Related papers: Angular reduction in multiparticle matrix elements
We explicitly establish a unitary correspondence between spherical irreducible tensor operators and cartesian tensor operators of any rank. That unitary relation is implemented by means of a basis of integer-spin wave functions that…
This article gives a natural decomposition of the suspension of generalized moment-angle complexes or {\it partial product spaces} which arise as {\it polyhedral product functors} described below. In the special case of the complements of…
The pixel values of an image can be casted into a real ket of a Hilbert space using an appropriate block structured addressing. The resulting state can then be rewritten in terms of its matrix product state representation in such a way that…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…
The multiscale entanglement renormalization ansatz (MERA) provides a constructive algorithm for realizing wavefunctions that are inherently scale invariant. Unlike conformally invariant partition functions however, the finite bond dimension…
Using a complete basis set we have obtained an analytic expression for the matrix elements of the Coulomb interaction. These matrix elements are written in a closed form. We have used the basis set of the three-dimensional isotropic quantum…
Recursion relations for integrals of amplitudes over the phase space, i.e. for partial wave amplitudes, are introduced. In their simplest form these integrals are proportional to the s-wave amplitudes and represent rigorous lower bounds on…
An algorithm is described for the construction of actions for scalar, spinor, and vector gauge fields that remains well-defined when the metric is degenerate and that involve no contravariant tensor fields. These actions produce the…
The computational cost associated with reducing tensor integrals to scalar integrals using the Passarino-Veltman method is dominated by the diagonalisation of large systems of equations. These systems of equations are sized according to the…
In this paper we study the effect of non-trivial spatial topology on quantum entanglement by examining the degenerate ground states of a topologically ordered system on torus. Using the string-net (fixed-point) wave-function, we propose a…
A classical tensor product $A \,\otimes\, B$ of complete lattices $A$ and $B$, consisting of all down-sets in $A \times B$ that are join-closed in either coordinate, is isomorphic to the complete lattice $Gal(A,B)$ of Galois maps from $A$…
Eigenfunctions of total angular momentum for a charged vector field interacting with a magnetic monopole are constructed and their properties studied. In general, these eigenfunctions can be obtained by applying vector operators to the…
We numerically examine the exterior solution of spherically symmetric and static configuration in scalar-tensor theories by using the nonminimally coupled scalar field with zero potential as our sample model. Our main purpose in this work…
Inspired by ER=EPR conjecture we present a mathematical tool providing a link between quantum entanglement and the geometry of spacetime. We start with the idea of operators in extended Hilbert space which, by definition, has no positive…
We derive analytic expressions for the two-body matrix elements in finite spherical quantum Hall systems in terms of a general scalar interaction expressed as a sum over Legendre polynomials, and we derive the corresponding pair…
Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear…
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…