1,926 research outputs found
Abelian 3-form gauge theory: superfield approach
We discuss a D-dimensional Abelian 3-form gauge theory within the framework
of Bonora-Tonin's superfield formalism and derive the off-shell nilpotent and
absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST
symmetry transformations for this theory. To pay our homage to Victor I.
Ogievetsky (1928-1996), who was one of the inventors of Abelian 2-form
(antisymmetric tensor) gauge field, we go a step further and discuss the above
D-dimensional Abelian 3-form gauge theory within the framework of BRST
formalism and establish that the existence of the (anti-)BRST invariant
Curci-Ferrari (CF) type of restrictions is the hallmark of any arbitrary p-form
gauge theory (discussed within the framework of BRST formalism).Comment: LaTeX file, 8 pages, Talk delivered at BLTP, JINR, Dubna, Moscow
Region, Russi
Toda lattice realization of integrable hierarchies
We present a new realization of scalar integrable hierarchies in terms of the
Toda lattice hierarchy. In other words, we show on a large number of examples
that an integrable hierarchy, defined by a pseudodifferential Lax operator, can
be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda
lattice hierarchy seems to be as general as the Drinfeld--Sokolov realization.Comment: 11 pages, Latex (minor changes, to appear in Lett.Math.Phys.
Nilpotent (anti-)BRST symmetry transformations for dynamical non-Abelian 2-form gauge theory: superfield formalism
We derive the off-shell nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the
dynamical non-Abelian 2-form gauge theory within the framework of geometrical
superfield formalism. We obtain the (anti-) BRST invariant coupled Lagrangian
densities that respect the above nilpotent symmetry transformations. We
discuss, furthermore, this (anti-) BRST invariance in the language of the
superfield formalism. One of the novel features of our investigation is the
observation that, in addition to the horizontality condition, we have to invoke
some other physically relevant restrictions to deduce the exact (anti-) BRST
symmetry transformations for all the fields of the topologically massive
non-Abelian gauge theory.Comment: LaTeX file, 8 pages, typos fixed in some equations, journal-versio
Supersymmetrization of horizontality condition: nilpotent symmetries for a free spinning relativistic particle
We derive the off-shell nilpotent and absolutely anticommuting
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a
supersymmetric system of a free spinning relativistic particle within the
framework of superfield approach to BRST formalism. A novel feature of our
present investigation is the consistent and clear supersymmetric modification
of the celebrated horizontality condition for the precise determination of the
proper (anti-)BRST symmetry transformations for all the bosonic and fermionic
dynamical variables of our theory which is considered on a (1, 2)-dimensional
supermanifold parameterized by an even (bosonic) variable (\tau) and a pair of
odd (fermionic) variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 =
0,\; \theta \bar\theta + \bar\theta \theta = 0) of the Grassmann algebra. One
of the most important features of our present investigation is the derivation
of (anti-)BRST invariant Curci-Ferrari type restriction which turns out to be
responsible for the absolute anticommutativity of the (anti-)BRST symmetry
transformations and existence of the coupled (but equivalent) Lagrangians for
the present theory of a supersymmetric system.Comment: LaTeX file, 24 pages, version to appear in EPJ
The integrable hierarchy constructed from a pair of KdV-type hierarchies and its associated algebra
For any two arbitrary positive integers `' and `', using the --th
KdV hierarchy and the --th KdV hierarchy as building blocks, we are able
to construct another integrable hierarchy (referred to as the --th KdV
hierarchy). The --algebra associated to the \shs\, of the --th KdV
hierarchy (called algebra) is isomorphic via a Miura map to the direct
sum of --algebra, --algebra and an additional current
algebra. In turn, from the latter, we can always construct a representation of
--algebra.Comment: 26p, latex, BONN--TH-94-17, SISSA-ISAS-118/94/EP, AS-ITP-94-43,
revised version with addition
BRST, anti-BRST and their geometry
We continue the comparison between the field theoretical and geometrical
approaches to the gauge field theories of various types, by deriving their
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST trasformation properties and
comparing them with the geometrical properties of the bundles and gerbes. In
particular, we provide the geometrical interpretation of the so--called
Curci-Ferrari conditions that are invoked for the absolute anticommutativity of
the BRST and anti-BRST symmetry transformations in the context of non-Abelian
1-form gauge theories as well as Abelian gauge theory that incorporates a
2-form gauge field. We also carry out the explicit construction of the 3-form
gauge fields and compare it with the geometry of 2--gerbes.Comment: A comment added. To appear in Jour. Phys. A: Mathemaical and
Theoretica
Notoph Gauge Theory: Superfield Formalism
We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and
anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory
by exploiting the superfield approach to BRST formalism. The antisymmetric
tensor gauge field of the above theory was christened as the "notoph" (i.e. the
opposite of "photon") gauge field by Ogievetsky and Palubarinov way back in
1966-67. We briefly outline the problems involved in obtaining the absolute
anticommutativity of the (anti-) BRST transformations and their resolution
within the framework of geometrical superfield approach to BRST formalism. One
of the highlights of our results is the emergence of a Curci-Ferrari type of
restriction in the context of 4D Abelian 2-form (notoph) gauge theory which
renders the nilpotent (anti-) BRST symmetries of the theory to be absolutely
anticommutative in nature.Comment: LaTeX file, 12 pages, Talk delivered at SQS'09 (BLTP, JINR, Dubna
BRST analysis of topologically massive gauge theory: novel observations
A dynamical non-Abelian 2-form gauge theory (with B \wedge F term) is endowed
with the "scalar" and "vector" gauge symmetry transformations. In our present
endeavor, we exploit the latter gauge symmetry transformations and perform the
Becchi-Rouet-Stora-Tyutin (BRST) analysis of the four (3 + 1)-dimensional (4D)
topologically massive non-Abelian 2-form gauge theory. We demonstrate the
existence of some novel features that have, hitherto, not been observed in the
context of BRST approach to 4D (non-)Abelian 1-form as well as Abelian 2-form
and 3-form gauge theories. We comment on the differences between the novel
features that emerge in the BRST analysis of the "scalar" and "vector" gauge
symmetries of the theory.Comment: LaTeX file, 14 pages, an appendix added, references expanded, version
to appear in EPJ
A note on the third family of N=2 supersymmetric KdV hierarchies
We propose a hamiltonian formulation of the supersymmetric KP type
hierarchy recently studied by Krivonos and Sorin. We obtain a quadratic
hamiltonian structure which allows for several reductions of the KP type
hierarchy. In particular, the third family of KdV hierarchies is
recovered. We also give an easy construction of Wronskian solutions of the KP
and KdV type equations
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