On the complete integrability of the two-dimensional classical Thirring model

1977 ◽  
Vol 30 (3) ◽  
pp. 193-200 ◽  
Author(s):  
E. A. Kuznetsov ◽  
A. V. Mikhailov
Keyword(s):  
Complete Integrability ◽  
Thirring Model ◽  
Two Dimensional

Periodic problem for the classical two-dimensional Thirring model

1980 ◽  
Vol 31 (4) ◽  
pp. 362-367
Author(s):  
A. K. Prikarpatskii ◽  
P. I. Golod
Keyword(s):  
Periodic Problem ◽  
Thirring Model ◽  
Two Dimensional

Exact results in the two-dimensional U(1)-symmetric Thirring model

1984 ◽  
Vol 230 (4) ◽  
pp. 511-547 ◽  
Author(s):  
G.I. Japaridze ◽  
A.A. Nersesyan ◽  
P.B. Wiegmann
Keyword(s):  
Thirring Model ◽  
Exact Results ◽  
Two Dimensional

Complete integrability and complex solitons for generalized Volterra system with branched dispersion

2020 ◽  
Vol 34 (29) ◽  
pp. 2050274 ◽  
Author(s):  
Corina N. Babalic
Keyword(s):  
Dispersion Relation ◽  
Asymptotic Analysis ◽  
Complete Integrability ◽  
Graphical Representations ◽  
Two Dimensional ◽  
Volterra System ◽  
Bilinear Formalism ◽  
Hirota Bilinear ◽  
Multisoliton Solutions ◽  
Periodic Reduction

In this paper, we show that complete integrability is preserved in a multicomponent differential-difference Volterra system with branched dispersion relation. Using the Hirota bilinear formalism, we construct multisoliton solutions for a system of coupled [Formula: see text] equations. We also show that one can obtain the same solutions through a periodic reduction starting from a two-dimensional completely integrable generalized Volterra system. For some particular cases, graphical representations of solitons are displayed and stability is discussed using an asymptotic analysis.

scholarly journals TWISTED BOSONIZATION IN TWO-DIMENSIONAL NONCOMMUTATIVE SPACETIME

2012 ◽  
Vol 27 (25) ◽  
pp. 1250149 ◽  
Author(s):  
ASRARUL HAQUE ◽  
T. R. GOVINDARAJAN
Keyword(s):  
Thirring Model ◽  
Weak Duality ◽  
Two Dimensional ◽  
Massive Thirring Model ◽  
Commutation Relations ◽  
Fermionic Operators ◽  
Dual Relationship ◽  
Noncommutative Spacetime ◽  
Sine Gordon Model

We study the twisted bosonization of massive Thirring model to relate to sine-Gordon model in Moyal spacetime using twisted commutation relations. We obtain the relevant twisted bosonization rules. We show that there exists dual relationship between twisted bosonic and fermionic operators. The strong–weak duality is also observed to be preserved as its commutative counterpart.

scholarly journals Nonperturbative aspects of the two-dimensional massive gauged Thirring model

2014 ◽  
Vol 29 (23) ◽  
pp. 1450122 ◽  
Author(s):  
R. Bufalo ◽  
B. M. Pimentel
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Thirring Model ◽  
Two Dimensional ◽  
Fermionic Fields ◽  
Massive Theory ◽  
Bosonic Representation

In this paper, we present a study based on the use of functional techniques on the issue of insertions of massive fermionic fields in the two-dimensional massless gauged Thirring model. As it will be shown, the fermionic mass contributes to the Green's functions in a surprisingly simple way, leaving therefore the original nonperturbative nature of the massless results still intact in the massive theory. Also, by means of complementarity, we present a second discussion of the massive model, now at its bosonic representation.

First integrals of generalized Ermakov systems via the Hamiltonian formulation

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640019 ◽  
Author(s):  
K. S. Mahomed ◽  
R. J. Moitsheki
Keyword(s):  
Angular Momentum ◽  
Hamiltonian Formulation ◽  
First Integral ◽  
First Integrals ◽  
Complete Integrability ◽  
Polar Form ◽  
Two Dimensional ◽  
Hamiltonian Method ◽  
Generalized Symmetry ◽  
The Relationship

We obtain first integrals of the generalized two-dimensional Ermakov systems, in plane polar form, via the Hamiltonian approaches. There are two methods used for the construction of the first integrals, viz. the standard Hamiltonian and the partial Hamiltonian approaches. In the first approach, [Formula: see text] and [Formula: see text] in the Ermakov system are related as [Formula: see text]. In this case, we deduce four first integrals (three of which are functionally independent) which correspond to the Lie algebra sl[Formula: see text] in a direct constructive manner. We recover the results of earlier work that uses the relationship between symmetries and integrals. This results in the complete integrability of the Ermakov system. By use of the partial Hamiltonian method, we discover four new cases: [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text]; [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text]; [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text] arbitrary and [Formula: see text] with [Formula: see text], [Formula: see text], [Formula: see text] arbitrary, where the [Formula: see text]s are constants in all cases. In the last two cases, we find that there are three operators each which give rise to three first integrals each. In both these cases, we have complete integrability of the Ermakov system. The first two cases each result in two first integrals each. For every case, both for the standard and partial Hamiltonian, the angular momentum type first integral arises and this is a consequence of the operator which depends on a momentum coordinate which is a generalized symmetry in the Lagrangian context.

scholarly journals TWO-DIMENSIONAL BOSONIZATION FROM VARIABLE SHIFTS IN THE PATH INTEGRAL

1999 ◽  
Vol 14 (12) ◽  
pp. 745-749 ◽  
Author(s):  
JAN B. THOMASSEN
Keyword(s):  
Explicit Form ◽  
Path Integral ◽  
Green's Functions ◽  
Green’S Functions ◽  
Thirring Model ◽  
Two Dimensional ◽  
Integral Property ◽  
Schwinger Model

A method to perform bosonization of a fermionic theory in (1+1) dimensions in a path integral framework is developed. The method relies exclusively on the path integral property of allowing variable shifts, and does not depend on the explicit form of Green's functions. Two examples, the Schwinger model and the massless Thirring model, are worked out.

scholarly journals A DIFFERENTIAL INTEGRABILITY CONDITION FOR TWO-DIMENSIONAL HAMILTONIAN SYSTEMS

2014 ◽  
Vol 54 (2) ◽  
pp. 139-141
Author(s):  
Ali Mostafazadeh
Keyword(s):  
Partial Differential Equations ◽  
Hamiltonian System ◽  
Differential Equations ◽  
Hamiltonian Systems ◽  
Harmonic Functions ◽  
Integrability Condition ◽  
Complete Integrability ◽  
Two Dimensional ◽  
Partial Differential ◽  
Generalized Coordinates

We review, restate, and prove a result due to Kaushal and Korsch [Phys. Lett. A 276, 47 (2000)] on the complete integrability of two-dimensional Hamiltonian systems whose Hamiltonian satisfies a set of four linear second order partial differential equations. In particular, we show that a two-dimensional Hamiltonian system is completely integrable, if the Hamiltonian has the form <em>H = T + V</em> where <em>V</em> and <em>T</em> are respectively harmonic functions of the generalized coordinates and the associated momenta.

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