Findings
Derived the Wigner functional for various free quantum fields.
Compared phase space formulation with other quantum field theory approaches.
Extended Jackiw's functional representation using Moyal's equation.
Abstract
We determine the form of the Wigner functional for several types of quantum free field theories in order to analyze the representation of QFT in phase space, as well as to compare it to other mainstream formulations. We use Jackiw's functional representation of a quantum field state and extrapolate it to the phase space formalism using an extension of Moyal's equation.
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Taxonomy
TopicsQuantum Mechanics and Applications · Cold Atom Physics and Bose-Einstein Condensates · Quantum Information and Cryptography