Euclidean Majorana fermions, fermionic integrals, and relative Pfaffians

• Type of Material: Article
• Authors: David Borthwick, Emory University
• Language: English
• Date: 1993-03
• Publisher: American Institute of Physics (AIP)
• Publication Version: Final Published Version
• Copyright Statement: © 2013 American Institute of Physics
• Final Published Version (URL): http://link.aip.org/link/doi/10.1063/1.530413
• Title of Journal or Parent Work: Journal of Mathematical Physics
• ISSN: 0022-2488
• Volume: 34
• Issue: 7
• Start Page: 2691
• End Page: 2712
• Grant/Funding Information: Supported in part by a National Science Foundation Graduate Fellowship.
• Research Categories: Mathematics; Physics, General

Abstract

The construction of Euclidean Majorana fermions on a two‐dimensional cylindrical space–time is discussed, based on a given real‐time theory. After a review of the basics of defining Euclidean fermions in the free theory, a functional integral formulation for the Euclidean theory is introduced. This functional integral connects the expectation values of the Euclidean fields with the theory of relative Pfaffians. A proof, which draws on these ideas, is given for the Feynman–Kac formula of a general interacting theory.