Titlebook: Operators, Geometry and Quanta; Methods of Spectral Dmitri Fursaev,Dmitri Vassilevich Book 2011 Springer Science+Business Media B.V. 2011

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Heat Equationes with examples of the heat trace for operators with known spectrum. The universal form of the heat trace asymptotics is stated. The rest of the Chapter is devoted to calculations of the coefficients in the asymptotic expansion (the celebrated heat kernel coefficients). First, the DeWitt method bas

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Non-linear Spectral Problems many physical applications and, in particular, in equations which determine spectra of single-particle modes. A NLSP is defined here as a linear combination of different powers of an eigenvalue multiplied by operator coefficients which do not commute to each other in general. After describing a met

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Quantum Anomalieslated by using spectral functions. The Chapter starts with formulation of the Noether theorems and derivation of Noether currents in a number of important examples with gauge and space-time symmetries. The following anomalies are derived by using the zeta-function techniques: axial anomaly, Einstein

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现实

Open Strings and Born-Infeld Actiontem are calculated in the presence of an external electromagnetic field by the methods of spectral theory. It is demonstrated, that these divergences vanish if the electromagnetic field satisfies equations of motion following from a non-linear action of the Born-Infeld type. By considering the Green

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