Related papers: Projection operator onto spin-S eigenspaces of tot…
This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two(many)-particle, `explicitly correlated' basis representation, necessary for…
The orbital angular momentum operator expansion turns to be a powerful tool to construct the fully covariant partial wave amplitudes of hadron decay reactions and hadron photo- and electroproduction processes. In this paper we consider a…
The problem of construction of projection operators on eigen-subspaces of symmetry operators is considered. This problem arises in many approximate methods for solving time-independent and time-dependent quantum problems, and its solution…
This paper gives a momentum-space representation of the Argonne V18 potential as an expansion in products of spin-isospin operators with scalar coefficient functions of the momentum transfer. Two representations of the scalar coefficient…
In classical electrodynamics all the measurable quantities can be derived from the gauge invariant Faraday tensor $F_{\alpha\beta}$. Nevertheless, it is often advantageous to work with gauge dependent variables. In [4],[2] and [8], and in…
We study the momentum-space 4-point correlation function of identical scalar operators in conformal field theory. Working specifically with null momenta, we show that its imaginary part admits an expansion in conformal blocks. The blocks…
This article is a revised, short and english version of my PhD thesis. First, we show a mirror theorem : the Frobenius manifold associated to the orbifold quantum cohomology of weighted projective space is isomorphic to the one attached to…
A new explicitly correlated functional form for expanding the wave function of an N-particle system with arbitrary angular momentum and parity is presented. We develop the projection-based approach, numerically exploited in our previous…
Spin Hamiltonians, like the Heisenberg model, are used to describe magnetic properties of exchange-coupled molecules and solids. For finite clusters, physical quantities such as heat capacities, magnetic susceptibilities or…
The not necessarily unitary evolution operator of a finite dimensional quantum system is studied with the help of a projection operators technique. Applying this approach to the Schr\"odinger equation allows the derivation of an alternative…
Orbital angular momentum eigenfunctions are readily understood in terms of spherical harmonic wavefunctions. However, the quantum mechanical phenomenon of spin is often said to be mysterious and hard to visualize, with no classical…
We study the connection between complete representations of gauge invariant operators and their Moebius representations acting in a limited space of functions. The possibility to restore the complete representations from Moebius forms in…
The observable algebra O of SO_q(3)-symmetric quantum mechanics is generated by the coordinates of momentum and position spaces (which are both isomorphic to the SO_q(3)-covariant real quantum space R_q^3). Their interrelations are…
This note discusses how an operator analog of the Lagrange polynomial naturally arises in the quantum-mechanical problem of constructing an explicit form of the spin projection operator.
We present a study of the properties of the transversal "spin angular momentum" and "orbital angular momentum" operators. We show that the "spin angular momentum" operators are generators of spatial translations which depend on helicity and…
In these lectures we develop the projection operator method for quantum groups. Here the term "quantum groups" means q-deformed universal enveloping algebras of contragredient Lie (super)algebras of finite growth. Contains of the lectures…
On the basis of the Wigner unitary representations of the covering group ISL(2,C) of the Poincar\'{e} group, we obtain spin-tensor wave functions of free massive particles with arbitrary spin. The wave functions automatically satisfy the…
The Holstein-Primakoff boson representation of quantum spins and associated large-$S$ expansion have been the standard framework for describing the spin wave excitations in magnetically order phases of quantum spin systems. However, we will…
Recently the molecular electronic structure theories for efficiently treating static (or strong) correlation in a black-box manner have attracted much attention. In these theories, a spin projection operator is used to recover the spin…
We construct the operator that projects on the physical states in loop quantum gravity. To this aim, we consider a diffeomorphism invariant functional integral over scalar functions. The construction defines a covariant, Feynman-like,…