K. Scharnhorst: *A functional integral equation for the
complete effective action in quantum field theory*.
International Journal of Theoretical Physics **36**:2(1997)281-343
(DOI: 10.1007/BF02435737) [University of Leipzig Preprint NTZ 16/1993,
arXiv:hep-th/9312137; published version abbreviated].
[INSPIRE record]

**Abstract**:
Based on a methodological analysis of the effective action
approach, certain conceptual foundations of quantum field
theory are reconsidered to establish a quest for an equation for
the effective action. Relying on the functional integral
formulation of Lagrangian quantum field theory, we propose
a functional integral equation for the complete effective action
which can be understood as a certain fixed-point condition.
This is motivated by a critical attitude towards the
distinction, artificial from an experimental point of view,
between classical and effective action. While for free field
theories nothing new is accomplished, for interacting theories
the concept differs from the established paradigm. The
analysis of this new concept concentrates on gauge field theories,
treating QED as the prototype model. An
approximative approach to the functional integral equation for the
complete effective action of QED is exploited to obtain
certain nonperturbative information about the quadratic kernels of
the action. As a particular application the
approximative calculation of the QED coupling constant alpha is
explicitly studied. It is understood as one of the
characteristics of a fixed point given as a solution of the
functional integral equation proposed. Finally, within the present
approach the vacuum energy problem is considered, as are possible
implications for the concept of induced gravity.

- Electronic copy of the article: International Journal of Theoretical Physics
- Electronic copy of the preprint version - University of Leipzig Preprint NTZ 16/1993: arXiv:hep-th/9312137
- Citations
- Misprints, errata, addenda:
- P. 343, in the ref. 'Shirkov, D.V. (1990)' the page number should read correctly: 239.
- P. 343, in the ref. 'Vilkovisky, G.A. (1992)' the page number should read correctly: 125.

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