# What is non/perturbative vacuum

#### Neitrino

Dear PF,

I have two questions

What is non-perturbative vacuum? A state - characterized by many non-vanishing condensates? (As explained in wikipedia). In what this non-perturbativeness is manifested when there are non -vanishing condensates? So why such vacuum is calld non-perturbative?

And I was reading something where was written "In the spontaneous summetry breaking one has to use the symmetry broken vacuum when evaluating the S-matrix" My question is how/why the evaluation of S-matrix is related whether the vacuum is broken or no?

Always thank you for assistance.

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#### DarMM

Gold Member
What is non-perturbative vacuum?
The actual vacuum of an interacting quantum field theory. Typically the vacuum we work with is the vacuum of the free theory and we approximate effects in the full theory by perturbation theory. For gauge theory this leaves many of the features of the true vacuum state outside your reach as they are nonperturbative, e.g. of order $\mathcal{O}\left(e^{\frac{1}{g}}\right)$, and thus invisible to perturbation theory, i.e. nonperturbative.

And I was reading something where was written "In the spontaneous symmetry breaking one has to use the symmetry broken vacuum when evaluating the S-matrix" My question is how/why the evaluation of S-matrix is related whether the vacuum is broken or no?
Well if the symmetry is broken, then the actual vacuum of your theory is the symmetry broken one and particles will be excitations about this vacuum. Using the symmetric one would not be applicable.

The problem however becomes that perturbation theory in quantum field theory assumes:
$$\langle \phi \rangle = 0$$
for your fields. When the vacuum breaks the symmetry, this first condition will be violated so you have to shift to new fields. This will alter your Lagnragian to a form reexpressed in terms of fields that give rise to particles. The original Lagrangian fields, though still physically present, no longer have particle states due to breaking the vanishing vacuum expectation value condition.

"What is non/perturbative vacuum"

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