2008/07/01 by Remo Garattini · 2 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Cosmology and Gravitation Theories #Eigenvalues and eigenvectors #Gravitation #Graviton #Mathematical analysis #Mathematical physics #Mathematics #Maxwell's equations #Noncommutative and Quantum Gravity Theories #Physics #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Quantum mechanics #Regularization (linguistics) #Renormalization #Riemann zeta function #Schwarzschild radius #Zeta function regularization #gr-qc #hep-th
paper · pdf · doi:10.1016/j.physletb.2008.06.070
published as Phys.Lett.B666:189-192,2008 · 6 pages. Accepted for publication in Physics Letters B
arxiv created 2008/07/01 · openalex publication_date 2008/07/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the Wheeler-De Witt equation as a device for finding eigenvalues of a Sturm-Liouville problem. In particular, we will focus our attention on the electric (magnetic) Maxwell charge. In this context, we interpret the Maxwell charge as an eigenvalue of the Wheeler-De Witt equation generated by the gravitational field fluctuations. A variational approach with Gaussian trial wave functionals is used as a method to study the existence of such an eigenvalue. We restrict the analysis to the graviton sector of the perturbation. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.