Zeta function regularization: Difference between revisions

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==Definition==

An example of zeta-function regularization is the calculation of the [[vacuum expectation value]] of the [[energy]] of a particle field in [[quantum field theory]]. It is worth mentioning that, more generally, the zeta-function approach can be used to regularize the whole [[energy-momentum tensor]] in curved spacetime {{ref|Mor97}}.

The unregulated value of the energy is given by a summation over the [[zero-point energy]] of all of the excitation modes of the vacuum:

:<math>\langle 0|T_{00} |0\rangle = \sum_n \frac{\hbar |\omega_n|}{2}</math>

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==References==

* {{note|Mor97}} Moretti, Valter ; ''Direct z-function approach and renormalization of one-loop stress tensor in curved spacetimes'', Phys. Rev.D 56, 7797 (1997). Full text available at: [http://arxiv.org/abs/hep-th/9705060 ''hep-th/9705060'']

* {{note|Hard16}}G.H. Hardy and J.E. Littlewood, "Contributions to the Theory of the Riemann Zeta-Function and the Theory of the Distribution of Primes", ''Acta Mathematica'', '''41'''(1916) pp.119-196. ''(See, for example, theorem 2.12)''

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