# Why is the periodicity of fields in finite temperature QCD consequence of Trace in the action?

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In finite temperature QCD, the gauge fields must be periodic in temporal direction. They say this is the consequence of trace in the action for gauge fields. How does trace imply that the fields must be periodic?

This post imported from StackExchange Physics at 2014-04-13 14:37 (UCT), posted by SE-user quantum
retagged Apr 19, 2014

This is related to the KMS condition. https://en.wikipedia.org/wiki/KMS_condition

I guess you mean the EUCLIDEAN temporal direction, and the period is $1/T$. This is part of the so called KMS condition as Arnold Neumaier already suggested. Actually, periodicity of the fields (or periodicity of the Euclidean temporal direction of the manifold where filds are defined) arises as soon as one tries to translate the KMS condition into the language of finite-temperature  path integral.

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