Calculation of general \(p\)-adic Feynman amplitude

DOI10.1007/BF02096946zbMath0797.46058MaRDI QIDQ1201416

Vladimir A. Smirnov

Publication date: 17 January 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

\(p\)-adic massless Feynman amplitude with arbitrary parameters of analytic regularization in arbitrary space-time dimensionsmaster two-loop diagramstar Feynman diagram

Mathematics Subject Classification ID

Functional analysis over fields other than (mathbb{R}) or (mathbb{C}) or the quaternions; non-Archimedean functional analysis (46S10) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) (p)-adic theory, local fields (11F85) Applications of functional analysis in quantum physics (46N50)

Related Items (16)

Can \(p\)-adic numbers be useful to regularize divergent expectation values of quantum observables? ⋮ Introduction: Advancing Non-Archimedean Mathematics ⋮ Introduction: Nature and Its Mathematics ⋮ Scalar fields on \(p\)AdS ⋮ Non-Archimedean white noise, pseudodifferential stochastic equations, and massive Euclidean fields ⋮ Feynman integrals with a \(p\)-adic argument in momentum space. III: Renormalization ⋮ Feynman integrals of \(p\)-adic argument in the momentum space. I: Convergence ⋮ Feynman integral evaluation by a sector decomposition approach (FIESTA) ⋮ Feynman integrals of \(p\)-adic argument in the momentum space. II: Explicit expressions ⋮ Construction of \(p\)-adic covariant quantum fields in the framework of white noise analysis ⋮ Tables of integrals for complex-valued functions of \(p\)-adic arguments ⋮ Regularization of \(p\)-adic string amplitudes, and multivariate local zeta functions ⋮ \texttt{FIESTA 2}: parallelizeable multiloop numerical calculations ⋮ On \(p\)-adic mathematical physics ⋮ Three-loop on-shell Feynman integrals with two masses ⋮ Acausal quantum theory for non-Archimedean scalar fields

Cites Work

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• Proof of the Bogoliubov-Parasiuk theorem on renormalization
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• p-adic strings, the Weil conjectures and anomalies
• p-adic space-time and string theory
• p-adic Feynman and string amplitudes
• p-adic quantum mechanics
• THE O(N) GROSS-NEVEU AND SUPERSYMMETRIC σ MODELS ON p-ADIC FIELDS
• RENORMALIZATION IN p-ADIC QUANTUM FIELD THEORY
• QUANTUM MECHANICS WITH p-ADIC NUMBERS

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