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The sine-Gordon model and the small k^+ region of light-cone perturbation theory | | Paul A. Griffin
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24 Jul 1992 | | Journal: | Phys.Rev. D46 (1992) 3538-3543 | | Subject: | hep-th hep-ph | | Abstract: | The non-perturbative ultraviolet divergence of the sine-Gordon model is used to study the $k^+ = 0$ region of light-cone perturbation theory. The light-cone vacuum is shown to be unstable at the non-perturbative $eta^2 = 8pi$ critical point by a light-cone version of Coleman’s variational method. Vacuum bubbles, which are $k^+=0$ diagrams in light-cone field theory and are individually finite and non-vanishing for all $eta$, conspire to generate ultraviolet divergences of the light-cone energy density. The $k^+ = 0$ region of momentum also contributes to connected Green’s functions; the connected two point function will not diverge, as it should, at the critical point unless diagrams which contribute only at $k^+ = 0$ are properly included. This analysis shows in a simple way how the $k^+ =0$ region cannot be ignored even for connected diagrams. This phenomenon is expected to occur in higher dimensional gauge theories starting at two loop order in light-cone perturbation theory. | | Source: | arXiv, hep-th/9207082 | | Services: | Forum | Review | PDF | Favorites | |
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