Dynamical Symmetry Breaking in Fractal Space

Details Dynamical Symmetry Breaking in Fractal Space Dynamical Symmetry Breaking in Fractal Space

1997-01-09

arxiv.org/abs/hep-th/9701036v1

Phys.Rev. D56 (1997) 1239-1249

Physics

High Energy Physics

High Energy Physics - Theory

28 pages, 5 figures, LaTeX with epsf macro

Scientific paper

10.1103/PhysRevD.56.1239

We formulate field theories in fractal space and show the phase diagrams of the coupling versus the fractal dimension for the dynamical symmetry breaking. We first consider the 4-dimensional Gross-Neveu (GN) model in the (4-d)-dimensional randomized Cantor space where the fermions are restricted to a fractal space by the high potential barrier of Cantor fractal shape. By the statistical treatment of this potential, we obtain an effective action depending on the fractal dimension. Solving the 1/N leading Schwinger-Dyson (SD) equation, we get the phase diagram of dynamical symmetry breaking with a critical line similar to that of the d-dimensional (2

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