2009/12/11 by Franco Ferrari, Ferrari, Franco
Engineering · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.0912.2361
15 pages, LaTeX + RevTeX 4, some misprints have been corrected, a new proof has been added
openalex publication_date 2009/12/11 · arxiv created 2010/03/27 · arxiv updated 2010/03/30 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
In this work a class of massive scalar field theories with self-interactions described by a general potential is studied. Under the sole condition that the potential admits the Fourier representation, it is shown that such theories may be mapped into a standard field theory, in which the interaction of the new fields is a polynomial of fourth degree. With some restrictions, this mapping allows the perturbative treatment of models that are otherwise intractable with standard field theoretical methods. A nonperturbative approach to these theories is attempted. The original scalar field is integrated out exactly at the price of introducing auxiliary vector fields. The latter are treated in a mean field theory approximation. The singularities that arise after the elimination of the auxiliary fields are cured using the dimensional regularization. The expression of the counterterms to be subtracted is computed.