BOSE-FERMI TRANSMUTATION 2+1 DIMENSIONS: EFFECT OF SELF-INTERACTIONS AND THE MAXWELL TERM

1991 ◽  
Vol 06 (26) ◽  
pp. 2379-2387 ◽  
Author(s):  
R. SHANKAR ◽  
M. SIVAKUMAR
Keyword(s):  
Mean Field ◽  
Scalar Fields ◽  
Coupling Constants ◽  
Abelian Gauge ◽  
Charged Scalar ◽  
Long Wavelength ◽  
Wavelength Approximation ◽  
The Mean ◽  
Chern Simons ◽  
Fermion Current

We show the partition function of self-interacting charged scalar fields coupled with Abelian gauge fields governed by Maxwell-Chern-Simons action is equivalent in the long-wavelength approximation to that of a massive four-Fermi theory. The coupling constants and mass of the fermionic theory is explicitly related to those of the bosonic theory. The gauge invariant charged scalar current is shown to be transmuted to fermion current. The physical mass of the fermion is computed at the mean field level and shown to be finite at large self-coupling.

ON BOSE-FERMI EQUIVALENCE IN A U(1) GAUGE THEORY WITH CHERN-SIMONS ACTION

1990 ◽  
Vol 05 (08) ◽  
pp. 593-603 ◽  
Author(s):  
N. SHAJI ◽  
R. SHANKAR ◽  
M. SIVAKUMAR
Keyword(s):  
Dirac Fermion ◽  
Complex Scalar ◽  
Abelian Gauge ◽  
Long Wavelength ◽  
Integral Methods ◽  
Fermion Fields ◽  
Long Wavelength Approximation ◽  
Complex Scalar Field ◽  
Wavelength Approximation ◽  
Chern Simons

We show, using path integral methods, that a complex scalar field in 2+1 dimensions coupled to an abelian gauge field with Chern-Simons action is equivalent to a free Dirac fermion. We show the equivalence of the vacuum functional and construct the fermion fields explicitly. Our proof is independent of the long wavelength approximation.

GAUGE THEORY OF ANTIFERROMAGNETISM IN TWO DIMENSIONS FOR LARGE RANK SYMMETRY GROUP

1990 ◽  
Vol 04 (01) ◽  
pp. 17-28 ◽  
Author(s):  
D. V. KHVESHCHENKO ◽  
P. B. WIEGMANN
Keyword(s):  
Gauge Theory ◽  
Symmetry Group ◽  
Mean Field ◽  
Two Dimensions ◽  
Magnetic Systems ◽  
Large Rank ◽  
Long Wavelength ◽  
The Mean ◽  
Chern Simons ◽  
Spin And Statistics

We examine long wavelength fluctuations in two-dimensional magnetic systems with the symmetry group of a large rank N. The mean field solution is obtained and the existence of the parity-violating ground state is established. On the basis of the 1/N expansion, an effective gauge theory containing the Chern-Simons term is derived, which allows one to obtain a spectrum, spin and statistics of long wavelength excitations.

scholarly journals Several Physical Properties of Two Interacting Complex Scalar Fields at Finite Density

2011 ◽  
Vol 21 (1) ◽  
pp. 1
Author(s):  
Tran Huu Phat ◽  
Phan Thi Duyen
Keyword(s):  
Mean Field ◽  
Scalar Fields ◽  
Meissner Effect ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Goldstone Theorem ◽  
Complex Scalar ◽  
Finite Density ◽  
Chemical Potentials ◽  
The Mean

The two interacting complex scalar fields at finite density is considered in the mean field approximation. It is shown that although the symmetry is spontaneously broken for the chemical potentials bigger than the meson masses in vacuum, but the Goldstone theorem is not preserved in broken phase. Then two mesons are condensed and their condensates turn out to be two-gap superconductor which is signaled by the appearance of the Meissner effect as well as the Abrikosov and non-Abrikosov vortices. Finally, there exhibits domain wall which is the plane, where two condensates flowing in opposite directions collide and generate two types of vortices with cores in the wall.

scholarly journals BOSONIC CHERN-SIMONS FIELD THEORY OF ANYON SUPERCONDUCTIVITY

1992 ◽  
Vol 07 (28) ◽  
pp. 2627-2636
Author(s):  
NATHAN WEISS
Keyword(s):  
Field Theory ◽  
Particle Density ◽  
Equations Of Motion ◽  
Mean Field ◽  
Meissner Effect ◽  
Quantum Corrections ◽  
Simple Explanation ◽  
Field Solution ◽  
The Mean ◽  
Chern Simons

We study the quantum field theory of non-relativistic bosons coupled to a Chern-Simons gauge field at nonzero particle density. This field theory is relevant to the study of anyon superconductors in which the anyons are described as bosons with a statistical interaction. We show that it is possible to find a mean field solution to the equations of motion for this system which has some of the features of Bose condensation. The mean field solution consists of a lattice of vortices each carrying a single quantum of statistical magnetic flux. We speculate on the effects of the quantum corrections to this mean field solution. We argue that the mean field solution is only stable under quantum corrections if the Chern-Simons coefficient N=2πθ/g2 is an integer. Consequences for anyon superconductivity are presented. A simple explanation for the Meissner effect in this system is discussed.

