Available online at www.sciencedirect.com
ScienceDirect
Nuclear Physics B 946 (2019) 114694
www.elsevier.com/locate/nuclphysb
The Minkowski quantum vacuum does not gravitate
Viacheslav A. Emelyanov
Institute for Theoretical Physics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
Received 9
April 2019; received in revised form 24 June 2019; accepted 8 July 2019
Available
online 12 July 2019
Editor: Stephan
Stieberger
Abstract
We
show that a non-zero renormalised value of the zero-point energy in λφ
4
-theory over Minkowski
spacetime is in tension with the scalar-field equation at two-loop order in perturbation theory.
© 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Quantum fields give rise to an infinite vacuum energy density [1–4], which arises from
quantum-field fluctuations taking place even in the absence of matter. Yet, assuming that semi-
classical quantum field theory is reliable only up to the Planck-energy scale, the cut-off estimate
yields zero-point-energy density which is finite, though, but in a notorious tension with astro-
ph
ysical observations.
In the presence of matter
, however, there are quantum effects occurring in nature, which can-
not be understood without quantum-field fluctuations. These are the spontaneous emission of a
photon by excited atoms, the Lamb shift, the anomalous magnetic moment of the electron, and
so forth [5]. This means quantum-field fluctuations do manifest themselv
es in nature and, hence,
the zero-point energy poses a serious problem.
Lorentz symmetry implies that v
acuum stress-energy tensor is proportional to the metric ten-
sor [2]. As a consequence, the vacuum energy density must equal a quarter of the stress-tensor
trace. In the case of Maxwell theory, the photon field cannot thus give a non-vanishing Lorentz-
invariant vacuum stress tensor, due to conformal in
variance of the theory. Still, its vacuum energy
E-mail address: viacheslav.emelyanov@kit.edu.
https://doi.org/10.1016/j.nuclphysb.2019.114694
0550-3213/© 2019
The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.