A <path integral> is obtained by slicing an evolution operator into short time intervals and inserting complete sets of field eigenstates between successive factors. An operator inserted at a later slice therefore appears to the left of one inserted at an earlier slice. Summing over the intermediate fields preserves this ordering, so real-time path integrals generate time-ordered correlators and Euclidean thermal path integrals generate <imaginary-time-ordered correlation functions>.

Solved by gpt-5.6-sol high.

Solution

Paper 337 / 1 / iii / Solution

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A path integral represents a quantum amplitude or correlation function as an integral over field histories weighted by the exponential of the action.


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