Year: 2019
Type: article
Abstract: It has recently been shown that vacuum expectation values and Feynman path integrals can be regularized using the Fourier integral operator ζ-function, yet the physical meaning of these ζ-regularized objects was unknown. Here, we show that ζ-regularized vacuum expectations appear as continuum limits using a certain discretization scheme. Furthermore, we study the rate of convergence for the discretization scheme using the example of a one-dimensional hydrogen atom in (−π, π) which we evaluate classically, using the Rigetti quantum virtual machine and on the Rigetti 8Q quantum chip “Agave” device. We also provide the free radiation field as an example for the computation of ζ-regularized vacuum expectation values in a gauge theory.
Source: Journal of Mathematical Physics
DOI: 10.1063/1.5085866
Authors: T. Hartung, K. Jansen
Institution: King's College London
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2967037620