arXiv subjects
Publications and source records attributed to Rabin Banerjee.
We consider a new approach for gravity theory coupled to Chaplygin matter in which the {\it{relativistic}} formulation of the latter is of crucial importance. We obtain a novel form of matter with dust like density $(\sim (volume)^{-1})$ and negative pressure. We explicitly show that our results are compatible with a relativistic generalization of the energy conservation principle, derived here.
Generators of the super-Poincaré algebra in the non-(anti)commutative superspace are represented using appropriate higher-derivative operators defined in this quantum superspace. Also discussed are the analogous representations of the conformal and superconformal symmetry generators in the deformed spaces. This construction is obtained by generalizing the recent work of Wess et al on the Poincaré generators in the $θ$-deformed Minkowski space, or by using the substitution rules we derived on the basis of the phase-space structures of non-(anti)commutative-space variables. Even with the nonzero deformation parameters the algebras remain unchanged although the comultiplication rules are deformed. The transformation of the fields under deformed symmetry is also discussed. Our construction can be used for systematic developments of field theories in the deformed spaces.
We describe the deformed Poincare-conformal symmetries implying the covariance of the noncommutative space obeying Snyder's algebra. Relativistic particle models invariant under these deformed symmetries are presented. A gauge (reparametrisation) independent derivation of Snyder's algebra from such models is given. The algebraic transformations relating the deformed symmetries with the usual (undeformed) ones are provided. Finally, an alternative form of an action yielding Snyder's algebra is discussed where the mass of a relativistic particle gets identified with the inverse of the noncommutativity parameter.
We construct the deformed generators of Schroedinger symmetry consistent with noncommutative space. The examples of the free particle and the harmonic oscillator, both of which admit Schroedinger symmetry, are discussed in detail. We construct a generalised Galilean algebra where the second central extension exists in all dimensions. This algebra also follows from the Inonu--Wigner contraction of a generalised Poincare algebra in noncommuting space.
We exploit the Seiberg-Witten maps for fields and currents in a U(1) gauge theory relating the noncommutative and commutative (usual) descriptions to obtain the O(θ) structure of the commutator anomalies in noncommutative electrodynamics. These commutators involve the (covariant) current-current algebra and the (covariant) current-field algebra. We also establish the compatibility of the anomalous commutators with the noncommutative covariant anomaly through the use of certain consistency conditions derived here.
A master action for the bosonic p-brane, interpolating between the Nambu--Goto and Polyakov formalisms, is discussed. The fundamental arbitrariness of extended structures (p-brane) embeded in space time manifold has been exploited to build an independent metric in the brane world volume. The cosmological term for the generic case follows naturally in the scheme. The dynamics of the structure leads to a natural emergence of the A--D--M like split of this world volume. The role of the gauge symmetries vis-à-vis reparametrization symmetries is analyzed by a constrained Hamiltonian approach.
A gauge-fixing procedure for the Yang-Mills theory on an n-dimensional sphere (or a hypersphere) is discussed in a systematic manner. We claim that Adler's gauge-fixing condition used in massless Euclidean QED on a hypersphere is not conventional because of the presence of an extra free index, and hence is unfavorable for the gauge-fixing procedure based on the BRST invariance principle (or simply BRST gauge-fixing procedure). Choosing a suitable gauge condition, which is proved to be equivalent to a generalization of Adler's condition, we apply the BRST gauge-fixing procedure to the Yang-Mills theory on a hypersphere to obtain consistent results. Field equations for the Yang-Mills field and associated fields are derived in manifestly O(n+1) covariant or invariant forms. In the large radius limit, these equations reproduce the corresponding field equations defined on the n-dimensional flat space.
We derive maps relating currents and their divergences in non-abelian U(N) noncommutative gauge theory with the corresponding expressions in the ordinary (commutative) description. For the U(1) theory, in the slowly-varying-field approximation, these maps are also seen to connect the star-gauge-covariant anomaly in the noncommutative theory with the standard Adler--Bell--Jackiw anomaly in the commutative version. For arbitrary fields, derivative corrections to the maps are explicitly computed up to O(θ^2).
We generalise the electric-magnetic duality in standard Maxwell theory to its non-commutative version. Both space-space and space-time non-commutativity are necessary. The duality symmetry is then extended to a general class of non-commutative gauge theories that goes beyond non-commutative electrodynamics. As an application of this symmetry, plane wave solutions are analysed. Dispersion relations following from these solutions show that general non-commutative gauge theories other than electrodynamics admits two waves with distinct polarisations propagating at different velocities in the same direction.
