scholarly journals A Self-Consistent Mean-Field Approach to the Dynamical Symmetry Breaking: The Effective Potential of the Nambu and Jona-Lasinio Model

1984 ◽  
Vol 71 (6) ◽  
pp. 1332-1345 ◽  
Author(s):  
T. Kunihiro ◽  
T. Hatsuda
Keyword(s):  
Symmetry Breaking ◽  
Effective Potential ◽  
Mean Field ◽  
Dynamical Symmetry ◽  
Dynamical Symmetry Breaking ◽  
Field Approach ◽  
Self Consistent

scholarly journals DYNAMICAL SYMMETRY BREAKING IN THE EXTERNAL GRAVITATIONAL AND CONSTANT MAGNETIC FIELDS

1999 ◽  
Vol 14 (04) ◽  
pp. 481-503 ◽  
Author(s):  
T. INAGAKI ◽  
S. D. ODINTSOV ◽  
YU. I. SHIL'NOV
Keyword(s):  
Magnetic Field ◽  
Gravitational Field ◽  
Magnetic Fields ◽  
Symmetry Breaking ◽  
Effective Potential ◽  
Constant Magnetic Field ◽  
Dynamical Symmetry ◽  
Green Functions ◽  
Dynamical Symmetry Breaking ◽  
Njl Model

We investigate the effects of the external gravitational and constant magnetic fields to the dynamical symmetry breaking. As simple models of the dynamical symmetry breaking we consider the Nambu–Jona-Lasinio (NJL) model and the supersymmetric Nambu–Jona-Lasinio (SUSY NJL) model nonminimally interacting with the external gravitational field and minimally interacting with constant magnetic field. The explicit expressions for the scalar and spinor Green functions are found to the first order in the space–time curvature and exactly for a constant magnetic field. We obtain the effective potential of the above models from the Green functions in the magnetic field in curved space–time. Calculating the effective potential numerically with the varying curvature and/or magnetic fields we show the effects of the external gravitational and magnetic fields to the phase structure of the theories. In particular, increase of the curvature in the spontaneously broken phase of the chiral symmetry due to the fixed magnetic field makes this phase to be less broken. At the same time the strong magnetic field quickly induces chiral symmetry breaking even in the presence of fixed gravitational field within the nonbroken phase.

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