Skip to main content

Research Repository

See what's under the surface

Advanced Search

Visualising quantum effective action calculations in zero dimensions

Millington, Peter; Saffin, Paul M

Authors

Peter Millington

Paul M Saffin



Abstract

We present an explicit treatment of the two-particle-irreducible (2PI) effective action for a zero-dimensional quantum field theory. The advantage of this simple playground is that we are required to deal only with functions rather than functionals, making complete analytic approximations accessible and full numerical evaluation of the exact result possible. Moreover, it permits us to plot intuitive graphical representations of the behaviour of the effective action, as well as the objects out of which it is built. We illustrate the subtleties of the behaviour of the sources and their convex-conjugate variables, and their relation to the various saddle points of the path integral. With this understood, we describe the convexity of the 2PI effective action and provide a comprehensive explanation of how the Maxwell construction arises in the case of multiple, classically stable saddle points, finding results that are consistent with previous studies of the one-particle-irreducible (1PI) effective action.

Journal Article Type Article
Publication Date Oct 4, 2019
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 52
Issue 40
Article Number 405401
APA6 Citation Millington, P., & Saffin, P. M. (2019). Visualising quantum effective action calculations in zero dimensions. Journal of Physics A: Mathematical and Theoretical, 52(40), https://doi.org/10.1088/1751-8121/ab37e6
DOI https://doi.org/10.1088/1751-8121/ab37e6
Keywords Modelling and Simulation; Statistics and Probability; Mathematical Physics; General Physics and Astronomy; Statistical and Nonlinear Physics
Publisher URL https://iopscience.iop.org/article/10.1088/1751-8121/ab37e6
Additional Information Journal title: Journal of Physics A: Mathematical and Theoretical; Article type: paper; Article title: Visualising quantum effective action calculations in zero dimensions; Copyright information: © 2019 IOP Publishing Ltd; Date received: 2019-05-28; Date accepted: 2019-08-01; Online publication date: 2019-09-12

Files





You might also like



Downloadable Citations

;