Probability distribution of the vacuum energy density

Understand

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.