Vacuum energy and relativistic invariance

TL;DR

The paper argues that relativistic invariance limits vacuum energy divergences to quadratic, not quartic, and that zero-point energies of free massless fields vanish, impacting the cosmological constant problem.

Contribution

It demonstrates that the divergence of zero-point energies is less severe than previously thought due to relativistic invariance constraints.

Findings

Zero-point energies diverge at most quadratically

Quartic divergence is an artifact of noninvariant regularization

Zero-point energies of free massless fields vanish

Abstract

It is argued that the zero-point energies of free quantum fields diverge at most quadratically and not quartically, as is generally believed. This is a consequence of the relativistic invariance which requires that the energy density of the vacuum $\rho$ and its pressure $p$ satisfy $\rho=-p$. The usually obtained quartic divergence is an artifact of the use of a noninvariant regularization which violates this relation. One consequence of our results is that the zero-point energies of free massless fields vanish. Implications for the cosmological constant problem are briefly discussed.