Topic
Analytic continuation
About: Analytic continuation is a research topic. Over the lifetime, 4573 publications have been published within this topic receiving 94886 citations.
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Book•
01 May 1994
TL;DR: In this article, the Riemann Zeta function analytic continuation is used for series summation asymptotic expansion of "zeta", and the Casimir effect in flat space-time with compact spatial part.
Abstract: Part 1 The Riemann Zeta function: Riemann, Hurwitz, Epstein, Selberg and related zeta functions analytic continuation - practical uses for series summation asymptotic expansion of "zeta". Part 2 Zeta-function regularization of sums over known spectrum: the zeta-function regularization theorem multiple zeta-functions with arbitrary exponents. Part 3 Zeta-function regularization when the spectrum is not known: zeta-function vs heat-kernel regularization small-"t" asymptotic expansion of the heat-kernel. Part 4 The Casimir effect in flat space-time with compact spatial part: simply connected compact manifold with constant curvature the Selberg trace formula for compact hyperbolic manifolds. Part 5 Finite temperature effects for theories defined on compact hyperbolic manifolds: basic formalism for the finite-temperature effective potential the finite-temperature thermodynamic potential for manifolds with a compact spatial part. Part 6 Properties of the chemical potential in higher-dimensional manifolds: the flat-manifold case the constant non-zero curvature case. Part 7 Strings at non-zero temperature and 2d gravity: free energy for the Bosonic string vacuum energy for Torus compactified strings. Part 8 Membranes at non-zero temperatures: supermembrane free energy free energy for the compactified supermembranes and modular invariance and others.
1,032 citations
TL;DR: In this article, a modified form of dimensional regularization is introduced which manifestly preserves gauge invariance, unitarity, and global supersymmetry, and also considers its application to supergravity.
987 citations
Book•
08 Jul 1990
TL;DR: The spectrum of a commutative Banach ring is described in this paper, and the dimension of a Banach algebra is defined in terms of the spectrum of an analytic space.
Abstract: The spectrum of a commutative Banach ring Affinoid spaces Analytic spaces Analytic curves Analytic groups and buildings The homotopy type of certain analytic spaces Spectral theory Perturbation theory The dimension of a Banach algebra.
980 citations
TL;DR: In this paper, the authors present a mathematical description of the condensation point for a simple class of models of first-order phase transitions and apply it to a simple model of a ferromagnet at temperatures well below the Curie point.
947 citations