4 Zeta function regularization for a scalar field in a compact domain
نویسندگان
چکیده
We express the zeta function associated to the Laplacian operator on S 1 r × M in terms of the zeta function associated to the Laplacian on M , where M is a compact connected Riemannian manifold. This gives formulas for the partition function of the associated physical model at low and high temperature for any compact domain M. Furthermore, we provide an exact formula for the zeta function at any value of r when M is a D-dimensional box or a D-dimensional torus; this allows a rigorous calculation of the zeta invariants and the analysis of the main thermodynamic functions associated to the physical models at finite temperature.
منابع مشابه
One-loop Effective Potential for Scalar and Vector Fields on Higher Dimensional Noncommutative Flat Manifolds
The effective potentials for massless scalar and vector quantum field theories on D dimensional manifold with p compact noncommutative extra dimensions are evaluated by means of dimensional regularization implemented by zeta function tecniques. It is found that, the zeta function associated with the one loop operator may not be regular at the origin. Thus, the related heat kernel trace has a lo...
متن کاملرد تانسور انرژی- تکانه و پسزنی گرانشی اسکالرهای شوینگر در فضازمان دوسیته سهبعدی
In this paper, we consider a massive charged scalar field coupled to a uniform electric field background in a 3 dimensional de Sitter spacetime. We consider the value of the dimensionless coupling constant of the scalar field to the scalar curvature of a 3 dimensional de Sitter spacetime equal to 1/8. We compute the expectation value of the trace of the energy-momentum tensor in the in-vacuum s...
متن کاملZeta - function Regularization , the Multiplicative Anomaly and the Wodzicki Residue
The multiplicative anomaly associated with the zeta-function regularized determinant is computed for the Laplace-type operators L1 = −∆+ V1 and L2 = −∆+ V2, with V1, V2 constant, in a D-dimensional compact smooth manifold MD, making use of several results due to Wodzicki and by direct calculations in some explicit examples. It is found that the multiplicative anomaly is vanishing for D odd and ...
متن کاملOne-loop effective potential on hyperbolic manifolds.
U.T.F. 284 Abstract: The one-loop effective potential for a scalar field defined on an ultrastatic space-time whose spatial part is a compact hyperbolic manifold, is studied using zeta-function regularization for the one-loop effective action. Other possible regularizations are discussed in detail. The renormalization group equations are derived and their connection with the conformal anomaly i...
متن کاملO ct 2 00 5 Multidimensional cut - off technique , odd - dimensional Epstein zeta functions and Casimir energy of massless scalar fields ∗
Quantum fluctuations of massless scalar fields represented by quantum fluctuations of the quasiparticle vacuum in a zero-temperature dilute Bose-Einstein condensate may well provide the first experimental arena for measuring the Casimir force of a field other than the electromagnetic field. This would constitute a real Casimir force measurement-due to quantum fluctuations-in contrast to thermal...
متن کامل