Effective field equations for expectation values

Details Effective field equations for expectation values Effective field equations for expectation values

Jan 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986phrvd..33..444j&link_type=abstract

Physical Review D (Particles and Fields), Volume 33, Issue 2, 15 January 1986, pp.444-454

Physics

195

Theory Of Quantized Fields

Scientific paper

We discuss functional methods which allow calculation of expectation values, rather than the usual in-out amplitudes, from a path integral. The technique, based on Schwinger's idea of summing over paths which go from the past to the future and then back to the past, provides effective field equations satisfied by the expectation value of the field. These equations are shown to be real and causal for a general theory up to two-loop order, and unitarity is checked to this order. These methods are applied to a simple quantum-mechanical example to illustrate the differences between the new formalism and the standard theory. When applied to the gravitational field, the new effective field equations should be useful for studies of quantum cosmology.

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