Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2004-04-27
J.Phys.A37:10409-10420,2004
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, based on contribution to "Progress in Supersymmetric Quantum Mechanics" (Valladolid U.), accepted in Journal of Phys
Scientific paper
10.1088/0305-4470/37/43/027
The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings. Indeed, the ordinary renormalization group differential equations can be supplemented with noise, making them into stochastic Langevin equations. Furthermore, if the renormalization group is a gradient flow, the space of couplings can be endowed with a supersymmetric structure a la Parisi-Sourlas. The formulation of the renormalization group as supersymmetric quantum mechanics is useful for analysing the topology of the space of couplings by means of Morse theory. We present simple examples with one or two couplings.
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