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).

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 Ghost symmetry of the discrete KP hierarchy

2015 ◽  
Vol 180 (4) ◽  
pp. 815-832 ◽  
Author(s):  
Chuanzhong Li ◽  
Jipeng Cheng ◽  
Kelei Tian ◽  
Maohua Li ◽  
Jingsong He
Keyword(s):  
Kp Hierarchy ◽  
Discrete Kp Hierarchy ◽  
Discrete Kp ◽  
Ghost Symmetry

scholarly journals THE GAUGE TRANSFORMATION OF THE CONSTRAINED SEMI-DISCRETE KP HIERARCHY

2013 ◽  
Vol 27 (06) ◽  
pp. 1350043 ◽  
Author(s):  
MAOHUA LI ◽  
JIPENG CHENG ◽  
JINGSONG HE
Keyword(s):  
Gauge Transformation ◽  
Generating Functions ◽  
Suitable Choice ◽  
Kp Hierarchy ◽  
Lax Operator ◽  
Discrete Kp Hierarchy ◽  
Discrete Kp

In this paper, the gauge transformation of the constrained semi-discrete KP(cdKP) hierarchy is constructed explicitly by the suitable choice of the generating functions. Under the m-step successive gauge transformation Tm, we give the transformed (adjoint) eigenfunctions and the τ-function of the transformed Lax operator of the cdKP hierarchy.

The gauge transformations of the constrainedq-deformed KP hierarchy

2018 ◽  
Vol 32 (16) ◽  
pp. 1850176 ◽  
Author(s):  
Lumin Geng ◽  
Huizhan Chen ◽  
Na Li ◽  
Jipeng Cheng
Keyword(s):  
Gauge Transformation ◽  
Generating Functions ◽  
Kp Hierarchy ◽  
Gauge Transformations ◽  
Lax Operator ◽  
Usual Case ◽  
Additional Constraints

In this paper, we mainly study the gauge transformations of the constrained q-deformed Kadomtsev–Petviashvili (q-KP) hierarchy. Different from the usual case, we have to consider the additional constraints on the Lax operator of the constrained q-deformed KP hierarchy, since the form of the Lax operator must be kept when constructing the gauge transformations. For this reason, the selections of generating functions in elementary gauge transformation operators [Formula: see text] and [Formula: see text] must be very special, which are from the constraints in the Lax operator. At last, we consider the successive applications of n-step of [Formula: see text] and k-step of [Formula: see text] gauge transformations.

The gauge transformations generated by the wave functions in the constrained modified KP hierarchy

2020 ◽  
Vol 34 (18) ◽  
pp. 2050205
Author(s):  
Yi Yang ◽  
Jipeng Cheng
Keyword(s):  
Gauge Transformation ◽  
Generating Functions ◽  
Wave Functions ◽  
Kp Hierarchy ◽  
Gauge Transformations

There are two ways to choose the generating functions of the gauge transformations [Formula: see text] and [Formula: see text], when dicussing the gauge transformations for the constrained modified KP hierarchy. The first is to select the (adjoint) eigenfunctions, while the second is the (adjoint) wave functions. In this paper, we will mainly discuss the gauge transformations obtained by the second method. The corresponding successive applications are considered. Also, we investigate the results of the gauge transformation derived through the union of these two methods.

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).

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