Related papers: Field on Poincare group and quantum description of…
Worldline quantum field theory (WQFT) has proven itself a powerful tool for classical two-body scattering calculations in general relativity. In this paper we develop a new worldline action involving bosonic oscillators, which enables the…
Making use of the real sl(2,R) Lie group algebra generating a spin 1/2 Lie group allows to create an explicitly given Lorentz invariant fermion wave. As the generators are real valued they can be interpreted as a deformation tensor in…
The extensive analysis of the dynamics of relativistic spinning particles is presented. Using the coadjoint orbits method the Hamiltonian dynamics is explicitly described. The main technical tool is the factorization of general Lorentz…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
World spinors are objects that transform w.r.t. double covering group $\bar{Diff}(4,R)$ of the Group of General Coordinate Transformations. The basic mathematical results and the corresponding physical interpretation concerning these,…
The questions of the existence, basic algebraic properties and relevant constraints that yield a viable physical interpretation of world spinors are discussed in details. Relations between spinorial wave equations that transform…
The connection between spin and symmetry was established by Wigner in his 1939 paper on the Poincar\'e group. For a massive particle at rest, the little group is O(3) from which the concept of spin emerges. The little group for a massless…
We present the consistent approach to finding the discrete transformations in the representation spaces of the proper Poincar\'e group. To this end we use the possibility to establish a correspondence between involutory automorphisms of the…
A quantum frame is defined by a material object subject to the laws of quantum mechanics. The present paper studies the relations between quantum frames, which in the classical case are described by elements of the Poincare' group. The…
We relate the Lounesto classification of regular and singular spinors to the orbits of the $Spin(3,1)$ group in the space of Dirac spinors. We find that regular spinors are associated with the principal orbits of the spin group while…
Relativistic quantum effects on physical observables of scalar charged particles are studied. Possible peculiarities of their behavior that can be verified in an experiment can confirm several fundamental conceptions of quantum mechanics.…
The relativistic three-body problem is approached via the extension of the SL(2,C) group to the Sp(4,C) one. In terms of Sp(4,C) spinors, a Dirac-like equation with three-body kinematics is composed. After introducing the linear in…
A consistent phenomenology of the interaction of particles of arbitrary spin requires covariant spinors, field operators, propagators and model interactions. Guided by an approach originally proposed by Weinberg, we construct from group…
A geometric approach to the standard model in terms of the Clifford algebra Cl_7 is advanced. A key feature of the model is its use of an algebraic spinor for one generation of leptons and quarks. Spinor transformations separate into…
A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated. Initial equations depend upon four complex…
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…
We quantize a relativistic massive complex spin-0 field and a relativistic massive spin-1/2 field on a space-time hyperboloid. We call this procedure point-form canonical quantization. Lorentz invariance of the hyperboloid implies that the…
We present a Lagrangian formulation for 4d integer-spin relativistic fields in the 5d space spanned by two conjugate Weyl spinors and a Lorentz-invariant proper-time coordinate. We construct a manifestly Poincare-invariant free classical…
The relativistic conception of space and time is challenged by the quantum nature of physical observables. It has been known for a long time that Poincar\'e symmetry of field theory can be extended to the larger conformal symmetry. We use…
We construct one-particle states as unitary, irreducible representations of Poincare group in front form, characterized by a special null vector, dubbed reference vector. We demonstrate that this construction has massive-massless…