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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Analytic continuations of integer-valued parameters can lead to profoundinsights, such as angular momentum in Regge theory, the number of replicas inspin glasses, the number of internal degrees of freedom, the spacetimedimension in dimensional regularization and Wilson's renormalization group. Inthis work, we consider a new kind of analytic continuation of correlationfunctions, inspired by two recent approaches to underdetermined Dyson-Schwingerequations in $D$-dimensional spacetime. If the Green's functions$G_n=\<\phi^n\>$ admit analytic continuation to complex values of $n$, the twodifferent approaches are unified by a novel principle for self-consistentproblems: Singularities in the complex plane should be minimal. This principlemanifests as the merging of different branches of Green's functions in thequartic theories. For $D=0$, we obtain the closed-form solutions of the general$g\phi^m$ theories, including the cases with complex coupling constant $g$ ornon-integer power $m$. For $D=1$, we derive rapidly convergent results for theHermitian quartic and non-Hermitian cubic theories by minimizing the complexityof the singularity at $n=\infty$.

Principle of minimal singularity for Green's functions