English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Based on the real-time formalism, especially, on Thermo Field Dynamics, wederive the Schwinger-Dyson gap equation for the fermion propagator in QED andFour-Fermion model at finite-temperature and -density. We discuss someadvantage of the real-time formalism in solving the self-consistent gapequation, in comparison with the ordinary imaginary-time formalism. Once wespecify the vertex function, we can write down the SD equation with onlycontinuous variables without performing the discrete sum over Matsubarafrequencies which cannot be performed in advance without further approximationin the imaginary-time formalism. By solving the SD equation obtained in thisway, we find the chiral-symmetry restoring transition at finite-temperature andpresent the associated phase diagram of strong coupling QED.  In solving the SD equation, we consider two approximations:instantaneous-exchange and $p_0$-independent ones. The former has a directcorrespondence in the imaginary time formalism, while the latter is a newapproximation beyond the former, since the latter is able to incorporate newthermal effects which has been overlooked in the ordinary imaginary-timesolution. However both approximations are shown to give qualitatively the sameresults on the finite-temperature phase transition.Comment: 28 pages+15 figures (figures: not included, available upon request

FINITE-TEMPERATURE AND FINITE-DENSITY QED: THE SCHWINGER-DYSON EQUATION IN THE REAL-TIME FORMALISM