scholarly journals Coulomb-quantum oscillator correspondence in two dimension, pure gauge field and half-quantized vortex

2019 ◽  
Vol 34 (16) ◽  
pp. 1950128 ◽  
Author(s):  
S. C. Tiwari
Keyword(s):  
Wave Function ◽  
Gauge Field ◽  
Vortex Structure ◽  
Quantized Vortex ◽  
Quantum Oscillator ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Hadron Spectrum ◽  
Complete Treatment ◽  
Local Gauge Transformation

Isotropic oscillator and Coulomb problems are known to have interesting correspondence. We focus on two-dimensional (2D) quantum problems and present complete treatment on the correspondence including the Schrödinger equation, eigenfunctions and eigenvalues, and the integrals of motion. We find only partial equivalence. The wave function correspondence is examined introducing local gauge transformation and the emergence of half-quantized vortex with the associated spin-half is established. Vortex structure of the electron proposed by us and the origin of charge are discussed in this paper. Outlook on the implications for QCD and hadron spectrum is outlined.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

scholarly journals Vertex Corrections in Gauge Theories for Two-dimensional Condensed Matter Systems

1998 ◽  
Vol 12 (16n17) ◽  
pp. 1673-1692 ◽  
Author(s):  
Peter Kopietz
Keyword(s):  
Gauge Field ◽  
Condensed Matter ◽  
Finite Energy ◽  
Energy Scale ◽  
Gauge Fields ◽  
Logarithmic Correction ◽  
Two Dimensional ◽  
Numerical Constant ◽  
Self Energy ◽  
Vertex Corrections

We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1/qη, 1<η≤ 2, the fermionic self-energy without vertex corrections vanishes for small frequencies ω as Σ(ω)∝ ωγ with γ=2/(1+η)<1. We show that inclusion of the leading radiative correction to the fermion-gauge field vertex leads to Σ(ω)∝ωγ [1-aη ln (ω0/ω)], where aη is a positive numerical constant and ω0 is some finite energy scale. The negative logarithmic correction is consistent with the scenario that higher order vertex corrections push the exponent γ to larger values.

scholarly journals ONE-ELECTRON SPECTRAL WEIGHT OF DOPED MOTT INSULATORS IN GAUGE FIELD THEORY APPROACH

1996 ◽  
Vol 10 (27) ◽  
pp. 3727-3736
Author(s):  
H.C. LEE
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Spectral Weight ◽  
Low Energy ◽  
Vertex Correction ◽  
Gauge Field Theory ◽  
Mott Insulators ◽  
Theory Approach ◽  
Two Dimensional ◽  
Second Order Perturbation Theory

The electron spectral weight of doped Mott insulators based on the two-dimensional slave boson gauge field theory is studied. The vertex correction with static gauge field is calculated in the second order perturbation theory. The vertex correction is found to be singular at low energy and requires non-perturbative treatments.

scholarly journals Integrable and Superintegrable Systems with Higher Order Integrals of Motion: Master Function Formalism

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Z. Alizadeh ◽  
H. Panahi
Keyword(s):  
Quantum Mechanics ◽  
Higher Order ◽  
Supersymmetric Quantum Mechanics ◽  
Two Dimensional ◽  
Integrals Of Motion ◽  
Function Formalism ◽  
Superintegrable Systems ◽  
Master Function

We construct two-dimensional integrable and superintegrable systems in terms of the master function formalism and relate them to Mielnik’s and Marquette’s construction in supersymmetric quantum mechanics. For two different cases of the master functions, we obtain two different two-dimensional superintegrable systems with higher order integrals of motion.

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