arXiv subjects
Publications and source records attributed to I. H. Duru.
Casimir energy changes are investigated for geometries obtained by small but arbitrary deformations of a given geometry for which the vacuum energy is already known for the massless scalar field. As a specific case, deformation of a spherical shell is studied. From the deformation of the sphere we show that the Casimir energy is a decreasing function of the surface to volume ratio. The decreasing rate is higher for less smooth deformations.
Following the derivation of the Green function for the massless scalar field satisfying the Dirichlet boundary condition on the Plane (x > 0, y = 0), we calculate the Casimir energy.
New Casimir energy results for massless scalar field in some 3 -dimensional cavities are presented. We attempted to discuss the correlation between the sign and the magnitude of the energy and the shape of the cavities.
Feynman propagator is calculated for the time dependent harmonic oscillator by converting the problem into a free particle motion
Casimir energy for a massless scalar field for a conical wedge and a conical cavity are calculated. The group generated by the images is employed in deriving the Green functions as well as the wave functions and the energy spectrum.
Casimir energy calculations for the conformally coupled massless scalar field for a wedge defined by three intersecting planes and for a pyramid with four triangular surfaces are presented. The group generated by reflections are employed in the formulation of the required Green functions and the wave functions.
For certain class of triangles (with angles proportional to $\frπ{N}$, $N\geq 3$) we formulate image method by making use of the group $G_N$ generated by reflections with respect to the three lines which form the triangle under consideration. We formulate the renormalization procedure by classification of subgroups of $G_N$ and corresponding fixed points in the triangle. We also calculate Casimir energy for such geometries, for scalar massless fields. More detailed calculation is given for odd $N$.
Casimir interactions (due to the massless scalar field fluctuations) of two surfaces which are close to each other are studied. After a brief general presentation, explicit calculations for co-axial cylinders, co-centric spheres and co-axial cones are performed.
Exact path integration for the one dimensional potential $V=b^2\cos 2q$ which describes the finite amplitude pendulum is presented.
Using the representation of E_q(2) on the non-commutative space zz^*-qz^*z=σ; q<1, σ>0 summation formulas for the product of two, three and four q-Kummer functions are derived.
SU(1,1) is considered as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the irreducible representations of the group are realized is explicitly constructed. The addition theorems are derived.
E(2) is studied as the automorphism group of the Heisenberg algebra H. The basis in the Hilbert space K of functions on H on which the unitary irreducible representations of the group are realized is explicitely constructed. The addition theorem for the Kummer functions is derived.
q-Neumann function of integer order N_n(x,q) is obtained and some of its properties are given. q-Psi function which is used in deriving N_n(x,q) is also introduced and some of its properties are presented.
Green function (which can be called the q-analogous of the Hankel function) on the quantum plane E_q^2= E_q(2)/U(1) is constructed.
Following the construction of the invariant integral and the scalar product for the quantum Euclidean group E_q(2), we obtained the full matrix elements of its unitary irreducible representations from SU_q(2) by contraction and then derived the Planscherel measure.
(2+2)-dimensional quantum mechanical q-phase space which is the semi-direct product of the quantum plane E_q(2)/U(1) and its dual algebra e_q(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ``Quantum mechanical q-Hamiltonian'' of the motion over the quantum plane is derived and the solution of the Schroedinger equation for the q-semiclassical motion governed by the expectation value of that Hamiltonian is solved.
An interference experiment in a magnetic field free region with non vanishing vector potential created by two perpendicularly intersecting planes carrying uniform currents is discussed. The relation of this configuration to the Aharonov-Bohm potential is examined. An experimental set up which is finite in the direction of the electronic motion is studied.
Following the introduction of the invariant distance on the non-commutative C-algebra of the quantum group SU_q(2), the Green function and the Kernel on the q-homogeneous space M=SU(2)_q/U(1) are derived. A path integration is formulated. Green function for the free massive scalar field on the non-commutative Einstein space R^1xM is presented.