Zeta function regularization: Difference between revisions

Revision as of 22:56, 4 December 2005

Revision as of 15:30, 16 December 2005

Line 1:

In [[mathematics]] and [[theoretical physics]], '''zeta function regularization''' is a [[summability method]] that allows one to give some meaningful values to seemingly meaningless expressions using the [[Riemann zeta function|zeta function]].

{{merge|zeta regularization}}

In [[mathematics]], '''zeta regularization''' is a [[summability method]] that allows one to give some meaningful values to seemingly meaningless expressions using the [[Riemann zeta function|zeta function]].

For example

Line 14 ⟶ 12:

gives the correct physically measurable result.

==Alternative text to be merged==

[[Category:Mathematical analysis]]

In [[theoretical physics]], '''zeta regularization''' is a method to assign finite values to superficially divergent sums. The method is based on generalizing the sum to the case of more general values of an exponent and treating the sum as an [[analytic function]] of the exponent -- namely a function related to the [[Riemann zeta function]]. An [[analytic continuation]] gives the desired result.

The most well-known example is the sum

: 1+2+3+4+5+ ... = -1/12

whose value may be calculated as [[Riemann zeta function|zeta(-1)]]. Such a regularization and the corresponding result are guaranteed to preserve various symmetries of the physical system such as [[conformal symmetry]]. This particular result also occurs in the [[Casimir effect]] and the critical [[spacetime]] dimension of [[string theory]].

{{phys-stub}}

{{math-stub}}

[[Category:Quantum field theory]]

[[Category:String theory]]

[[Category:Mathematical analysis]]