Calculation of generalp-adic Feynman amplitude
Copyright policy )Calculation of generalp-adic Feynman amplitude
The general \(p\)-adic massless Feynman amplitude with arbitrary parameters of analytic regularization in arbitrary space-time dimensions is calculated. First, the cases of two- and three-point Feynman amplitudes are considered, and the results are then generalized for arbitrary \(n\)- point amplitudes. The Feynman amplitude is written as a sum over hierarchies of the set of vertices of the given graph. These results are applied to simplest cases: the master two-loop diagram and the star Feynman diagram with three external and one internal vertices. Ultra- violet and infrared divergences of Feynman amplitudes are also analyzed. It is concluded that in the massless case, the \(p\)-adic Feynman amplitude can possess only logarithmical ultraviolet and infrared divergences.
- Lomonosov Moscow State University Russian Federation
- Synergy University Russian Federation
\(p\)-adic massless Feynman amplitude with arbitrary parameters of analytic regularization in arbitrary space-time dimensions, 81T18, star Feynman diagram, Feynman integrals and graphs; applications of algebraic topology and algebraic geometry, 81T15, \(p\)-adic theory, local fields, master two-loop diagram, Applications of functional analysis in quantum physics, 11Z50, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, 11S80
\(p\)-adic massless Feynman amplitude with arbitrary parameters of analytic regularization in arbitrary space-time dimensions, 81T18, star Feynman diagram, Feynman integrals and graphs; applications of algebraic topology and algebraic geometry, 81T15, \(p\)-adic theory, local fields, master two-loop diagram, Applications of functional analysis in quantum physics, 11Z50, Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis, 11S80
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