Related papers: Group projector generalization of dirac-heisenberg…
The planar dynamics of spin-1/2 quantum relativistic particles is important for several physical systems. In this paper we derive, by a simple method, the generators for the continuous symmetries of the 3+1 Dirac equation for planar motion,…
We establish the functorial transfer of generic, automorphic representations from the quasi-split general spin groups to general linear groups over arbitrary number fields, completing an earlier project. Our results are definitive and, in…
While either spin or point-group adaptation is straightforward when considered independently, the standard technique for factoring isotropic spin Hamiltonians by the total spin S and the irreducible representation of the point-group is…
The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is…
Starting with an operator in the universal enveloping algebra of a semi-simple, complex Lie group the nearest neighbor statistics of the spectra of this operator along a sequence of representations are discussed. After a short introduction…
The (group and spin space) matrix Hamiltonian describing the dynamics of a nonrelativistic spin 1/2 particle moving in a static, but spatially dependent, non-Abelian magnetic field in two spatial dimensions is shown to take the form of an…
We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this…
Following the idea of a field quantization of gravity as realized in group field theory, we construct a minisuperspace model where the wavefunction of canonical quantum cosmology (either Wheeler-DeWitt or loop quantum cosmology) is promoted…
Interactions and particles in the standard model are characterized by the action of internal and external symmetry groups. The four symmetry regimes involved are related to each other in the context of induced group representations. In…
We describe a Riemannian space class where the second Dirac operator arises and prove that the operator is always equivalent to a standard Dirac one. The particle state in this gravitational field is degenerate to some extent and we…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time…
General relativity is derived from an action which is quadratic in the covariant derivative of certain spinor one-form gravitational potentials. Either a pair of 2-component spinor one-forms or a single Dirac spinor one-form can be…
The 2(2s+1)-component relativistic basis spinors for the arbitrary spin particles are established in position, momentum and four-dimensional spaces, where s=0,1 / 2,1, 3 / 2, 2, ... . These spinors for integral- and half-integral spins are…
We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary…
Exact diagonalization and other numerical studies of quantum spin systems are notoriously limited by the exponential growth of the Hilbert space dimension with system size. A common and well-known practice to reduce this increasing…
The $(3 + 1)$-dimensional (generalized) Dirac equation is shown to have the same form as the equation expressing the condition that a given point lies on a given line in 3-dimensional projective space. The resulting Hamiltonian with a…
A composite quantum system comprising a finite number k of subsystems which are described with position and momentum variables in Z_{n_{i}}, i=1,...,k, is considered. Its Hilbert space is given by a k-fold tensor product of Hilbert spaces…
We study the geometry and partial differential equations arising from the consideration of group-determinants, and representation theory. The simplest and most striking such example is undoubtedly that of the Humbert operator, associated…
We consider a relativistic superalgebra in the picture in which the time and spatial derivative cannot be presented in the operators of the particle. The supersymmetry generators as well as the Hamilton operators for the massive…