Related papers: Lens space determinants
In this part of the series I show how five-tensors can be used for describing in a coordinate-independent way finite and infinitesimal Poincare transformations in flat space-time. As an illustration, I reformulate the classical mechanics of…
This paper considers paired operators in the context of the Lebesgue Hilbert space $L^2$ on the unit circle and its subspace, the Hardy space $H^2$. The kernels of such operators, together with their analytic projections, which are…
Elementary properties of the Koornwinder-Macdonald multivariable Askey-Wilson polynomials are discussed. Studied are the orthogonality, the difference equations, the recurrence relations, and the orthonormalization constants for these…
Different practical problems, espesially, problems of hydrodynamics, elasticity theory, geophysics and aerodynamics can be reduced to finding of an optimal shape. The investigation of these problems is based on the study of depending domain…
In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.
Recent general results on Hamiltonian reductions under polar group actions are applied to study some reductions of the free particle governed by the Laplace-Beltrami operator of a compact, connected, simple Lie group. The reduced systems…
In strong gravitational lens systems, the light bending is usually dominated by one main galaxy, but may be affected by other mass along the line of sight (LOS). Shear and convergence can be used to approximate the contributions from less…
In quantum field theories, field redefinitions are often employed to remove redundant operators in the Lagrangian, making calculations simpler and physics more evident. This technique requires some care regarding, among other things, the…
The Bargmann-Michel-Telegdi equation, which describes the precession of the spin of a charged Dirac particle moving in a homogeneous electromagnetic field, is generalized to include also other homogeneous background fields. The treatment…
Homodyne tomography provides a way for measuring generic field-operators. Here we analyze the determination of the most relevant quantities: intensity, field, amplitude and phase. We show that tomographic measurements are affected by…
We introduce a collection of statistics appropriate for the study of spinorial quantities defined in three dimensions, focussing on applications to cosmological weak gravitational lensing studies in 3D. In particular, we concentrate on…
This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references…
The nonzero level sets of a homogeneous, logarithmically homogeneous, or translationally homogeneous function are affine spheres if and only if the Hessian determinant of the function is a multiple of a power or an exponential of the…
We experimentally generate three-dimensional speckles with customized intensity statistics. By modulating the phase front of a laser beam, far-field speckle patterns maintain the designed intensity probability density function while…
We derive all heat kernel coefficients for Laplacians acting on scalars, vectors, and tensors on fully symmetric spaces, in any dimension. Final expressions are easy to evaluate and implement, and confirmed independently using spectral sums…
When the gravitational lensing potential can be approximated by that of circularly symmetric system affected by weak perturbations, it is found that the shape of the resulting (tangential) caustics is entirely specified by the local…
Bidirectional transformation, also called lens, has played important roles in maintaining consistency in many fields of applications. A lens is specified by a pair of forward and backward functions which relate to each other in a consistent…
The optical matrix formalism is applied to find parameters such as focal distance, back and front focal points, principal planes, and the equation relating object and image distances for a thick spherical lens immerse in air. Then, the…
Observations suggest that our universe is spatially flat on the largest observable scales. Exactly six different compact orientable three-dimensional manifolds admit flat metrics. These six manifolds are therefore the most natural choices…
For many-particle systems defined on lattices we investigate the global structure of effective Hamiltonians and observables obtained by means of a suitable basis transformation. We study transformations which lead to effective Hamiltonians…