Spectral Zeta Functions in Non-Commutative Spacetimes

Details Spectral Zeta Functions in Non-Commutative Spacetimes Spectral Zeta Functions in Non-Commutative Spacetimes

2001-05-15

arxiv.org/abs/hep-th/0105145v1

Nucl.Phys.Proc.Suppl. 104 (2002) 157-160

Physics

High Energy Physics

High Energy Physics - Theory

4 pages, no figures

Scientific paper

10.1016/S0920-5632(01)01603-6

Formulas for the most general case of the zeta function associated to a quadratic+linear+constant form (in {\bf Z}) are given. As examples, the spectral zeta functions $\zeta_\alpha (s)$ corresponding to bosonic ($\alpha =2$) and to fermionic ($\alpha =3$) quantum fields living on a noncommutative, partially toroidal spacetime are investigated. Simple poles show up at $s=0$, as well as in other places (simple or double, depending on the number of compactified, noncompactified, and noncommutative dimensions of the spacetime). This poses a challenge to the zeta-function regularization procedure.

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