We discuss a general method of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. Starting from the commuting algebra in the conventional gauge, it is possible to obtain a noncommuting algebra in a nonstandard gauge. The change of variables relating the algebra in the two gauges is systematically derived using gauge/reparametrisation transformations.
We explicitly derive, following a Noether-like approach, the criteria for preserving Poincare invariance in noncommutative gauge theories. Using these criteria we discuss the various spacetime symmetries in such theories. It is shown that, interpreted appropriately, Poincare invariance holds. The analysis is performed in both the commutative as well as noncommutative descriptions and a compatibility between the two is also established.
We discuss some exact Seiberg--Witten-type maps for noncommutative electrodynamics. Their implications for anomalies in different (noncommutative and commutative) descriptions are also analysed.
We study noncommutative (NC) field theory of a real NC tachyon and NC U(1) gauge field, describing the dynamics of an unstable D$p$-brane. For every given set of diagonal component of open string metric $G_{0}$, NC parameter $θ_{0}$, and interpolating electric field ${\hat E}$, we find all possible static NC kinks as exact solutions, in spite of complicated NC terms, which are classified by an array of NC kink-antikink and topological NC kinks. By computing their tensions and charges, those configurations are identified as an array of D0${\bar {\rm D}}$0 and single stable D0 from the unstable D1, respectively. When the interpolating electric field has critical value as $G_{0}^{2}={\hat E}^{2}$, the obtained topological kink becomes a BPS object with nonzero thickness and is identified as BPS D0 in the fluid of fundamental strings. Particularly in the scaling limit of infinite $θ_{0}$ and vanishing $G_{0}$ and ${\hat E}$, while keeping $G_{0}θ_{0}={\hat E}θ_{0}=1$, finiteness of the tension of NC kink corresponds to tensionless kink in ordinary effective field theory. An extension to stable D$(p-1)$ from unstable D$p$ is straightforward for pure electric cases with parallel NC parameter and interpolating two-form field.
We revisit the exact Seiberg-Witten (SW) map on Dirac-Born-Infeld actions, making a connection with the deformation quantization scheme. The picture on field dependent induced gravity from noncommutativity becomes more transparent in the context of deformation quantization. We also find an exact SW map for an adjoint scalar field, consistent with that deduced from RR couplings of unstable non-BPS D-branes. The dual description via the exact SW map can again be interpreted as the ordinary field theory coupling to gravity induced by gauge fields. Using the exact SW maps, we further discuss several aspects of topological invariants in noncommutative (NC) gauge theory. Especially, it is shown that the K-theory class on NC instantons is mapped to the usual second Chern class via exact SW map and it leads to an exact SW map between commutative and NC Chern-Simons terms.
A master action for bosonic strings and membranes, interpolating between the Nambu--Goto and Polyakov formalisms, is discussed. The role of the gauge symmetries vis-à-vis reparametrization symmetries of the various actions is analyzed by a constrained Hamiltonian approach. This analysis reveals the difference between strings and higher branes, which is essentially tied to a degree of freedom count. The cosmological term for membranes follows naturally in this scheme. The conncetion of our aproach with the Arnowitt--Deser--Misner representation in general relativity is illuminated.
We provide a general method for studying manifestly $O(n+1)$ covariant formulation of $p$-form gauge theories by stereographically projecting these theories, defined in flat Euclidean space, onto the surface of a hypersphere. The gauge fields in the two descriptions are mapped by conformal Killing vectors while conformal Killing spinors are necessary for the matter fields, allowing for a very transparent analysis and compact presentation of results. General expressions for these Killing vectors and spinors are given. The familiar results for a vector gauge theory are reproduced.
We derive maps relating the currents and energy-momentum tensors in noncommutative (NC) gauge theories with their commutative equivalents. Some uses of these maps are discussed. Especially, in NC electrodynamics, we obtain a generalization of the Lorentz force law. Also, the same map for anomalous currents relates the Adler-Bell-Jackiw type NC covariant anomaly with the standard commutative-theory anomaly. For the particular case of two dimensions, we discuss the implications of these maps for the Sugawara-type energy-momentum tensor.
An intriguing connection, based on duality symmetry, between ordinary (commutative) Born-Infeld type theory and non-commutative Maxwell type theory, is pointed out. Both discrete as well as continuous duality transformations are considered and their implications for self duality condition and Legendre transformations are analysed.