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

This is the second paper on semiclassical approach based on the densitymatrix given by the Euclidean time path integral with fixed coincidingendpoints. The classical path, interpolating between this point and theclassical vacuum, called "flucton", plus systematic one- and two-loopcorrections, has been calculated in the first paper \cite{Escobar-Ruiz:2016aqv}for double-well potential and now extended for a number of quantum-mechanicalproblems (anharmonic oscillator, sine-Gordon potential). The method is based onsystematic expansion in Feynman diagrams and thus can be extended to QFTs. Weshow that the loop expansion in QM reminds the leading log-approximations inQFT. In this sequel we present complete set of results obtained using thismethod in unified way. Alternatively, starting from the Schr\"{o}dingerequation we derive a {\it generalized} Bloch equation which semiclassical-like,iterative solution generates the loop expansion. We re-derive two loopexpansions for all three above potentials and now extend it to three loops,which has not yet been done via Feynman diagrams. All results for both methodsare fully consistent with each other. Asymmetric (tilted) double-well potential(non-degenerate minima) is also studied using the second method.

Fluctuations in quantum mechanics and field theories from a new version of semiclassical theory. II