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We show that the attempt to introduce all of the discrete space-time transformations into the spinor representation of the Lorentz group as wholly independent transformations (as in the vectorial representation) leads to an 8-component…
The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions…
This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to…
One- and two-dimensional operators which originate from the asymptotic form of the three-body Coulomb wave equation in parabolic coordinates are treated within the context of square integrable basis set. The matrix representations of…
Having started with the general formulation of the quantum theory of the real scalar field (QFT) in the general Riemannian space--time $ V_{1,3} $, the general--covariant quasinonrelativistic quantum mechanics of a point-like spinless…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
We present a general derivation of semi-fermionic representation for spin operators in terms of a bilinear combination of fermions in real and imaginary time formalisms. The constraint on fermionic occupation numbers is fulfilled by means…
To most physicists, quantum mechanics must embrace the imaginary number i = square root of minus one is at least a common belief if not a mystery. We use the famous example pq -qp = h/(2 pi i) to demonstrate the possible elimination of i…
In this paper the system of a semi-relativistic particle interacting with a scalar Bose field is investigated. The ultraviolet cutoff condition is imposed on the Bose field. In the main theorem, the functional integral representation of the…
We give a tentative definition of the recently introduced Root-$T\bar{T}$ operator in a generic, two dimensional quantum conformal field theory with continuous spectrum of scaling weights. The definition assumes certain factorization…
The volume operator plays a central role in both the kinematics and dynamics of canonical approaches to quantum gravity which are based on algebras of generalized Wilson loops. We introduce a method for simplifying its spectral analysis,…
The detailed consideration of the relativistic canonical quantum-mechanical model of an arbitrary spin-multiplet is given. The group-theoretical analysis of the algebra of experimentally observables physical quantities for the spin 1/2…
Starting from the defining transformations of complex matrices for the SO(4) group, we construct the fundamental representation and the tensor and spinor representations of the group SO(4). Given the commutation relations for the…
The spin-4/3 fractional superstring is characterized by a chiral algebra involving a spin-4/3 current on the world-sheet in addition to the energy-momentum tensor. These currents generate physical state conditions on the fractional…
We predict that spin-waves in an ordered square quantum antiferromagnet in a transverse magnetic field (h) may demonstrate three modes of spin excitations. Starting from the self-consistent rotation-invariant Green's function method, a new…
A Green's function approach to the inclusive quasielastic ($e,e'$) scattering is presented. The components of the nuclear response are written in terms of the single-particle optical model Green's function. The explicit calculation of the…
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
There exists a Klein-Gordon-like equation for a spin-1/2 particle in an electromagnetic field with 2-spinors as wave functions that is a direct consequence of the corresponding Dirac equation. Thus, it reproduces the same binding energies…
It is an easily deduced fact that any four-component spin 1/2 state for a massive particle is a linear combination of pairs of two-component simultaneous rotation eigenstates, where `simultaneous' means the eigenspinors of a given pair…