Remarks on Defining the DLCQ of Quantum Field Theory as a Light-Like Limit

Details Remarks on Defining the DLCQ of Quantum Field Theory as a Light-Like Limit Remarks on Defining the DLCQ of Quantum Field Theory as a Light-Like Limit

1999-09-30

arxiv.org/abs/hep-th/9909220v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, no figures, uses phy macro (provided)

Scientific paper

The issue of defining discrete light-cone quantization (DLCQ) in field theory as a light-like limit is investigated. This amounts to studying quantum field theory compactified on a space-like circle of vanishing radius in an appropriate kinematical setting. While this limit is unproblematic at the tree-level, it is non-trivial for loop amplitudes. In one-loop amplitudes, when the propagators are written using standard Feynman $\alpha$-parameters we show that, generically, in the limit of vanishing radius, one of the $\alpha$-integrals is replaced by a discrete sum and the (UV renormalized) one-loop amplitude has a finite light-like limit. This is analogous to what happens in string theory. There are however exceptions and the limit may diverge in certain theories or at higher loop order. We give a rather detailed analysis of the problems one might encounter. We show that quantum electrodynamics at one loop has a well-defined light-like limit.

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