Abstract
The objects of small-distance-behaviour analysis, so far as it is developped until now, are (the Fourier transforms of) the Euclidean Green’s functions, or Schwinger functions (1). These are the restrictions of the analytic Wightman functions to Schwinger points (2): time components of all arguments imaginary, space components real, or, alternatively, the corresponding analytic continuations of vacuum expectation values (VEVs) of time-ordered products of field operators (Feynman amplitudes) to such points. The Fourier-transforms of the Schwinger functions are the analytic continuations (2) to imaginary energy, real space components, in all momenta arguments of the Fourier transforms of the Feynman amplitudes, or Minkowski Green’s functions.
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Symanzik, K. (1974). Short Review of Small-Distance-Behaviour Analysis. In: Caianiello, E.R. (eds) Renormalization and Invariance in Quantum Field Theory. NATO Advanced Study Institutes Series, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8909-9_11
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