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

During the '70, several relativistic quantum field theory models in $D=1+1$and also in $D=2+1$ have been constructed in a non-perturbative way. That wasdone in the so-called {\it constructive quantum field theory} approach, whosemain results have been obtained by a clever use of Euclidean functionalmethods. Although in the construction of a single model there are severaltechnical steps, some of them involving long proofs, the constructive quantumfield theory approach contains conceptual insights about relativistic quantumfield theory that deserved to be known and which are accessible withoutentering in technical details. The purpose of this note is to illustrate suchinsights by providing an oversimplified schematic exposition of the simple caseof $\lambda\Phi^4$ (with $m>0$) in $D=1+1$. Because of the absence ofultraviolet divergences in its perturbative version, this simple example-although does not capture all the difficulties in the constructive quantumfield theory approach- allows to stress those difficulties inherent to thenon-perturbative definition. We have made an effort in order to avoid severalof the long technical intermediate steps without missing the main ideas andmaking contact with the usual language of the perturbative approach.

Non-perturbative \lambda\Phi^4 in D=1+1: an example of the constructive quantum field theory approach in a schematic way