ANOMALOUS MAGNETIC MOMENTUM IN 3D SPACE-TIME AND SELF-INTERACTING ANYONS

1991 ◽  
Vol 06 (38) ◽  
pp. 3525-3530 ◽  
Author(s):  
S. LATINKSY ◽  
D. SOROKIN
Keyword(s):  
Space Time ◽  
Statistical Properties ◽  
3D Space ◽  
Particular Solution ◽  
Chern Simons ◽  
Matter Fields

The statistical properties of matter fields with anomalous magnetic momentum interacting with the Chern-Simons-Maxwell (CSM) field are considered. It is shown that in the theory with pure Chern-Simons (CS) action the Semenoff gauge results in anyons with self-interaction. Even in the presence of the Maxwell term there is a particular solution for which the anyonic system with (current) x (current) self-interaction arises.

1D BOSONIZATION, 3D EXTENDED SUPERPARTICLES, CHERN-SIMONS, AND TWISTORS

1990 ◽  
Vol 05 (32) ◽  
pp. 2767-2772
Author(s):  
W. SIEGEL
Keyword(s):  
Extended Supersymmetry ◽  
Space Time ◽  
3D Space ◽  
Chern Simons

Various properties of simple and extended supersymmetry in 3D space-time are discussed and related.

THE PAULI TERM AS A GENERATOR OF FRACTIONAL SPIN

2011 ◽  
Vol 26 (19) ◽  
pp. 1427-1432
Author(s):  
J. S. N. FURTADO ◽  
F. A. S. NOBRE
Keyword(s):  
Fractional Statistics ◽  
Fractional Spin ◽  
Chern Simons ◽  
Matter Fields

In this work, we show that contrary to what is commonly accepted by the community, the Chern–Simons term is not essential to fractional statistics. A Lagrangian whose dynamics is governed only by the Pauli term coupled to matter fields leads to the fractional spin. Despite its simplicity, development of this Lagrangian gives rise to essentially the same terms that appear in Chern–Simons models, such as those reported by Nobre and Almeida.13,8,9

scholarly journals EDGE CURRENTS AND VERTEX OPERATORS FOR CHERN-SIMONS GRAVITY

1993 ◽  
Vol 08 (04) ◽  
pp. 653-682 ◽  
Author(s):  
G. BIMONTE ◽  
K.S. GUPTA ◽  
A. STERN
Keyword(s):  
Boundary Conditions ◽  
Vertex Operator ◽  
Vacuum State ◽  
Space Time ◽  
Moody Algebra ◽  
Functional Integrals ◽  
Gravitational Fields ◽  
Dimensional Gravity ◽  
Discrete Mass ◽  
Chern Simons

We apply elementary canonical methods for the quantization of 2+1 dimensional gravity, where the dynamics is given by E. Witten’s ISO(2, 1) Chern-Simons action. As in a previous work, our approach does not involve choice of gauge or clever manipulations of functional integrals. Instead, we just require the Gauss law constraint for gravity to be first class and also to be everywhere differentiable. When the spatial slice is a disc, the gravitational fields can either be unconstrained or constrained at the boundary of the disc. The unconstrained fields correspond to edge currents which carry a representation of the ISO(2, 1) Kac-Moody algebra. Unitary representations for such an algebra have been found using the method of induced representations. In the case of constrained fields, we can classify all possible boundary conditions. For several different boundary conditions, the field content of the theory reduces precisely to that of 1+1 dimensional gravity theories. We extend the above formalism to include sources. The sources take into account self-interactions. This is done by punching holes in the disc, and erecting an ISO(2, 1) Kac–Moody algebra on the boundary of each hole. If the hole is originally sourceless, a source can be created via the action of a vertex operator V. We give an explicit expression for V. We shall show that when acting on the vacuum state, it creates particles with a discrete mass spectrum. The lowest mass particle induces a cylindrical space-time geometry, while higher mass particles give an n fold covering of the cylinder. The vertex operator therefore creates cylindrical space-time geometries from the vacuum.

