scholarly journals BRST INVARIANT CP1 MODEL THROUGH IMPROVED DIRAC QUANTIZATION

2001 ◽  
Vol 16 (21) ◽  
pp. 1361-1376 ◽  
Author(s):  
SOON-TAE HONG ◽  
YOUNG-JAI PARK ◽  
KUNIHARU KUBODERA ◽  
FRED MYHRER
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Rigid Rotator ◽  
Dirac Quantization ◽  
Collective Coordinate ◽  
Integral Procedure ◽  
Physical Fields ◽  
Invariant Gauge

The Batalin–Fradkin–Tyutin (BFT) scheme, which is an improved version of Dirac quantization, is applied to the CP1 model, and the compact form of a nontrivial first-class Hamiltonian is directly obtained by introducing the BFT physical fields. We also derive a BRST-invariant gauge fixed Lagrangian through the standard path-integral procedure. Furthermore, performing collective coordinate quantization we obtain energy spectrum of rigid rotator in the CP1 model. Exploiting the Hopf bundle, we also show that the CP1 model is exactly equivalent to the O(3) nonlinear sigma model at the canonical level.

scholarly journals DIRAC QUANTIZATION OF A NONMINIMAL GAUGED O(3) SIGMA MODEL

2005 ◽  
Vol 20 (13) ◽  
pp. 1005-1012 ◽  
Author(s):  
K. C. MENDES ◽  
R. R. LANDIM ◽  
C. A. S. ALMEIDA
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Nonminimal Coupling ◽  
Dirac Quantization ◽  
Chern Simons

The (2+1)-dimensional gauged O(3) nonlinear sigma model with Chern–Simons term is canonically quantized. Furthermore, we study a nonminimal coupling in this model implemented by means of a Pauli-type term. It is shown that the set of constraints of the model is modified by the introduction of the Pauli coupling. Moreover, we found that the quantum commutator relations in the nominimal case is independent of the Chern–Simons coefficient, in contrast to the minimal one.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

scholarly journals An emergent universe supported by a nonlinear sigma model

2009 ◽  
Vol 26 (7) ◽  
pp. 075017 ◽  
Author(s):  
A Beesham ◽  
S V Chervon ◽  
S D Maharaj
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Emergent Universe

scholarly journals Isolated skyrmions in the CP2 nonlinear sigma model with a Dzyaloshinskii-Moriya type interaction

2021 ◽  
Vol 103 (6) ◽  
Author(s):  
Yutaka Akagi ◽  
Yuki Amari ◽  
Nobuyuki Sawado ◽  
Yakov Shnir
Keyword(s):  
Sigma Model ◽  
Nonlinear Sigma Model ◽  
Type Interaction

scholarly journals DEFORMATION QUANTIZATION OF THE ISOTROPIC ROTATOR

1995 ◽  
Vol 10 (05) ◽  
pp. 399-407 ◽  
Author(s):  
A. STERN ◽  
I. YAKUSHIN
Keyword(s):  
Energy Spectrum ◽  
Quantum System ◽  
Chiral Symmetry ◽  
Deformation Quantization ◽  
Rigid Rotator

We perform a deformation quantization of the classical isotropic rigid rotator. The resulting quantum system is not invariant under the usual SU (2) × SU (2) chiral symmetry, but instead [Formula: see text]. We give the energy spectrum for the resulting system.

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