Self-consistency equation for the order parameter and restoration of chiral symmetry

1988 ◽  
Vol 37 (1) ◽  
pp. 190-194 ◽  
Author(s):  
Liu Bao-hua ◽  
Li Jia-rong
Keyword(s):  
Chiral Symmetry ◽  
Order Parameter ◽  
Consistency Equation ◽  
Self Consistency

SPONTANEOUS CHIRAL-SYMMETRY BREAKING AND SCALING LAW IN THREE-DIMENSIONAL QED

1990 ◽  
Vol 05 (06) ◽  
pp. 407-416 ◽  
Author(s):  
KEI-ICHI KONDO ◽  
HAJIME NAKATANI
Keyword(s):  
Chiral Symmetry ◽  
Order Parameter ◽  
Chiral Symmetry Breaking ◽  
Scaling Law ◽  
Three Dimensional ◽  
Dyson Equation ◽  
Dirac Fermion ◽  
Dynamical Mass ◽  
Planar Approximation ◽  
Spontaneous Breakdown

We analyze the critical behavior associated with spontaneous breakdown of chiral symmetry in QED3 (three-dimensional QED with four-component Dirac fermion using the SD (Schwinger-Dyson) equation. In the quenched planar approximation, we find an approximate solution such that QED3 resides in only one phase where the chiral symmetry is broken. Moreover, we predict the scaling law for the dynamical mass and chiral order parameter by an analytic study of the SD equation, which is then confirmed by solving the SD equation numerically. This scaling law is consistent with the Monte Carlo result in the quenched approximation.

scholarly journals Chiral symmetry breaking, entanglement, and the nucleon spin decomposition

2019 ◽  
Vol 35 (08) ◽  
pp. 2050048 ◽  
Author(s):  
Silas R. Beane ◽  
Peter J. Ehlers
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Order Parameter ◽  
Chiral Symmetry Breaking ◽  
Entanglement Entropy ◽  
Reduced Density Matrix ◽  
Nucleon Spin ◽  
Maximal Entanglement ◽  
Nucleon State ◽  
Reduced Density

The nucleon is naturally viewed as a bipartite system of valence spin — defined by its non-vanishing chiral charge — and non-valence or sea spin. The sea spin can be traced over to give a reduced density matrix, and it is shown that the resulting entanglement entropy acts as an order parameter of chiral symmetry breaking in the nucleon. In the large-[Formula: see text] limit, the entanglement entropy vanishes and the valence spin accounts for all of the nucleon spin, while in the limit of maximal entanglement entropy, the nucleon loses memory of the valence spin and consequently has spin dominated by the sea. The nucleon state vector in the chiral basis, fit to low-energy data, gives a valence spin content consistent with experiment and lattice QCD determinations, and has large entanglement entropy.

scholarly journals Effects of order parameter self-consistency in as±−sjunction

2016 ◽  
Vol 93 (21) ◽  
Author(s):  
Rosa Rodríguez-Mota ◽  
Erez Berg ◽  
T. Pereg-Barnea
Keyword(s):  
Order Parameter ◽  
Self Consistency

scholarly journals A CONSTRAINT ON THE ANOMALOUS GREEN’S FUNCTION

1996 ◽  
Vol 10 (12) ◽  
pp. 555-565 ◽  
Author(s):  
YONG-JIHN KIM
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Weak Localization ◽  
Physical Constraint ◽  
Gap Equation ◽  
Homogeneous Systems ◽  
Consistency Equation ◽  
Self Consistency

It is shown that the physical constraint of the Anomalous Green’s function gives a natural pairing condition. The resulting self-consistency equation is directly related to the BCS gap equation. Both inhomogeneous and homogeneous systems are considered to illustrate the importance of the constraint. Especially we find weak localization correction to the phonon-mediated interaction.

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