Applications in physics of the multiplicative anomaly formula involving some basic differential operators

Abstract

In the framework leading to the multiplicative anomaly formula ---which is here proven to be valid even in cases of known spectrum but non-compact manifold (very important in Physics)--- zeta-function regularisation techniques are shown to be extremely efficient. Dirac like operators and harmonic oscillators are investigated in detail, in any number of space dimensions. They yield a non-zero anomaly which, on the other hand, can always be expressed by means of a simple analytical formula. These results are used in several physical examples, where the determinant of a product of differential operators is not equal to the product of the corresponding functional determinants. The simplicity of the Hamiltonian operators chosen is aimed at showing that such situation may be quite widespread in mathematical physics. However, the consequences of the existence of the determinant anomaly have often been overlooked.

20 pages, LaTex

References in corpus (6)

• Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue
• The $a_5$ heat kernel coefficient on a manifold with boundary
• Regularization schemes and the multiplicative anomaly
• On the relevance of the multiplicative anomaly
• Is the multiplicative anomaly relevant ?
• Is the multiplicative anomaly dependent on the regularization ?

Cited by in corpus (23)

• One-loop f(R) gravity in de Sitter universe
• String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
• One-loop corrections to the photon propagator in the curved-space QED
• One-loop Modified Gravity in de Sitter Universe, Quantum Corrected Inflation, and its Confrontation with the Planck Result
• Fluctuations of quantum fields via zeta function regularization
• Zeta Function Methods and Quantum Fluctuations
• Heat Kernel Coefficients for Chern-Simons Boundary Conditions in QED
• 2D Quantum Gravity at One Loop with Liouville and Mabuchi Actions
• On the Dimensional Reduction Procedure
• From tracial anomalies to anomalies in Quantum Field Theory
• Functional Determinant of the Massive Laplace Operator and the Multiplicative Anomaly
• Zeta function regularization in Casimir effect calculations and J.S. Dowker's contribution
• Multiplicative anomaly and zeta factorization
• Functional Determinants in Higher Derivative Lagrangian Theories
• Universality and ambiguity in fermionic effective actions
• Finite cut-off JT and Liouville quantum gravities on the disk at one loop
• The Multiplicative Anomaly of Regularized Functional Determinants
• Local $\zeta$-functions, stress-energy tensor, field fluctuations, and all that, in curved static spacetime
• Multiplicative anomaly and finite charge density
• Generalized Zeta Function Regularization and the Multiplicative Anomaly
• Anomalies and Analytic Torsion on Hyperbolic Manifolds
• Consistent, covariant and multiplicative anomalies
• Form factors and non-local Multiplicative Anomaly for fermions with background torsion