Aleksandr Trenogin (Saint Petersburg State University)

Multi-loop calculations in \(\varphi^4 + \varphi^6\) theory

The first part of the report is devoted to multi-loop calculations in the \(\varphi^4 + \varphi^6\) model. At the beginning the model will be discussed and compared with the \(\varphi^4\) model. A computer program have been developed using GraphState and Graphine libraries to do multi-loop calculations. An implementation of the program and its internal structure will be considered. We will briefly discuss used calculation methods and libraries the program is based on. With the help of the program we have carried out six-loop calculations. The obtained results will be presented and compared with previously known ones. In the second part of the report we will discuss the star-triangle transformation and try to use some considerations to get a more general relation than the uniqueness relation.