SOLITON OPERATORS OF FRACTIONAL SPIN IN 2+1 DIMENSIONS

1991 ◽  
Vol 06 (08) ◽  
pp. 1369-1383 ◽  
Author(s):  
DIMITRA KARABALI
Keyword(s):  
Configuration Space ◽  
Sigma Model ◽  
Canonical Quantization ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Fractional Spin ◽  
Spin And Statistics

Soliton operators of fractional spin and statistics are constructed using canonical quantization of the O(3) nonlinear sigma model with a topological Hopf action in 2+1 dimensions. The role of the Hopf term as the nontrivial holonomy of a flat connection in the configuration space is emphasized.

Fractional spin via canonical quantization of the O(3) nonlinear sigma model

1986 ◽  
Vol 271 (3-4) ◽  
pp. 417-428 ◽  
Author(s):  
Mark J. Bowick ◽  
Dimitra Karabali ◽  
L.C.R. Wijewardhana
Keyword(s):  
Sigma Model ◽  
Canonical Quantization ◽  
Nonlinear Sigma Model ◽  
Fractional Spin

Fractional spin via canonical quantization of the O(3) nonlinear sigma model

1986 ◽  
Vol 271 (2) ◽  
pp. 417-428 ◽  
Author(s):  
Mark J. Bowick ◽  
Dimitra Karabali ◽  
L.C.R. Wijewardhana
Keyword(s):  
Sigma Model ◽  
Canonical Quantization ◽  
Nonlinear Sigma Model ◽  
Fractional Spin

Symmetries from the solution manifold

2015 ◽  
Vol 12 (08) ◽  
pp. 1560016 ◽  
Author(s):  
Víctor Aldaya ◽  
Julio Guerrero ◽  
Francisco F. Lopez-Ruiz ◽  
Francisco Cossío
Keyword(s):  
Symplectic Structure ◽  
Vector Fields ◽  
Sigma Model ◽  
Canonical Quantization ◽  
General Concept ◽  
Noether Theorem ◽  
Preliminary Step ◽  
Hamiltonian Vector Fields ◽  
Solution Manifold

We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré–Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton–Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.

scholarly journals QUANTUM HALL SKYRMIONS IN THE FRAMEWORK OF O(4) NONLINEAR SIGMA MODEL

2004 ◽  
Vol 18 (02) ◽  
pp. 171-184
Author(s):  
B. BASU ◽  
S. DHAR ◽  
P. BANDYOPADHYAY
Keyword(s):  
Sigma Model ◽  
Quantum Hall ◽  
Nonlinear Sigma Model ◽  
New Framework ◽  
Spin And Statistics

A new framework for quantum Hall skyrmions in O(4) nonlinear sigma model is studied here. The size and energy of the skyrmions are determined incorporating the quartic stability term in the Lagrangian. Moreover, the introduction of a θ-term determines the spin and statistics of these skyrmions.

scholarly journals EXACT SOLUTIONS OF SO(3) NONLINEAR SIGMA MODEL IN A CONIC SPACE BACKGROUND

2005 ◽  
Vol 14 (11) ◽  
pp. 1927-1940 ◽  
Author(s):  
V. B. BEZERRA ◽  
C. ROMERO ◽  
SERGEY CHERVON
Keyword(s):  
Exact Solutions ◽  
Minkowski Space ◽  
Sigma Model ◽  
Space Time ◽  
Nonlinear Sigma Model ◽  
Field Equations ◽  
Minkowski Space Time ◽  
Deficit Angle ◽  
Spatial Coordinates

We consider a nonlinear sigma model coupled to the metric of a conic space. We obtain restrictions for a nonlinear sigma model to be a source of the conic space. We then study a nonlinear sigma model in the conic space background. We find coordinate transformations which reduce the chiral fields equations in the conic space background to field equations in Minkowski space–time. This enables us to apply the same methods for obtaining exact solutions in Minkowski space–time to the case of a conic space–time. In the case the solutions depend on two spatial coordinates we employ Ivanov's geometrical ansatz. We give a general analysis and also present classes of solutions in which there is dependence on three and four coordinates. We discuss with special attention the intermediate, instanton and meron solutions and their analogous in the conic space. We find differences in the total actions and topological charges of these solutions and discuss the role of the deficit angle.

scholarly journals FURTHER COMMENTS ON THE SYMMETRIC SUBTRACTION OF THE NONLINEAR SIGMA MODEL

2008 ◽  
Vol 23 (02) ◽  
pp. 211-232 ◽  
Author(s):  
DANIELE BETTINELLI ◽  
RUGGERO FERRARI ◽  
ANDREA QUADRI
Keyword(s):  
Sigma Model ◽  
Dimensional Regularization ◽  
Formal Proof ◽  
Tree Level ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Subtraction Procedure ◽  
Feynman Rules ◽  
Local Functional ◽  
Two Parameters

Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled to the nonlinear sigma model constraint (flat connection formalism). The construction is based on a local functional equation, which overcomes the problems due to the presence (already at one loop) of nonchiral symmetric divergences. The subtraction procedure of the divergences in the loop expansion is performed by means of minimal subtraction of properly normalized amplitudes in dimensional regularization. In this paper we complete the study of this subtraction procedure by giving the formal proof that it is symmetric to all orders in the loopwise expansion. We provide further arguments on the issue that, within our subtraction strategy, only two parameters can be consistently used as physical constants.

NOVEL TOPOLOGICAL FEATURES OF THE O(3) NONLINEAR SIGMA MODEL IN 2+1 DIMENSIONS

1989 ◽  
Vol 04 (15) ◽  
pp. 1457-1462 ◽  
Author(s):  
T.R. GOVINDARAJAN ◽  
R. SHANKAR
Keyword(s):  
Boundary Conditions ◽  
Fundamental Group ◽  
Configuration Space ◽  
Periodic Boundary ◽  
Sigma Model ◽  
Periodic Boundary Conditions ◽  
Nonlinear Sigma Model ◽  
Homotopic Class ◽  
Hopf Invariant ◽  
Topological Features

We investigate the configuration space topology of the O(3) nonlinear sigma model in 2+1 dimensions, when the fields satisfy periodic boundary conditions. We show the fundamental group of the configuration space to be nonabelian. We associate three integer invariants to each homotopic class of paths, one of which is related to the Hopf invariant. We find that consistent quantization requires the coefficient of the Hopf term in the action to be 0 to π.

scholarly journals Vector–Tensor Duality

1997 ◽  
Vol 12 (35) ◽  
pp. 2699-2705 ◽  
Author(s):  
Amitabha Lahiri
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Flat Connection ◽  
Mass Generation ◽  
Goldstone Bosons ◽  
Abelian Case ◽  
Vector Bosons ◽  
Topological Mass

A dynamical non-Abelian two-form potential gives masses to vector bosons via a topological coupling.1 Unlike in the Abelian case, the two-form cannot be dualized to Goldstone bosons. Duality is restored by coupling a flat connection to the theory in a particular way, and the new action is then dualized to a nonlinear sigma model. The presence of the flat connection is crucial, which saves the original mechanism of Higgs-free topological mass generation from being dualized to a sigma model.

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