One loop stress tensor renormalization in curved background: The Relation between zeta function and point splitting approaches, and an improved point splitting procedure
Aug, 1998Citations per year
Abstract: (arXiv)
We conclude the rigorous analysis of a previous paper concerning the relation between the (Euclidean) point-splitting approach and the local -function procedure to renormalize physical quantities at one-loop in (Euclidean) QFT in curved spacetime. The stress tensor is now considered in general -dimensional closed manifolds for positive scalar operators . Results obtained in previous works (in the case D=4 and ) are rigorously proven and generalized. It is also proven that, in static Euclidean manifolds, the method is compatible with Lorentzian-time analytic continuations. It is found that, for , the result of the function procedure is the same obtained from an improved version of the point-splitting method which uses a particular choice of the term in the Hadamard expansion of the Green function. This point-splitting procedure works for any value of the field mass . Furthermore, in the case D=4 and , the given procedure generalizes the Euclidean version of Wald's improved point-splitting procedure. The found point-splitting method should work generally, also dropping the hypothesis of a closed manifold, and not depending on the -function procedure. This fact is checked in the Euclidean section of Minkowski spacetime for where the method gives rise to the correct stress tensor for automatically.Note:
- To appear in J. Math. Phys.
- field theory: Euclidean
- space-time
- regularization: zeta function
- regularization: point splitting
- tensor: energy-momentum
- renormalization
- any-dimensional
- expansion: heat kernel
- field theory: scalar
References(11)
Figures(0)