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- W4299968245 abstract "This paper is essentially a short version of hep-th/9404046. We compute multiplicative anomaly det(AB)/(detA detB) =F(A,B) for elliptic pseudo-differential operators (PDOs) A, B on a closed manifold M in terms of their symbols. We prove that F(A,B)=1 for elliptic differential operators close to positive-definite ones on an odd-dimensional M. For such M we introduce a holomorphic determinant. Its monodromy lies in a finite group of roots of unity. In general case, we relate the multiplicative anomaly with a central extension of the group of elliptic symbols and with an invariant quadratic form on this extension. We compute the Lie algebra of the central extension in terms of logarithmic symbols. The main tool is a new trace-type functional defined on classical PDOs of non-integer orders. A canonical det of elliptic PDOs generalizing the zeta-regularized det is introduced." @default.
- W4299968245 created "2022-10-03" @default.
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- W4299968245 date "1994-06-21" @default.
- W4299968245 modified "2023-09-28" @default.
- W4299968245 title "Geometry of determinants of elliptic operators" @default.
- W4299968245 doi "https://doi.org/10.48550/arxiv.hep-th/9406140" @default.
- W4299968245 hasPublicationYear "1994" @default.
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