Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-01-22
Physics
High Energy Physics
High Energy Physics - Theory
LaTeX, 18 pages, 2 Postscript figures, Talk delivered at the Xth International Workshop on High Energy Physics and Quantum Fie
Scientific paper
We give a review of the exact renormalization group (ERG) approach and illustrate its applications in scalar and fermionic theories. The derivative expansion and approximations based on the derivative expansion with further truncation in the number of fields (mixed approximation) are discussed. We analyse the mixed approximation for a three-dimensional scalar theory and show that it is less effective than the pure derivative expansion. For pure fermionic theories analytical solutions for the pure derivative expansion and mixed approximation in the limit $N \to \infty $, where $N$ is the number of fermionic species, are found. For finite $N$ a few series of fixed point solutions with their anomalous dimensions and critical exponents are computed numerically. We argue that one of the fermionic solutions can be identified with that of Dashen and Frishman, whereas the others seem to be new ones. The issues of spurious solutions and scheme dependence of the results are discussed.
Comellas Jordi
Kubyshin Yuri
Moreno Enrique
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