2013/11/26 by Jesús García de Dueñas, J. G. Dueñas, N. F. Svaiter
Mathematics · Physics and Astronomy · #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #hep-th #math-ph #math.MP #math.NT
paper · pdf · doi:10.1142/s0217751x14500511
9 pages
arxiv created 2013/11/26 · openalex publication_date 2014/03/31 · arxiv updated 2014/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The sequence of nontrivial zeros of the Riemann zeta function is zeta regularizable. Therefore, systems with countably infinite number of degrees of freedom described by self-adjoint operators whose spectra is given by this sequence admit a functional integral formulation. We discuss the consequences of the existence of such self-adjoint operators in field theory framework. We assume that they act on a massive scalar field coupled to a background field in a (d+1)-dimensional flat space–time where the scalar field is confined to the interval [0, a] in one of its dimensions and there are no restrictions in the other dimensions. The renormalized zero-point energy of this system is presented using techniques of dimensional and analytic regularization. In even-dimensional space–time, the series that defines the regularized vacuum energy is finite. For the odd-dimensional case, to obtain a finite vacuum energy per unit area, we are forced to introduce mass counterterms. A Riemann mass appears, which is the correction to the mass of the field generated by the nontrivial zeros of the Riemann zeta function.