ζ-function regularization, the multiplicative anomaly, and finite temperature quantum field theory
نویسندگان
چکیده
منابع مشابه
Zeta - function Regularization , the Multiplicative Anomaly and the Wodzicki Residue
The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators L1 = −∆+ V1 and L2 = −∆+ V2, with V1, V2 constant, in a D-dimensional compact smooth manifold MD, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the multiplicative anomaly is vanishing for D odd and ...
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We apply the concept of reflection-transmission (RT) algebra, originally developed in the context of integrable systems in 1+1 space-time dimensions, to the study of finite temperature quantum field theory with impurities in higher dimensions. We consider a scalar field in (s + 1) + 1 space-time dimensions, interacting with impurities localized on s-dimensional hyperplanes, but without self-int...
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Elizalde, Vanzo, and Zerbini have shown that the effective action of two free Euclidean scalar fields in flat space contains a ‘multiplicative anomaly’ when ζfunction regularization is used. This is related to the Wodzicki residue. I show that there is no anomaly when using a wide range of other regularization schemes and that the anomaly can be removed by an unusual choice of renormalization s...
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Hilbert and Pólya put forward the idea that the zeros of the Riemann zeta function may have a spectral origin : the values of tn such that 1 2 + itn is a non trivial zero of ζ might be the eigenvalues of a self-adjoint operator. This would imply the Riemann Hypothesis. From the perspective of Physics one might go further and consider the possibility that the operator in question corresponds to ...
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In these notes we review some properties of Statistical Quantum Field Theory at equilibrium, i.e Quantum Field Theory at finite temperature. We explain the relation between finite temperature quantum field theory in (d, 1) dimensions and statistical classical field theory in d + 1 dimensions. This identification allows to analyze the finite temperature QFT in terms of the renormalization group ...
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ژورنال
عنوان ژورنال: Physical Review D
سال: 1998
ISSN: 0556-2821,1089-4918
DOI: 10.1103/physrevd.58.105001