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

Global conformal invariance (GCI) of quantum field theory (QFT) in two andhigher space-time dimensions implies the Huygens' principle, and hence,rationality of correlation functions of observable fields (see Commun. Math.Phys. 218 (2001) 417-436; hep-th/0009004). The conformal Hamiltonian $H$ hasdiscrete spectrum assumed here to be finitely degenerate. We then prove thatthermal expectation values of field products on compactified Minkowski spacecan be represented as finite linear combinations of basic (doubly periodic)elliptic functions in the conformal time variables (of periods 1 and $\tau$)whose coefficients are, in general, formal power series in$q^{1/2}=e^{i\pi\tau}$ involving spherical functions of the "space-like"fields' arguments. As a corollary, if the resulting expansions converge tomeromorphic functions, then the finite temperature correlation functions areelliptic. Thermal 2-point functions of free fields are computed and shown todisplay these features. We also study modular transformation properties ofGibbs energy mean values with respect to the (complex) inverse temperature$\tau$ ($Im(\tau)=\beta/(2\pi)>0$). The results are used to obtain thethermodynamic limit of thermal energy densities and correlation functions.Comment: LaTex. 56 pages. The concept of global conformal invariance set in a  historical perspective (new Sect. 1.1 in the Introduction), references added;  minor corrections in the rest of the pape

ELLIPTIC THERMAL CORRELATION FUNCTIONS AND MODULAR FORMS IN A GLOBALLY CONFORMAL INVARIANT QFT