Zeta function regularization: Difference between revisions

Revision as of 02:07, 17 December 2008

Revision as of 12:46, 24 February 2009

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

Here, <math>T_{00}</math> is the zero'th component of the [[energy-momentum tensor]] and the sum (which may be an integral) is understood to extend over all (positive and negative) energy modes <math>\omega_n</math>; the absolute value reminding us that the energy is taken to be positive. This sum, as written, is clearlyusually infinite (<math>\omega_n</math> is typically linear in n). The sum may be [[regularization (physics)|regularized]] by writing it as

:<math>\langle 0|T_{00}(s) |0\rangle =