Whether an Enormously Large Energy Density of the Quantum Vacuum Is Catastrophic

Vladimir Mostepanenko,Galina Klimchitskaya

doi:10.3390/sym11030314

Vladimir Mostepanenko, Galina Klimchitskaya

Open Access

https://doi.org/10.3390/sym11030314

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Journal: Symmetry	Publication Date: Mar 2, 2019
Citations: 12	License type: CC BY 4.0

Affiliation: Russian Academy of Sciences

Abstract

The problem of an enormously large energy density of the quantum vacuum is discussed in connection with the concept of renormalization of physical parameters in quantum field theory. Using the method of dimensional regularization, it is recalled that the normal ordering procedure of creation and annihilation operators is equivalent to a renormalization of the cosmological constant leading to its zero and nonzero values in Minkowski space-time and in the standard cosmological model, respectively. It is argued that a frequently discussed gravitational effect, resulting from an enormously large energy density described by the nonrenormalized (bare) cosmological constant, might be nonobservable much like some other bare quantities introduced in the formalism of quantum field theory.

Highlights

The elaboration of the quantum field theory has raised a number of fundamental problems that remain to be resolved
One of them is the problem of the quantum vacuum, which is of crucial importance for physics of elementary particles and cosmology
Unlike a widely believed opinion that an enormously large vacuum energy density should produce large gravitational effect, we argue that the zero-point energy is not directly observable and, in particular, does not gravitate

Summary

Introduction

The elaboration of the quantum field theory has raised a number of fundamental problems that remain to be resolved. In the framework of quantum field theory, the special procedure was elaborated which makes the vacuum expectation values of physical observables, such as the energy density and pressure, equal to zero It is the normal ordering of creation and annihilation operators (note, that nonzero vacuum expectation values may occur due to the spontaneous symmetry breaking). Using the method of dimensional regularization, we demonstrate rigorously that the vacuum stress-energy tensor of quantized fields is proportional to the metrical tensor On this basis, it is argued that the bare (non-renormalized) value of the cosmological constant might be excluded from theoretical description of the measurement results much as it holds for the bare electron mass and charge in standard quantum electrodynamics.

Divergences in Quantum Field Theory and the Quantum Vacuum

Geometric Structure of the Vacuum Stress-Energy Tensor

The Quantum Vacuum and Gravitation

Discussion

Conclusions