Fluctuations of quantum fields via zeta function regularization

Abstract

Explicit expressions for the expectation values and the variances of some observables, which are bilinear quantities in the quantum fields on a D-dimensional manifold, are derived making use of zeta function regularization. It is found that the variance, related to the second functional variation of the effective action, requires a further regularization and that the relative regularized variance turns out to be 2/N, where N is the number of the fields, thus being independent on the dimension D. Some illustrating examples are worked through.

15 pages, latex, typographical mistakes corrected

References in corpus (4)

• Explicit Zeta Functions for Bosonic and Fermionic Fields on a Noncommutative Toroidal Spacetime
• Effective Finite Temperature Partition Function for Fields on Non-Commutative Flat Manifolds
• One-loop effective potential for scalar and vector fields on higher dimensional noncommutative flat manifolds
• Quantum Fluctuations of Effective Fields and the Correspondence Principle

Cited by in corpus (12)

• Stochastic Gravity: Theory and Applications
• Stochastic Gravity: Theory and Applications
• Stochastic Gravity: A Primer with Applications
• Quantum fluctuations on a thick de Sitter brane
• Noise Kernel and Stress Energy Bi-Tensor of Quantum Fields in Hot Flat Space and Gaussian Approximation in the Optical Schwarzschild Metric
• Stress-energy Tensor Correlators of a Quantum Field in Euclidean $R^N$ and $Ad{S}^N$ spaces via the generalized zeta-function method
• Surface vacuum energy and stresses for a brane in de Sitter spacetime
• Quantum probing of null-singularities
• Non perturbative regularization of one loop integrals at finite temperature
• Quantum Fluctuations of a Coulomb potential
• Riemann zeta zeros and zero-point energy
• Correlations of the stress-energy tensor in AdS spaces via the generalized zeta-function method