Remarks on Defining the DLCQ of Quantum Field Theory as a Light-Like Limit
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 1999
- DOI:
- 10.48550/arXiv.hep-th/9909220
- arXiv:
- arXiv:hep-th/9909220
- Bibcode:
- 1999hep.th....9220B
- Keywords:
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- High Energy Physics - Theory
- E-Print:
- 20 pages, no figures, uses phy macro (provided)