scholarly journals The applications of the gauge transformation for the BKP hierarchy

2014 ◽  
Vol 410 (2) ◽  
pp. 989-1001 ◽  
Author(s):  
Jipeng Cheng ◽  
Jingsong He
Keyword(s):  
Gauge Transformation ◽  
Bkp Hierarchy

Some results of the BKP hierarchy as the Kupershmidt reduction of the modified KP hierarchy

2020 ◽  
pp. 2050433
Author(s):  
Yi Yang ◽  
Xiaoli Wang ◽  
Jipeng Cheng
Keyword(s):  
Gauge Transformation ◽  
Wave Functions ◽  
Kp Hierarchy ◽  
Gauge Transformations ◽  
Bkp Hierarchy

In this paper, the BKP hierarchy is viewed as the Kupershmidt reduction of the modified KP hierarchy. Then based upon this fact, the gauge transformation of the BKP hierarchy are obtained again from the corresponding results of the modified KP hierarchy. Also the constrained BKP hierarchy is constructed from the constrained modified KP hierarchy, and the corresponding gauge transformations are investigated. Particularly, it is found that there is a new kind of gauge transformations generated by the wave functions in the constrained BKP hierarchy.

scholarly journals N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

scholarly journals LOOP VARIABLES AND GAUGE-INVARIANT INTERACTIONS — II

2001 ◽  
Vol 16 (10) ◽  
pp. 1679-1701 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Scattering Amplitudes ◽  
String Theory ◽  
Gauge Transformation ◽  
Dimensional Reduction ◽  
Mass Shell ◽  
Bosonic String ◽  
Higher Dimension ◽  
Gauge Invariant ◽  
Gauge Transformations ◽  
Variable Approach

We continue the discussion of our previous paper on writing down gauge-invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space–time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba–Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the free mass shell).

Smoothness of the action of the gauge transformation group on connections

1986 ◽  
Vol 27 (10) ◽  
pp. 2469-2474 ◽  
Author(s):  
M. C. Abbati ◽  
R. Cirelli ◽  
A. Manià ◽  
P. Michor
Keyword(s):  
Gauge Transformation ◽  
Transformation Group

scholarly journals EXTENSION OF THE POINCARÉ GROUP AND NON-ABELIAN TENSOR GAUGE FIELDS

2010 ◽  
Vol 25 (31) ◽  
pp. 5765-5785 ◽  
Author(s):  
GEORGE SAVVIDY
Keyword(s):  
Gauge Group ◽  
Gauge Transformation ◽  
Space Time ◽  
Gauge Fields ◽  
Poincaré Group ◽  
Matrix Representations ◽  
Poincare Group ◽  
Yang Mills ◽  
The Matrix ◽  
Transversal Plane

In the recently proposed generalization of the Yang–Mills theory, the group of gauge transformation gets essentially enlarged. This enlargement involves a mixture of the internal and space–time symmetries. The resulting group is an extension of the Poincaré group with infinitely many generators which carry internal and space–time indices. The matrix representations of the extended Poincaré generators are expressible in terms of Pauli–Lubanski vector in one case and in terms of its invariant derivative in another. In the later case the generators of the gauge group are transversal to the momentum and are projecting the non-Abelian tensor gauge fields into the transversal plane, keeping only their positively definite spacelike components.

Chiral bosonic field theories and the quantum Hall effect

2001 ◽  
Vol 79 (9) ◽  
pp. 1121-1131 ◽  
Author(s):  
P Bracken
Keyword(s):  
Hall Effect ◽  
Gauge Transformation ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Equation Of Motion ◽  
Hall Conductivity ◽  
Field Theories ◽  
Bosonic Field ◽  
Chern Simons

The gauge-transformation properties of the actions of certain scalar and Chern–Simons theories are investigated, including contributions from the boundary. By imposing chirality constraints on the fields, these types of theories can be used to describe the quantum Hall effect. It is shown that the corresponding equation of motion for the associated current for the theory generates an anomaly, which can be related directly to the Hall conductivity. PACS Nos.: 73.43, 03.70, 11.10, 11.30R

scholarly journals COVARIANT DESCRIPTION OF PARAMETRIZED NONRELATIVISTIC HAMILTONIAN SYSTEMS

2004 ◽  
Vol 19 (15) ◽  
pp. 2473-2493 ◽  
Author(s):  
MAURICIO MONDRAGÓN ◽  
MERCED MONTESINOS
Keyword(s):  
Phase Space ◽  
Gauge Transformation ◽  
Hamiltonian Systems ◽  
Symplectic Structure ◽  
Canonical Formalism ◽  
Extended Phase Space ◽  
Extended Phase ◽  
Algebra Of Observables ◽  
Covariant Description ◽  
Constraint Surface

The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism there exists a freedom in the choice of the symplectic structure on the extended phase space and in the choice of the equations that define the constraint surface with the only restriction that these two choices combine in such a way that any pair (of these two choices) generates the same gauge transformation. The consequence of this freedom on the algebra of observables is also discussed.

Sign in / Sign up

Export Citation Format

Share Document