# Higgs vacuum expectation value imples what energy density?

1. Dec 12, 2011

### johne1618

I understand that the the Higgs field has a vacuum expectation value of 246 GeV.

I think that means that the expectation of the Hamiltonian energy operator applied to the vacuum state is 246 GeV.

What does this imply for the energy density of the Higgs field in the vacuum (i.e. in Joules / m^3) ?

John

Last edited: Dec 12, 2011
2. Dec 12, 2011

### Bill_K

johne1618, As you say, the vacuum expectation value of the Higgs field is v = 246 GeV. It serves to set the scale for the other particle masses induced by the Higgs, for example mW = ½vg where g is one of the weak coupling constants. But it's not the expectation value of the Hamiltonian. The Higgs term that appears in the Hamiltonian and Lagrangian is a quartic, V(φ) = μ2φ*φ + λ(φ*φ)2, where φ = v is the point at which V is a minimum. But regardless, we adjust the energy scale so that the energy of the vacuum at this point is zero.