Abstract
When one tries to take into account the non-trivial vacuum structure of Quantum Field Theory, the standard functional-integral tools such as generating functionals or transitional amplitudes, are often quite inadequate for such purposes. Here we propose a generalized generating functional for Green's functions which allows to easily distinguish among a continuous set of vacua that are mutually connected via unitary canonical transformations. In order to keep our discussion as simple as possible, we limit ourselves to Quantum Mechanics where the generating functional of Green's functions is constructed by means of phase-space path integrals. The quantum-mechanical setting allows to accentuate the main logical steps involved without embarking on technical complications such as renormalization or inequivalent representations that should otherwise be addressed in the full-fledged Quantum Field Theory. We illustrate the inner workings of the generating functional obtained by discussing Green's functions among vacua that are mutually connected via translations and dilatations. Salient issues, including connection with Quantum Field Theory, vacuum-to-vacuum transition amplitudes and perturbation expansion in the vacuum parameter are also briefly discussed.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.