Dynamical symmetry breaking in fractal space

Journal Article · Tue Jul 01 04:00:00 EDT 1997 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.56.1239· OSTI ID:527097

Nagatani, Y ^[1]

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1. Department of Physics, Nagoya University, Nagoya 464-01 (Japan)

We formulate field theories in fractal space and show the phase diagrams of the coupling versus the fractal dimension for dynamical symmetry breaking. We first consider the four-dimensional Gross-Neveu (GN) model in (4{minus}d)-dimensional randomized Cantor space where the fermions are restricted to a fractal space by the high potential barrier of the 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{lt}d{le}4) GN model except for the system-size dependence. We also consider four-dimensional QED with only the fermions formally compactified to d dimensions. Solving the ladder SD equation, we obtain the phase diagram of dynamical chiral symmetry breaking with a linear critical line, which is consistent with the known results for d=4 (the Maskawa-Nakajima case) and d=2 (the case with the external magnetic field). {copyright} {ital 1997} {ital The American Physical Society}

• OSTI ID: 527097
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 2 Vol. 56; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
AXIOMATIC FIELD THEORY
CHIRAL SYMMETRY
COUPLING
DYNAMICAL GROUPS
FERMIONS
FOUR-DIMENSIONAL CALCULATIONS
FRACTALS
PHASE DIAGRAMS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
SYMMETRY BREAKING