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High Energy Physics - Theory

arXiv:hep-th/9810104 (hep-th)
[Submitted on 14 Oct 1998 (v1), last revised 6 Oct 1999 (this version, v3)]

Title:A manifestly gauge invariant exact renormalization group

Authors:Tim R. Morris
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Abstract: In these lectures we describe the construction of a gauge invariant renormalization group equation for pure non-Abelian gauge theory. In the process, a non-perturbative gauge invariant continuum Wilsonian effective action is precisely defined. The formulation makes sense without gauge fixing and thus manifest gauge invariance may be preserved at all stages. In the large N limit (of SU(N) gauge theory) the effective action simplifies: it may be expressed through a path integral for a single particle whose trajectory describes a Wilson loop. Regularization is achieved with the help of a set of Pauli-Villars fields whose formulation follows naturally in this picture. Finally, we show how the one loop beta function was computed, for the first time without any gauge fixing.
Comments: Invited lectures at the Workshop on the Exact Renormalization Group, Faro, Portugal, Sept. 10-12, 1998. 32 pages including 24 figs. Conventions and notation changed to correspond to imminent papers, plus minor corrections
Subjects: High Energy Physics - Theory (hep-th); Condensed Matter (cond-mat); High Energy Physics - Lattice (hep-lat); High Energy Physics - Phenomenology (hep-ph)
Report number: SHEP 98-12
Cite as: arXiv:hep-th/9810104
  (or arXiv:hep-th/9810104v3 for this version)
  https://doi.org/10.48550/arXiv.hep-th/9810104

Submission history

From: Tim R. Morris [view email]
[v1] Wed, 14 Oct 1998 16:50:31 UTC (41 KB)
[v2] Fri, 16 Oct 1998 20:54:48 UTC (41 KB)
[v3] Wed, 6 Oct 1999 16:59:42 UTC (48 KB)
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