STOCHASTIC QUANTIZATION OF NAMBU-JONA-LASINIO MODEL

1993 ◽  
Vol 08 (10) ◽  
pp. 903-916
Author(s):  
MASATOSHI ITO ◽  
HIROMI KASE ◽  
KATSUSADA MORITA
Keyword(s):  
Langevin Equation ◽  
Effective Potential ◽  
Order Parameter ◽  
Numerical Solutions ◽  
Mass Term ◽  
Stochastic Quantization ◽  
Bare Mass ◽  
Equilibrium Limit ◽  
Effective Potentials

Stochastic quantizations of the Nambu-Jona-Lasinio model with and without the bare mass term are carried out. It is shown that, although the linear fermion Langevin equation is not chiral-invariant, one obtains the chiral-invariant effective potential in the equilibrium limit when the bare mass vanishes. Numerical solutions of the growing order parameter and two kinds of effective potentials, which take qualitatively different forms if the bare mass is nonvanishing, are presented.

scholarly journals NONLINEAR PHENOMENA IN CANONICAL STOCHASTIC QUANTIZATION

2008 ◽  
Vol 18 (09) ◽  
pp. 2787-2791
Author(s):  
HELMUTH HÜFFEL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Gauge Field Theories ◽  
Higgs Mechanism ◽  
Nonlinear Phenomena ◽  
Quantum Field ◽  
Stochastic Quantization ◽  
Statistical System ◽  
Equilibrium Limit ◽  
Euclidean Quantum Field Theory

Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical system coupled to a thermal reservoir. Nonlinear phenomena in stochastic quantization arise when employing nonlinear Brownian motion as an underlying stochastic process. We discuss a novel formulation of the Higgs mechanism in QED.

scholarly journals Kinetic transition in the order–disorder transformation at a solid/liquid interface

2018 ◽  
Vol 376 (2113) ◽  
pp. 20170207 ◽  
Author(s):  
P. K. Galenko ◽  
I. G. Nizovtseva ◽  
K. Reuther ◽  
M. Rettenmayr
Keyword(s):  
Long Range ◽  
Phase Field ◽  
Order Parameter ◽  
Numerical Solutions ◽  
Liquid Interface ◽  
Range Order ◽  
Field Analysis ◽  
Range Order Parameter ◽  
Long Range Order ◽  
Kinetic Transition

Phase-field analysis for the kinetic transition in an ordered crystal structure growing from an undercooled liquid is carried out. The results are interpreted on the basis of analytical and numerical solutions of equations describing the dynamics of the phase field, the long-range order parameter as well as the atomic diffusion within the crystal/liquid interface and in the bulk crystal. As an example, the growth of a binary A 50 B 50 crystal is described, and critical undercoolings at characteristic changes of growth velocity and the long-range order parameter are defined. For rapidly growing crystals, analogies and qualitative differences are found in comparison with known non-equilibrium effects, particularly solute trapping and disorder trapping. The results and model predictions are compared qualitatively with results of the theory of kinetic phase transitions (Chernov 1968 Sov. Phys. JETP 26 , 1182–1190) and with experimental data obtained for rapid dendritic solidification of congruently melting alloy with order–disorder transition (Hartmann et al. 2009 Europhys. Lett. 87 , 40007 ( doi:10.1209/0295-5075/87/40007 )). This article is part of the theme issue ‘From atomistic interfaces to dendritic patterns’.

scholarly journals MONOPOLE-INSTANTON SOLUTIONS FOR THE MASSIVE SU(2) YANG–MILLS–HIGGS THEORY

2010 ◽  
Vol 25 (22) ◽  
pp. 4291-4300
Author(s):  
ROSY TEH ◽  
KHAI-MING WONG ◽  
PIN-WAI KOH
Keyword(s):  
Gauge Theories ◽  
Numerical Solutions ◽  
Higgs Field ◽  
Mass Term ◽  
Regular Solutions ◽  
Instanton Solution ◽  
Expectation Value ◽  
Yang Mills ◽  
Finite Action ◽  
Chern Simons

Monopole-instanton in topologically massive gauge theories in 2+1 dimensions with a Chern–Simons mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang–Mills–Higgs model with an additional Chern–Simons mass term in the action. Pisarski argued that there is a monopole-instanton solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern–Simons term strength and for several fixed values of Higgs field strength. The monopole-instanton's action is real but infinite. The action vanishes for large Chern–Simons term only when the Higgs field expectation value vanishes.

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