p-adic Feynman and string amplitudes

DOI10.1007/BF01218622zbMath0671.22011OpenAlexW2013994210MaRDI QIDQ1119754

S. H. Smith

Publication date: 1989

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

Full work available at URL: https://doi.org/10.1007/bf01218622

zbMATH Keywords

quantum field theoryrenormalization groupFeynman diagramsp-adic numbersfield theoryDyson's hierarchical modelsp-adic Feynman amplitudesstring scattering

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Applications of Lie groups to the sciences; explicit representations (22E70) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Renormalization group methods applied to problems in quantum field theory (81T17) Applications of global differential geometry to the sciences (53C80) Kaluza-Klein and other higher-dimensional theories (83E15) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Congruences for modular and (p)-adic modular forms (11F33) Representations of Lie and linear algebraic groups over local fields (22E50) Strings (74K05)

Related Items (23)

Hierarchical Dyson model and \(p\)-adic conformal invariance ⋮ Functional integral via functional equation ⋮ Graphs, local zeta functions, log-Coulomb gases, and phase transitions at finite temperature ⋮ 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 integrals of \(p\)-adic argument in the momentum space. II: Explicit expressions ⋮ Functional Fourier transformation and renormalization group transformation in bosonic field theory models ⋮ Unnamed Item ⋮ \(p\)-adic conformal invariance and the Bruhat-Tits tree ⋮ Tables of integrals for complex-valued functions of \(p\)-adic arguments ⋮ Meromorphic continuation of Koba-Nielsen string amplitudes ⋮ Calculation of general \(p\)-adic Feynman amplitude ⋮ Regularization of \(p\)-adic string amplitudes, and multivariate local zeta functions ⋮ Asymptotic properties of combinatorial optimization problems in \(p\)-adic space ⋮ \(p\)-adic renormalization group solutions and the Euclidean renormalization group conjectures ⋮ Adelic Feynman amplitudes in lower orders of perturbation theory ⋮ INTERACTION MEASURES ON THE SPACE OF DISTRIBUTIONS OVER THE FIELD OF p-ADIC NUMBERS ⋮ Methods and applications of ultrametric and \(p\)-adic analysis: from wavelet theory to biophysics ⋮ Invariant manifolds of \(p\)-adic renormalization groups ⋮ Functional equations and renormalizations in \(p\)-adic field theories ⋮ Continuum limit in the fermionic hierarchical model ⋮ On vertex parts of \(p\)-adic Feynman amplitudes ⋮ Dimensional renormalization in \(p\)-adic models of field theory

Cites Work

• p-adic strings, the Weil conjectures and anomalies
• Construction of non-Gaussian self-similar random fields with hierarchical structure
• Number theory as the ultimate physical theory

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