Probability distribution of the vacuum energy density

TL;DR

This paper analytically derives the probability distribution of vacuum energy density for massless scalar fields in Minkowski space, revealing that the distribution is broad and the expectation value does not fully characterize the vacuum energy.

Contribution

It provides the first analytical calculation of the probability distribution of vacuum energy density for massless scalar fields in Minkowski space.

Findings

Probability distribution is broad.

Vacuum expectation value is not fully representative.

Distribution differs for real and complex fields.

Abstract

As the vacuum state of a quantum field is not an eigenstate of the Hamiltonian density, the vacuum energy density can be represented as a random variable. We present an analytical calculation of the probability distribution of the vacuum energy density for real and complex massless scalar fields in Minkowski space. The obtained probability distributions are broad and the vacuum expectation value of the Hamiltonian density is not fully representative of the vacuum energy density.