Gauge transformations of the multi-component BKP and CKP hierarchies

2017 ◽  
Vol 31 (30) ◽  
pp. 1750280 ◽  
Author(s):  
Tao Song ◽  
Chuanzhong Li ◽  
Xinyue Li
Keyword(s):  
Gauge Transformation ◽  
Gauge Transformations ◽  
Ckp Hierarchy ◽  
The One

In this paper, we give the definition and multi-folds gauge transformations of the multi-component B-type Kakomtsev–Petviashvili (MBKP) hierarchy and multi-component CKP (MCKP) hierarchy. Besides, we derive new solutions after the one-fold gauge transformation of the MBKP hierarchy. The remarkable differences between the BKP (CKP) hierarchy and the MBKP(MCKP) hierarchy are given in this paper. What is more, we introduce some facts about the multi-component constrained BKP and multi-component constrained CKP hierarchies including some obstacles and some new multi-component equations.

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).

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.

GEOMETRIC REGULARIZATION AND GAUGE INVARIANCE IN CHERN–SIMONS THEORIES

1992 ◽  
Vol 07 (02) ◽  
pp. 235-256 ◽  
Author(s):  
MANUEL ASOREY ◽  
FERNANDO FALCETO
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauge Condition ◽  
Simons Theory ◽  
Coupling Constant ◽  
Gauge Transformations ◽  
Yang Mills ◽  
The One ◽  
Chern Simons ◽  
Three Dimensional Space

Some perturbative aspects of Chern–Simons theories are analyzed in a geometric-regularization framework. In particular, we show that the independence from the gauge condition of the regularized theory, which insures its global meaning, does impose a new constraint on the parameters of the regularization. The condition turns out to be the one that arises in pure or topologically massive Yang–Mills theories in three-dimensional space–times. One-loop calculations show the existence of nonvanishing finite renormalizations of gauge fields and coupling constant which preserve the topological meaning of Chern–Simons theory. The existence of a (finite) gauge-field renormalization at one-loop level is compensated by the renormalization of gauge transformations in such a way that the one-loop effective action remains gauge-invariant with respect to renormalized gauge transformations. The independence of both renormalizations from the space–time volume indicates the topological nature of the theory.

scholarly journals The Electromagnetic and Proca Fields Revisited: A Unified Quantization

1997 ◽  
Vol 12 (20) ◽  
pp. 3609-3623 ◽  
Author(s):  
Víctor Aldaya ◽  
Manuel Calixto ◽  
Miguel Navarro
Keyword(s):  
Gauge Transformation ◽  
Vector Fields ◽  
Mass Shell ◽  
Local Group ◽  
Equations Of Motion ◽  
Generalized Equations ◽  
Photon Mass ◽  
New Approach ◽  
Gauge Transformations ◽  
Group Law

Quantizing the electromagnetic field with a group formalism faces the difficulty of how to turn the traditional gauge transformation of the vector potential, Aμ(x) → Aμ(x) + ∂μ φ (x), into a group law. In this paper, it is shown that the problem can be solved by looking at gauge transformations in a slightly different manner which, in addition, does not require introducing any BRST-like parameter. This gauge transformation does not appear explicitly in the group law of the symmetry but rather as the trajectories associated with generalized equations of motion generated by vector fields with null Noether invariants. In the new approach the parameters of the local group, U (1)(x,t), acquire dynamical content outside the photon mass shell, a fact which also allows a unified quantization of both the electromagnetic and Proca fields.

scholarly journals Hamiltonian analysis of a topological theory in the presence of boundaries

2019 ◽  
Vol 28 (06) ◽  
pp. 1950075 ◽  
Author(s):  
Alejandro Corichi ◽  
Tatjana Vukašinac
Keyword(s):  
Boundary Conditions ◽  
Degrees Of Freedom ◽  
Boundary Theory ◽  
Gauge Transformations ◽  
Canonical Variables ◽  
Dimensional Spacetime ◽  
Constraint Structure ◽  
Generic Boundary ◽  
The One ◽  
Hamiltonian Analysis

We perform the canonical Hamiltonian analysis of a topological gauge theory, that can be seen both as a theory defined on a four-dimensional spacetime region with boundaries — the bulk theory —, or as a theory defined on the boundary of the region — the boundary theory —. In our case, the bulk theory is given by the 4-dimensional [Formula: see text] Pontryagin action and the boundary one is defined by the [Formula: see text] Chern–Simons action. We analyze the conditions that need to be imposed on the bulk theory so that the total Hamiltonian, smeared constraints and generators of gauge transformations be well defined (differentiable) for generic boundary conditions. We pay special attention to the interplay between the constraints and boundary conditions in the bulk theory on the one side, and the constraints in the boundary theory, on the other side. We illustrate how both theories are equivalent, despite the different canonical variables and constraint structure, by explicitly showing that they both have the same symmetries, degrees of freedom and observables.