scholarly journals ON THE UNIQUENESS OF D = 11 INTERACTIONS AMONG A GRAVITON, A MASSLESS GRAVITINO AND A THREE-FORM II: THREE-FORM AND GRAVITINI

2008 ◽  
Vol 23 (30) ◽  
pp. 4841-4859 ◽  
Author(s):  
EUGEN-MIHĂIŢĂ CIOROIANU ◽  
EUGEN DIACONU ◽  
SILVIU CONSTANTIN SĂRARU
Keyword(s):  
Master Equation ◽  
Gauge Field ◽  
Space Time ◽  
Free Solution ◽  
Coupling Constant ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Lorentz Covariance ◽  
Brst Cohomology ◽  
Chern Simons

The interactions that can be introduced between a massless Rarita–Schwinger field and an Abelian three-form gauge field in 11 space–time dimensions are analyzed in the context of the deformation of the "free" solution of the master equation combined with local BRST cohomology. Under the hypotheses of smoothness of the interactions in the coupling constant, locality, Poincaré invariance, Lorentz covariance, and the presence of at most two derivatives in the Lagrangian of the interacting theory (the same number of derivatives as in the free Lagrangian), we prove that there are neither cross-couplings nor self-interactions for the gravitino in D = 11. The only possible term that can be added to the deformed solution to the master equation is nothing but a generalized Chern–Simons term for the three-form gauge field, which brings contributions to the deformed Lagrangian, but does not modify the original, Abelian gauge transformations.

scholarly journals Worldlines and worldsheets for non-abelian lattice field theories: Abelian color fluxes and Abelian color cycles

2018 ◽  
Vol 175 ◽  
pp. 11007 ◽  
Author(s):  
Christof Gattringer ◽  
Daniel Göschl ◽  
Carlotta Marchis
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Space Time ◽  
Field Theories ◽  
Gauge Fields ◽  
Chiral Model ◽  
Staggered Fermions ◽  
Lattice Field ◽  
Principal Chiral Model ◽  
Matter Fields

We discuss recent developments for exact reformulations of lattice field theories in terms of worldlines and worldsheets. In particular we focus on a strategy which is applicable also to non-abelian theories: traces and matrix/vector products are written as explicit sums over color indices and a dual variable is introduced for each individual term. These dual variables correspond to fluxes in both, space-time and color for matter fields (Abelian color fluxes), or to fluxes in color space around space-time plaquettes for gauge fields (Abelian color cycles). Subsequently all original degrees of freedom, i.e., matter fields and gauge links, can be integrated out. Integrating over complex phases of matter fields gives rise to constraints that enforce conservation of matter flux on all sites. Integrating out phases of gauge fields enforces vanishing combined flux of matter-and gauge degrees of freedom. The constraints give rise to a system of worldlines and worldsheets. Integrating over the factors that are not phases (e.g., radial degrees of freedom or contributions from the Haar measure) generates additional weight factors that together with the constraints implement the full symmetry of the conventional formulation, now in the language of worldlines and worldsheets. We discuss the Abelian color flux and Abelian color cycle strategies for three examples: the SU(2) principal chiral model with chemical potential coupled to two of the Noether charges, SU(2) lattice gauge theory coupled to staggered fermions, as well as full lattice QCD with staggered fermions. For the principal chiral model we present some simulation results that illustrate properties of the worldline dynamics at finite chemical potentials.

scholarly journals Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D

2017 ◽  
Vol 45 ◽  
pp. 1760005 ◽  
Author(s):  
Ivan Morales ◽  
Bruno Neves ◽  
Zui Oporto ◽  
Olivier Piguet
Keyword(s):  
Dimensional Space ◽  
Cosmological Solution ◽  
Space Time ◽  
Gravitation Theory ◽  
Simons Theory ◽  
De Sitter ◽  
Field Equations ◽  
Sitter Group ◽  
Dimensional Space Time ◽  
Chern Simons

We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

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