EFFECTIVE P, T RESTORATION IN CHERN–SIMONS SUPERCONDUCTIVITY

1994 ◽  
Vol 08 (08n09) ◽  
pp. 561-570 ◽  
Author(s):  
S. S. MANDAL ◽  
S. RAMASWAMY ◽  
V. RAVISHANKAR
Keyword(s):  
Dielectric Constant ◽  
Magnetic Susceptibility ◽  
Normal State ◽  
Time Reversal ◽  
Finite Temperature ◽  
Narrow Range ◽  
Mean Field ◽  
Smooth Transition ◽  
The Mean ◽  
Chern Simons

We present an analysis of the finite temperature Chern–Simons superconductivity model within the mean field framework. Using analytical and numerical means we compute the changes in the magnetic susceptibility, conductivity, the dielectric constant, and the specific heat as the temperature is increased. Over a narrow range of temperatures the properties of the system show a smooth transition to the normal state. Accompanying this is the near vanishing of the off-diagonal conductivity, signifying the effective restoration of parity and time reversal symmetries.

FERMIONIZATION OF SELF-INTERACTING CHARGED SCALAR FIELDS COUPLED TO ABELIAN CHERN-SIMONS GAUGE FIELDS IN 2+1 DIMENSIONS

1991 ◽  
Vol 06 (07) ◽  
pp. 553-558 ◽  
Author(s):  
SAMIR K. PAUL ◽  
R. SHANKAR ◽  
M. SIVAKUMAR
Keyword(s):  
Perturbation Theory ◽  
Scalar Fields ◽  
Gauge Fields ◽  
Charged Scalar ◽  
Text Interaction ◽  
Chern Simons

We show, to all orders in perturbation theory, that the theory of charged scalars in 2+1 dimensions with a |ϕ|4 self-interaction coupled to Chern-Simons gauge fields is equivalent to a theory of self-interacting fermions with a [Formula: see text] interaction.

BULK PROPERTIES OF CHERN–SIMONS SUPERCONDUCTIVITY AT FINITE TEMPERATURES

1994 ◽  
Vol 08 (22) ◽  
pp. 3095-3135 ◽  
Author(s):  
S. S. MANDAL ◽  
S. RAMASWAMY ◽  
V. RAVISHANKAR
Keyword(s):  
Mean Field Theory ◽  
Free Field ◽  
Mean Field ◽  
Form Factors ◽  
Spin Correlation ◽  
Thermal Fluctuations ◽  
Correlation Factor ◽  
Electromagnetic Response ◽  
The Mean ◽  
Chern Simons

We study Chern–Simons (CS) superconductivity at finite temperatures for a system of two dimensional 'spin-1/2' fermions which are minimally coupled to both the CS and Maxwell gauge fields. We evaluate the electromagnetic response of the system as well as its thermodynamic properties within the mean field formalism. Our results for magnetic susceptibility, conductivity and dielectric constant show a sharp transition to the normal state over a narrow range of temperatures. The vanishing of the off-diagonal conductivity due to a corresponding fall in parity and time reversal [Formula: see text] violating correlation factor may be interpreted to be an effective restoration of [Formula: see text] symmetries in the macroscopic state. We find that the spin correlation function has a negligibly small numerical value at all temperatures, which implies that the thermal fluctuations dominate over the quantum fluctuations in the spin state. To explore the validity of mean field theory at high temperatures (HT), we compare the responses as well as the form factors for both mean field and free field (perturbative) formalism and find that they are essentially equivalent at HT. Finally, we present a coarse criterion for the validity of the mean field ansatz by regulating the CS Lagrangian with a Maxwell term.

On the mean field type bubbling solutions for Chern–Simons–Higgs equation

2018 ◽  
Vol 338 ◽  
pp. 1141-1188 ◽  
Author(s):  
Chang-Shou Lin ◽  
Shusen Yan
Keyword(s):  
Mean Field ◽  
Field Type ◽  
The Mean ◽  
Chern Simons

scholarly journals Uniqueness of bubbling solutions of mean field equations with non-quantized singularities

2020 ◽  
pp. 2050038
Author(s):  
Lina Wu ◽  
Lei Zhang
Keyword(s):  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Mean Field ◽  
Field Equations ◽  
Field Type ◽  
Dirac Mass ◽  
Mean Field Equations ◽  
The Mean ◽  
Chern Simons

For singular mean field equations defined on a compact Riemann surface, we prove the uniqueness of bubbling solutions if some blowup points coincide with the singularities of the Dirac data. If the strength of the Dirac mass at each blowup point is not a multiple of [Formula: see text], we prove that bubbling solutions are unique. This paper extends previous results of Lin-Yan [C. S. Lin and S. S. Yan, On the mean field type bubbling solutions for Chern–Simons–Higgs equation, Adv. Math. 338 (2018) 1141–1188] and Bartolucci et al. [D. Bartolucci, A. Jevnikar, Y. Lee and W. Yang, Uniqueness of bubbling solutions of mean field equations, J. Math. Pures Appl. (9) 123 (2019) 78–126].

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