scholarly journals GAUGE TRANSFORMATIONS OF THE NON-ABELIAN TWO-FORM

2002 ◽  
Vol 17 (25) ◽  
pp. 1643-1650 ◽  
Author(s):  
AMITABHA LAHIRI
Keyword(s):  
Vector Field ◽  
Gauge Transformation ◽  
Degrees Of Freedom ◽  
Local Symmetry ◽  
Classical Field ◽  
Field Theories ◽  
Gauge Transformations ◽  
Four Dimensions ◽  
Local Constraint ◽  
Classical Field Theories

A novel inhomogeneous gauge transformation law is proposed for a non-Abelian adjoint two-form potential in four dimensions. Rules for constructing actions invariant under this are given. The auxiliary vector field which appears in some of these theories transforms like a second connection. Some of the actions also show a local symmetry which is not generated by any local constraint, a novelty for classical field theories. Both types of symmetries change the action by total divergences, suggesting that boundary degrees of freedom have to be taken into account for local quantization.

scholarly journals THE RADION AND THE PERTURBATIVE METRIC IN RS1

2004 ◽  
Vol 19 (01) ◽  
pp. 37-47 ◽  
Author(s):  
MANUEL TOHARIA
Keyword(s):  
Gauge Transformation ◽  
Linear Expansion ◽  
Einstein Equations ◽  
Brane Model ◽  
The One

We calculate the linearized metric perturbations in the five-dimensional two-brane model of Randall and Sundrum. In a carefully chosen gauge, we write down and decouple Einstein equations for the perturbations and get the final and simple perturbative metric ansatz. This ansatz turns out to be equal to the linear expansion of the metric solution of Charmousis et al.1 We show that this ansatz, the metric ansatz of Boos et al.2 and the one of Das and Mitov3 are not incompatible, as it appears on the surface, but completely equivalent by an allowed gauge transformation that we give.

The Successive Applications of Two Types of Gauge Transformations for the q-Deformed Modified Kadomtsev-Petviashvili Hierarchy

2018 ◽  
Vol 73 (4) ◽  
pp. 345-356 ◽  
Author(s):  
Na Li ◽  
Jipeng Cheng
Keyword(s):  
Gauge Transformation ◽  
Gauge Transformations

AbstractIn this paper, the successive applications of two types of gauge transformation TD and TI for the q-deformed modified Kadomtsev-Petviashvili hierarchy are discussed. It is found that TD and TI can commute with each other. We mainly studied products of n terms of TD and k terms of TI in three cases for different values of n and k. Finally, some applications of these results are also given.

scholarly journals Note on the bundle geometry of field space, variational connections, the dressing field method, & presymplectic structures of gauge theories over bounded regions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
J. François ◽  
N. Parrini ◽  
N. Boulanger
Keyword(s):  
Gauge Theories ◽  
Field Method ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Field Independent ◽  
Field Dependent ◽  
Presymplectic Structure ◽  
The One ◽  
Phase Space Methods ◽  
Special Case

Abstract In this note, we consider how the bundle geometry of field space interplays with the covariant phase space methods so as to allow to write results of some generality on the presymplectic structure of invariant gauge theories coupled to matter. We obtain in particular the generic form of Noether charges associated with field-independent and field-dependent gauge parameters, as well as their Poisson bracket. We also provide the general field-dependent gauge transformations of the presymplectic potential and 2-form, which clearly highlights the problem posed by boundaries in generic situations. We then conduct a comparative analysis of two strategies recently considered to evade the boundary problem and associate a modified symplectic structure to a gauge theory over a bounded region: namely the use of edge modes on the one hand, and of variational connections on the other. To do so, we first try to give the clearest geometric account of both, showing in particular that edge modes are a special case of a differential geometric tool of gauge symmetry reduction known as the “dressing field method”. Applications to Yang-Mills theory and General Relativity reproduce or generalise several results of the recent literature.

Gauge transformations of constrained discrete modified KP systems with self-consistent sources

2017 ◽  
Vol 14 (04) ◽  
pp. 1750052 ◽  
Author(s):  
Ran Huang ◽  
Tao Song ◽  
Chuanzhong Li
Keyword(s):  
Gauge Transformation ◽  
Kp Hierarchy ◽  
Gauge Transformations ◽  
Self Consistent ◽  
Basic Facts ◽  
Discrete Kp ◽  
Ghost Symmetry

In this paper, we firstly recall some basic facts about the discrete KP(d-KP) and discrete modified KP(d-mKP) hierarchies, and then we find that d-KP hierarchy and d-mKP hierarchy are linked by a gauge transformation. What’s more, we give three gauge transformation operators of the d-mKP hierarchy and give their successive applications. We further construct the ghost symmetry and use this symmetry to give the definition the d-mKP hierarchy with self-consistent sources. We also give gauge transformations of a newly defined constrained d-mKP(cd-mKP) hierarchy and the constrained d-mKP hierarchy with self-consistent sources(cd-mKPHSCSs).

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