1,087 research outputs found
Non-commutative solitons and strong-weak duality
Some properties of the non-commutative versions of the sine-Gordon model
(NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our
method relies on the NC extension of integrable models and the master
Lagrangian approach to deal with dual theories. The master Lagrangians turn out
to be the NC versions of the so-called affine Toda model coupled to matter
fields (NCATM) associated to the group GL(2), in which the Toda field belongs
to certain representations of either or corresponding
to the Lechtenfeld et al. (NCSG) or Grisaru-Penati (NCSG) proposals
for the NC versions of the sine-Gordon model, respectively. Besides, the
relevant NCMT models are written for two (four) types of Dirac fields
corresponding to the Moyal product extension of one (two) copy(ies) of the
ordinary massive Thirring model. The NCATM models share the same
one-soliton (real Toda field sector of model 2) exact solutions, which are
found without expansion in the NC parameter for the corresponding Toda
and matter fields describing the strong-weak phases, respectively. The
correspondence NCSG NCMT is promising since it is
expected to hold on the quantum level.Comment: 24 pages, 1 fig., LaTex. Typos in star products of eqs. (3.11)-(3.13)
and footnote 1 were corrected. Version to appear in JHE
A Representation of the Virasoro Algebra via Wigner-Heisenberg Algebraic Technique to Bosonic Systems
Using the Wigner-Heisenberg algebra for bosonic systems in connection with
oscillators we find a new representation for the Virasoro algebra.Comment: Revised version. Revtex, 7 pages, no figures. This work was presented
in the XXII Brazilian National Meeting on Particles and Fields
(October/2001), to appear in Braz. J. of Phys., 33, 1 (2003
G\"odel-type Spacetimes in Induced Matter Gravity Theory
A five-dimensional (5D) generalized G\"odel-type manifolds are examined in
the light of the equivalence problem techniques, as formulated by Cartan. The
necessary and sufficient conditions for local homogeneity of these 5D manifolds
are derived. The local equivalence of these homogeneous Riemannian manifolds is
studied. It is found that they are characterized by three essential parameters
, and : identical triads correspond to
locally equivalent 5D manifolds. An irreducible set of isometrically
nonequivalent 5D locally homogeneous Riemannian generalized G\"odel-type
metrics are exhibited. A classification of these manifolds based on the
essential parameters is presented, and the Killing vector fields as well as the
corresponding Lie algebra of each class are determined. It is shown that the
generalized G\"odel-type 5D manifolds admit maximal group of isometry
with , or depending on the essential parameters ,
and . The breakdown of causality in all these classes of homogeneous
G\"odel-type manifolds are also examined. It is found that in three out of the
six irreducible classes the causality can be violated. The unique generalized
G\"odel-type solution of the induced matter (IM) field equations is found. The
question as to whether the induced matter version of general relativity is an
effective therapy for these type of causal anomalies of general relativity is
also discussed in connection with a recent article by Romero, Tavakol and
Zalaletdinov.Comment: 19 pages, Latex, no figures. To Appear in J.Math.Phys.(1999
Division Algebras and Extended N=2,4,8 SuperKdVs
The first example of an N=8 supersymmetric extension of the KdV equation is
here explicitly constructed. It involves 8 bosonic and 8 fermionic fields. It
corresponds to the unique N=8 solution based on a generalized hamiltonian
dynamics with (generalized) Poisson brackets given by the Non-associative N=8
Superconformal Algebra. The complete list of inequivalent classes of
parametric-dependent N=3 and N=4 superKdVs obtained from the ``Non-associative
N=8 SCA" is also furnished. Furthermore, a fundamental domain characterizing
the class of inequivalent N=4 superKdVs based on the "minimal N=4 SCA" is
given.Comment: 14 pages, LaTe
Residual Symmetries in the Presence of an EM Background
The symmetry algebra of a QFT in the presence of an external EM background
(named "residual symmetry") is investigated within a Lie-algebraic, model
independent scheme. Some results previously encountered in the literature are
here extended. In particular we compute the symmetry algebra for a constant EM
background in D=3 and D=4 dimensions. In D= 3 dimensions the residual symmetry
algebra is isomorphic to , with the
centrally extended 2-dimensional Poincar\'e algebra. In D=4 dimension the
generic residual symmetry algebra is given by a seven-dimensional solvable Lie
algebra which is explicitly computed. Residual symmetry algebras are also
computed for specific non-constant EM backgrounds.Comment: 11 pages, Late
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