A functional analytic framework for local zeta regularization and the scalar Casimir effect

5 ottobre 2015
5 ottobre 2015
Contatti: 
Staff Dipartimento di Matematica

Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at] unitn.it

Luogo: Polo Scientifico e Tecnologico "Fabio Ferrari" Povo1, via Sommarive, 5 - Povo (TN) - Aula A220
ore 14.30

Relatore:

  • Davide Fermi (Università degli Studi di Milano)

Abstract:
Zeta regularization is a method allowing to give meaning via analytic continuation to ill-defined expressions arising in many areas of mathematics and physics, such as quantum field theory. In this talk, in view of applications to QFT, I will first describe an abstract framework based on an infinite scale of Hilbert spaces, associated to the powers of some given, positive self-adjoint operator; this framework provides a natural language to study the regularity properties and the analytic continuation of the integral kernels related to the given operator. Next, I will use this approach for the canonical quantization of a Hermitian scalar field on an arbitrary spatial domain, with a classical background potential. Zeta regularization is implemented using complex powers of the elliptic operator appearing in the field equation; the renormalized vacuum expectation value of the stress-energy tensor and other related observables are defined via analytic continuation of the corresponding kernels. Finally, to exhibit the computational efficiency of the above methods, I will discuss some explicit amples. (Joint work with Livio Pizzocchero. References: rXiv:1505.00711, arXiv:1505.01044, arXiv:1505.01651, arXiv:1505.03276).

Referente: Valter Moretti