How to quantize the ''mathematical'' fluctuation field in statistics?

[ndung200790]

Please teach me this:
The general effort is to quantize the fields of elementary particles and gravitons.But I wonder about ''mathematical'' fields such as the fluctuation fields in statistical physics.I think there may be many ''continuous'' fields in physics.Could the functional integral formalism
say any things about ''the quantum'' of field?Because this formalism is only a powerful tool to canculate the correlation function,but say nothing(it seem to me) about the quantization(about ''quantum'' of fields).
Thank you very much in advance

 

[ndung200790]

Then could we always pose the commutators and anticommutators for any fields in physics or not?(with the theories are renormalizable)

 

[ndung200790]

It seem to me that because the canonical and functional quantization have the exactly same result.Then the functional formalism also deduces the ''discontiuous'' quantum of fields.So any fields can represent by functional integral formalism are ''quantizable''.Is that correct?

 

[Galron]

It seem to me that because the canonical and functional quantization have the exactly same result.Then the functional formalism also deduces the ''discontiuous'' quantum of fields.So any fields can represent by functional integral formalism are ''quantizable''.Is that correct?

Yes.

Any field that is not integrable is discounted by the renormalization conditions.

A field that is non linear and non quantizable is a white elephant.