arXiv subjects
Publications and source records attributed to B. Yapiskan.
A recent method of constructing quantum mechanics in noncommutative coordinates, alternative to implying noncommutativity by means of star product is discussed. Within this approach we study Hall effect as well as quantum phases in noncommutative coordinates. The $θ$--deformed phases which we obtain are velocity independent.
Equivalence of partition functions for U(1) gauge theory and its dual in appropriate phase spaces is established in terms of constrained hamiltonian formalism of their parent action. Relations between the electric--magnetic duality transformation and the (S) duality transformation which inverts the strong coupling domains to the weak coupling domains of noncommutative U(1) gauge theory are discussed in terms of the lagrangian and the hamiltonian densities. The approach presented for the commutative case is utilized to demonstrate that noncommutative U(1) gauge theory and its dual possess the same partition function in their phase spaces at the first order in the noncommutativity parameter θ.
Parent actions for component fields are utilized to derive the dual of supersymmetric U(1) gauge theory in 4 dimensions. Generalization of the Seiberg-Witten map to the component fields of noncommutative supersymmetric U(1) gauge theory is analyzed. Through this transformation we proposed parent actions for noncommutative supersymmetric U(1) gauge theory as generalization of the ordinary case.Duals of noncommutative supersymmetric U(1) gauge theory are obtained. Duality symmetry under the interchange of fields with duals accompanied by the replacement of the noncommutativity parameter Θ_{μν} with \tildeΘ_{μν} = ε_{μνρσ}Θ^{ρσ} of the non--supersymmetric case is broken at the level of actions. We proposed a noncommutative parent action for the component fields which generates actions possessing this duality symmetry.
We solve the Einstein equations for the 2+1 dimensions with and without scalar fields. We calculate the entropy, Hawking temperature and the emission probabilities for these cases. We also compute the Newman-Penrose coefficients for different solutions and compare them.
Lagrangians of the Abelian Gauge Theory and its dual are related in terms of a shifted action. We show that in d=4 constrained Hamiltonian formulation of the shifted action yields Hamiltonian description of the dual theory, without referring to its Lagrangian. We apply this method, at the first order in the noncommutativity parameter theta, to the noncommutative U(1) gauge theory possessing spatial noncommutativity. Its dual theory is effectively a space--time noncommutative U(1) gauge theory. However, we obtain a Hamiltonian formulation where time is commuting. Space-time noncommutative D3--brane worldvolume Hamiltonian is derived as the dual of space noncommutative U(1) gauge theory. We show that a BPS like bound can be obtained and it is saturated for configurations which are the same with the ordinary D3-brane BIon and dyon solutions.
We review our previous work on the the calculation of the stress-energy tensor for a scalar particle in the background metric of different types of spherical impulsive, spherical shock and plane impulsive gravitational waves.