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Zeta function regularization

In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators. The technique is now commonly applied to problems in physics, but has its origins…

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Definition

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Relation to other regularizations

Relation to Dirichlet series

Heat kernel regularization

History

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Zeta function regularization

Nodes70
Edges69
Triples124
Avg. degree1.97
Density0.028571
Components1

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Zeta function regularization

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related to References · 93
Zeta function regularization → Acta Mathematica, Advances, Alberto, Amer, Analytic Aspects, Apostol, BF01626516, Bibcode, Bytsenko, Calderón, Canadian Journal, Casimir, Chicago, CJM-1949-021-5, Cognola, Communications, Complex, Contributions, Critchley, Direct
related to history · 12
Zeta function regularization → Also, Cahen, Emilio Elizalde, Hardy, Hawking, In, Littlewood, Mellin, Much, Raymond Critchley, Stuart Dowker, The
related to Example · 7
Zeta function regularization → An, Casimir, However, In, More, Riemann, The
related to Definition · 3
Zeta function regularization → One, Re, There
related to Relation to other regularizations · 2
Zeta function regularization → However, Zeta
is a · 1
Zeta function regularization → type of regularization or summability method that assigns finite values to divergent sums or products

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regularization function zeta sum series physics analytic zeta-function method used displaystyle theory example divergent number sums regularized energy doi mathematics

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SubjectPredicateObjectConfidenceSrc
Zeta function regularizationis atype of regularization or summability method that assigns finite values to divergent sums or products0.90text
on the horizon of black holesinstance ofHe studied zeta function regularization in order to calculate the partition functions for thermal graviton and matter's quanta in curved background0.80text
on de Sitter background using the relation by the inverse Mellin transformation to the trace of the kernel of heat equationsinstance ofHe studied zeta function regularization in order to calculate the partition functions for thermal graviton and matter's quanta in curved background0.80text
dimensional regularizationinstance ofAlso unlike other regularizations0.80text
analytic regularizationinstance ofAlso unlike other regularizations0.80text
zeta regularization has no countertermsinstance ofAlso unlike other regularizations0.80text
gives only finite resultsinstance ofAlso unlike other regularizations0.80text
Zeta function regularizationrelated to DefinitionThere0.60section
Zeta function regularizationrelated to DefinitionOne0.60section
Zeta function regularizationrelated to DefinitionRe0.60section
Zeta function regularizationrelated to ExampleThe0.60section
Zeta function regularizationrelated to ExampleCasimir0.60section

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