2001/08/03 by Chris Harvey-Fros, Christopher Simon Francis Harvey-Fros, Harvey-Fros, Chris
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/0108018
Thesis, March 1999. LaTeX, 126 pages, 25 figs
arxiv created 2001/08/03 · openalex publication_date 2001/08/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce Wilson's, or Polchinski's, exact renormalization group, and review the Local Potential Approximation as applied to scalar field theory. Focusing on the Polchinski flow equation, standard methods are investigated, and by choosing restrictions to some sub-manifold of coupling constant space we arrive at a very promising variational approximation method. Within the Local Potential Approximation, we construct a function, C, of the coupling constants; it has the property that (for unitary theories) it decreases monotonically along flows and is stationary only at fixed points - where it `counts degrees of freedom', i.e. is extensive, counting one for each Gaussian scalar. In the latter part of the thesis, the Local Potential Approximation is used to derive a non-trivial Polchinski flow equation to include Fermi fields. Our flow equation does not support chirally invariant solutions and does not reproduce the features associated with the corresponding invariant theories. We solve both for a finite number of components, N, and within the large N limit. The Legendre flow equation provides a comparison with exact results in the large N limit. In this limit, it is solved to yield both chirally invariant and non-invariant solutions.