The Epstein–Glaser causal approach to the light-front QED{sub 4}. I: Free theory
In this work we present the study of light-front field theories in the realm of the axiomatic theory. It is known that when one uses the light-cone gauge pathological poles (k{sup +}){sup −n} arises, demanding a prescription to be employed in order to tame these ill-defined poles and to have the correct Feynman integrals due to the lack of Wick rotation in such theories. In order to shed a new light on this long standing problem we present here a discussion based on the use of rigorous mathematical machinery of the distributional theory combined with physical concepts, such as causality, to show how to deal with these singular propagators in a general fashion without making use of any prescription. The first step of our development will consist in showing how the analytic representation for propagators arises by requiring general physical properties within the framework of Wightman’s formalism. From that we shall determine the equal-time (anti)commutation relations in the light-front form for the scalar and fermionic fields, as well as for the dynamical components of the electromagnetic field. In conclusion, we introduce the Epstein–Glaser causal method in order to have a mathematical rigorous description of the free propagators of the theory, allowing us to discuss a general treatment for propagators of the type (k{sup +}){sup −n}. Afterwards, we show that at given conditions our results reproduce known prescriptions in the literature. - Highlights: • We develop the analytic representation for propagators in Wightman’s framework. • We make use of the analytic representation to obtain equal-time (anti)commutation relations in the light-front. • We derive the free Feynman propagators for the light-front quantum electrodynamics in the Epstein–Glaser approach. • We determine a general expression for the propagator associated to the light-cone poles (k{sup +}){sup −n} in the causal approach.
- OSTI ID:
- 22403514
- Journal Information:
- Annals of Physics (New York), Vol. 351; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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