Dichotomic Functions and Bell's Theorems

It is shown that correlations of dichotomic functions can not conform to results from Quantum Mechanics. Also, it is seen that the assumptions attendant to optical tests of Bell's Inequalities actually are consistent with classical physics so that in conclusion, Bell's Theorems do not preclude hidden variable interpretations of Quantum Mechanics

Spinor particle. An indeterminacy in the motion of relativistic dynamical systems with separately fixed mass and spin

We give an argument that a broad class of geometric models of spinning relativistic particles with Casimir mass and spin being separately fixed parameters, have indeterminate worldline (while other spinning particles have definite worldline). This paradox suggests that for a consistent description of spinning particles something more general than a worldline concept should be used. As a particular case, we study at the Lagrangian level the Cauchy problem for a spinor particle and then, at the constrained Hamiltonian level, we generalize our result to other particles.Comment: 10 pages, 1 figur

On the use of the group SO(4,2) in atomic and molecular physics

In this paper the dynamical noninvariance group SO(4,2) for a hydrogen-like atom is derived through two different approaches. The first one is by an established traditional ascent process starting from the symmetry group SO(3). This approach is presented in a mathematically oriented original way with a special emphasis on maximally superintegrable systems, N-dimensional extension and little groups. The second approach is by a new symmetry descent process starting from the noninvariance dynamical group Sp(8,R) for a four-dimensional harmonic oscillator. It is based on the little known concept of a Lie algebra under constraints and corresponds in some sense to a symmetry breaking mechanism. This paper ends with a brief discussion of the interest of SO(4,2) for a new group-theoretical approach to the periodic table of chemical elements. In this connection, a general ongoing programme based on the use of a complete set of commuting operators is briefly described. It is believed that the present paper could be useful not only to the atomic and molecular community but also to people working in theoretical and mathematical physics.Comment: 31 page

Rotation of electromagnetic fields and the nature of optical angular momentum

The association of spin and orbital angular momenta of light with its polarization and helical phase fronts is now well established. The problems in linking this with electromagnetic theory, as expressed in Maxwell's equations, are rather less well known. We present a simple analysis of the problems involved in defining spin and orbital angular momenta for electromagnetic fields and discuss some of the remaining challenges. Crucial to our investigation is the duplex symmetry between the electric and magnetic fields

The Heat Kernel on AdSAdS

We explicitly evaluate the heat kernel for the Laplacian of arbitrary spin tensor fields on the thermal quotient of (Euclidean) $AdS_N$ for $N\geq 3$ using the group theoretic techniques employed for $AdS_3$ in arXiv:0911.5085. Our approach is general and can be used, in principle, for other quotients as well as other symmetric spaces.Comment: Added references, added appendix on heat kernel in even dimensio

Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations

One may ask whether the relations between energy and frequency and between momentum and wave vector, introduced for matter waves by de Broglie, are rigorously valid in the presence of gravity. In this paper, we show this to be true for Dirac equations in a background of gravitational and electromagnetic fields. We first transform any Dirac equation into an equivalent canonical form, sometimes used in particular cases to solve Dirac equations in a curved spacetime. This canonical form is needed to apply the Whitham Lagrangian method. The latter method, unlike the WKB method, places no restriction on the magnitude of Planck's constant to obtain wave packets, and furthermore preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac fields in a curved spacetime, that the probability current has a Gordon decomposition into a convection current and a spin current, and that the spin current vanishes in the Whitham approximation, which explains the negligible effect of spin on wave packet solutions, independent of the size of Planck's constant. We further discuss the classical-quantum correspondence in a curved spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham equations. We show that the generalized de Broglie relations in a curved spacetime are a direct consequence of Whitham's Lagrangian method, and not just a physical hypothesis as introduced by Einstein and de Broglie, and by many quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac equations. Added section on Gordon decomposition of the probability current. Encapsulated main results in the statement of Theorem

Superconformal symmetry and maximal supergravity in various dimensions

In this paper we explore the relation between conformal superalgebras with 64 supercharges and maximal supergravity theories in three, four and six dimensions using twistorial oscillator techniques. The massless fields of N=8 supergravity in four dimensions were shown to fit into a CPT-self-conjugate doubleton supermultiplet of the conformal superalgebra SU(2,2|8) a long time ago. We show that the fields of maximal supergravity in three dimensions can similarly be fitted into the super singleton multiplet of the conformal superalgebra OSp(16|4,R), which is related to the doubleton supermultiplet of SU(2,2|8) by dimensional reduction. Moreover, we construct the ultra-short supermultiplet of the six-dimensional conformal superalgebra OSp(8*|8) and show that its component fields can be organized in an on-shell superfield. The ultra-short OSp(8*|8) multiplet reduces to the doubleton supermultiplet of SU(2,2|8) upon dimensional reduction. We discuss the possibility of a chiral maximal (4,0) six-dimensional supergravity theory with USp(8) R-symmetry that reduces to maximal supergravity in four dimensions and is different from six-dimensional (2,2) maximal supergravity, whose fields cannot be fitted into a unitary supermultiplet of a simple conformal superalgebra. Such an interacting theory would be the gravitational analog of the (2,0) theory.Comment: 54 pages, PDFLaTeX, Section 5 and several references added. Version accepted for publication in JHE

Gauge fields in (A)dS within the unfolded approach: algebraic aspects

It has recently been shown that generalized connections of the (A)dS space symmetry algebra provide an effective geometric and algebraic framework for all types of gauge fields in (A)dS, both for massless and partially-massless. The equations of motion are equipped with a nilpotent operator called $\sigma_-$ whose cohomology groups correspond to the dynamically relevant quantities like differential gauge parameters, dynamical fields, gauge invariant field equations, Bianchi identities etc. In the paper the $\sigma_-$-cohomology is computed for all gauge theories of this type and the field-theoretical interpretation is discussed. In the simplest cases the $\sigma_-$-cohomology is equivalent to the ordinary Lie algebra cohomology.Comment: 59 pages, replaced with revised verio

Renormalization of the QED of self-interacting second order spin 1/2 fermions

We study the one-loop level renormalization of the electrodynamics of spin 1/2 fermions in the Poincar\'e projector formalism, in arbitrary covariant gauge and including fermion self-interactions, which are dimension four operators in this framework. We show that the model is renormalizable for arbitrary values of the tree level gyromagnetic factor g within the validity region of the perturbative expansion, \alpha g^2 << 1. In the absence of tree level fermion self-interactions, we recover the pure QED of second order fermions, which is renormalizable only for |g|=2. Turning off the electromagnetic interaction we obtain a renormalizable Nambu-Jona-Lasinio-like model with second order fermions in four space-time dimensions.Comment: 32 pages, 9 figures. Published versio