Related papers: Generalized Spin-Statistics Theorem
We investigate the intrinsic reason for spin statistics connection. It is found that if a free field theory is rotationally (SU(2)) invariant, and has time reversal ($T$) and charge conjugation ($C$) symmetries, it obeys the spin statistics…
Particles states transforming in one of the infinite spin representations of the Poincar\'e group (as classified by E. Wigner) are consistent with fundamental physical principles, but local fields generating them from the vacuum state…
In a generalized Heisenberg/Schroedinger picture we use an invariant space-time transformation to describe the motion of a relativistic particle. We discuss the relation with the relativistic mechanics and find that the propagation of the…
In this second paper in a series, we show that the the general statistical approach to nonrelativistic quantum mechanics developed in the first paper yields a representation of quantum spin and magnetic moments based on classical…
The principal series of unitary representations of the Lorentz group has been considered in the helicity basis. Decompositions of tensor products of the spinspaces are studied in the framework of projective representations of the symmetric…
\noindent 1. Generalities\hfil\break 2. Lie groups and Lie algebras\hfil\break 3. The unitary groups\hfil\break 4. Representations of the SU(n) groups (and of their algebras)\hfil\break 5. The tensor method for unitary groups, and\hb the…
A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A…
Infinite statistics in which all representations of the symmetric group can occur is known as a special case of quon theory. However, the validity of relativistic quon theories is still in doubt. In this paper we prove that there exists a…
The spin-statistics connection has been proved for nonrelativistic quantum mechanics (Jabs, A., 2010: Found. Phys., {\bf 40}, 776-792). The proof is extended here to the relativistic regime using the parametrized Dirac equation. A causality…
I present explicit examples of generalizations in relativistic quantum mechanics. First of all, I discuss the generalized spin-1/2 equations for neutrinos. They have been obtained by means of the Gersten-Sakurai method for derivations of…
In previous works, the universal mapping class group was taken to be the group PPSL(2,Z) of all piecewise PSL(2,Z) homeomorphisms of the unit circle S^1 with finitely many breakpoints among the rational points, and in fact, the Thompson…
In order to avoid the difficulties encountered by relativistic quantum theory of single particles, we pursue a deductive development of the theory from physical principles, without canonical quantization, by making use of group-theoretical…
In this article, we begin with a review of Pauli's version of the spin-statistics theorem and then show, by re-defining the parameter associated with the Lie-Algebra structure of angular momentum, that another interpretation of the theorem…
A model-independent, locally generally covariant formulation of quantum field theory over four-dimensional, globally hyperbolic spacetimes will be given which generalizes similar, previous approaches. Here, a generally covariant quantum…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…
We present a short review of the spin curvatures that arise within the framework of one of the Infeld-van der Waerden formalisms for general relativity. All the spinor symmetries borne by the inner structure of general relativity are thus…
Recently a sufficient and necessary condition for Pauli's spin- statistics connection in nonrelativistic quantum mechanics has been established [quant-ph/0208151]. The two-dimensional part of this result is extended to n-particle systems…
An explicit construction of theories of spinning particles, both massive and massless, is given with arbitrary extended supersymmetry on the world-line. As an application of our results, we give a universal description of 3D (and via…
The spin-statistics theorem is generalized to include quantum entanglement. Specifically, within the context of spin entanglement, we prove that isotropic spin-correlated (ISC) states must occur in pairs. This pairing process can be…
In a previous paper, we have shown that the classical and quantum relativistic dynamics of the Stueckelberg-Horwitz-Piron [SHP] theory can be embedded in general relativity (GR). We briefly review the SHP theory here, and, in particular,…