Related papers: (1/2,1/2) Representation space: An ab initio const…
The Klein-Gordon and Dirac equations in a semi-infinite lab ($x > 0$), in the background metric $\ds^2 = u^2(x) (-\dt^2 + \dx^2) + \dy^2 + \dz^2$, are investigated. The resulting equations are studied for the special case $ u(x) = 1 + g x$.…
Considering real spacetime as a Lorentzian fiber in a complex manifold, there is a mismatch of the elementary linear representations of their symmetry groups, the real and complex Poincar\'{e} groups. No spinors are allowed as linear…
We investigate the structure of SO(3)-invariant quantum systems which are composed of two particles with spins j_1 and j_2. The states of the composite spin system are represented by means of two complete sets of rotationally invariant…
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 derive the spin-statistics theorem in both relativistic and non-relativistic first-quantized form, extending considerably the earlier proofs. Our derivation is based on the representation theories of the groups SU (2) and SL(2,C), latter…
It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle…
The Hilbert space H^3q of the three quarks with one excited quark is decomposed into Lorentz group representations. It is shown that the quantum numbers of the reported and ``missing'' resonances fall apart and populate distinct…
Inspired by Bohr's dictum that "physical phenomena are observed relative to different experimental setups", this article investigates the notion of relativity in Bohr's sense, starting from a set of binary elements. The most general form of…
Neutrino oscillation experiments presently suggest that neutrinos have a small but finite mass. If neutrinos are to have mass, there should be a Lorentz frame in which they can be brought to rest. This paper discusses how Wigner's little…
We generalize the results of [B. Coecke, Helv. Phys. Acta 68, 396 (1995)] for the representation of coherent states of a spin-1 entity to spin-S entities with S>1 and to non-coherent spin states: through the introduction of 'hidden…
Special relativity, the symmetry breakdown in the electroweak standard model, and the dichotomy of the spacetime related transformations with the Lorentz group, on the one side, and the chargelike transformations with the hypercharge and…
We derive the second-order equations in the (1/2,0)+(0,1/2) representation on using the Ryder postulates. Similar equations has been proposed in the 60s and the 70s in order to understand different mass states of leptons. We give some…
By describing the evolution of a quantum state with the trajectories of the Majorana stars on a Bloch sphere, Majorana's stellar representation provides an intuitive geometric perspective to comprehend a quantum system with high-dimensional…
In this paper we use a constructive approach based on gauge invariant description of massive high spin particles for investigation of possible interactions of massive spin 2 particle. We work with general case of massive spin 2 particle…
We consider solutions of the 2x2 matrix Hamiltonians of the physical systems within the context of the su(2) and su(1,1) Lie algebra. Our technique is relatively simple when compared with the others and treats those Hamiltonians which can…
The Majorana stellar representation is used to characterize spin states that have a maximally negative Wigner quasiprobability distribution on a spherical phase space. These maximally Wigner-negative spin states generally exhibit a partial…
We generalize the Stueckelberg formalism in the (1/2,1/2) representation of the Lorentz Group. Some relations to other modern-physics models are found.
A `covariant' field that transforms like a relativistic field operator is required to be a linear combination of `canonical' fields that transform like annihilation and creation operators and with invariant coefficients. The Invariant…
We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries,…
The very existence of partially massless spin 2 supermultiplet tell us that partially massless spin 2 has two natural superpartners: massless spin 3/2 and massive spin 3/2 with some special value of mass. As for any pair of fields connected…