I have asked this question once, but noone seemed to notice it, so I'll try again. In my book the time ordering operator is used to rewrite an operator product:(adsbygoogle = window.adsbygoogle || []).push({});

U(β,τ)A(τ)U(τ,τ')B(τ')U(τ',0) = T_τ(U(β,0)A(τ)B(τ'))

To refresh your memories the time ordering operator T_τ orders operators according to time such that:

T_τ(A(τ)B(τ')) = A(τ)B(τ') for τ>τ' and B(τ')A(τ) for τ'>τ

And the operator U(t,t') is a unitary operator that propagates a state from t' to t and has the property that:

U(t,t')=U(t,t'')U(t'',t')

I am still unsure how the rewriting is done though. One key ingredient is to use the property of the unitary above to write:

This way we have:

U(0,β)=U(0,τ')U(τ',τ)U(τ,β)

And i think the idea is then to insert in the expression and use time-order but I am not sure how to.

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# Time ordering in QFT

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