Could Only Fermions Be Elementary?

In standard Poincare and anti de Sitter SO(2,3) invariant theories, antiparticles are related to negative energy solutions of covariant equations while independent positive energy unitary irreducible representations (UIRs) of the symmetry group are used for describing both a particle and its antiparticle. Such an approach cannot be applied in de Sitter SO(1,4) invariant theory. We argue that it would be more natural to require that (*) one UIR should describe a particle and its antiparticle simultaneously. This would automatically explain the existence of antiparticles and show that a particle and its antiparticle are different states of the same object. If (*) is adopted then among the above groups only the SO(1,4) one can be a candidate for constructing elementary particle theory. It is shown that UIRs of the SO(1,4) group can be interpreted in the framework of (*) and cannot be interpreted in the standard way. By quantizing such UIRs and requiring that the energy should be positive in the Poincare approximation, we conclude that i) elementary particles can be only fermions. It is also shown that ii) C invariance is not exact even in the free massive theory and iii) elementary particles cannot be neutral. This gives a natural explanation of the fact that all observed neutral states are bosons.Comment: The paper is considerably revised and the following results are added: in the SO(1,4) invariant theory i) the C invariance is not exact even for free massive particles; ii) neutral particles cannot be elementar

Fluctuations of the Lyapunov exponent in 2D disordered systems

We report a numerical investigation of the fluctuations of the Lyapunov exponent of a two dimensional non-interacting disordered system. While the ratio of the mean to the variance of the Lyapunov exponent is not constant, as it is in one dimension, its variation is consistent with the single parameter scaling hypothesis

Zero Modes in Electromagnetic Form Factors of the Nucleon in a Light-Cone Diquark Model

We use a diquark model of the nucleon to calculate the electromagnetic form factors of the nucleon described as a scalar and axialvector diquark bound state. We provide an analysis of the zero-mode contribution in the diquark model. We find there are zero-mode contributions to the form factors arising from the instantaneous part of the quark propagator, which cannot be neglected compared with the valence contribution but can be removed by the choice of wave function. We also find that the charge and magnetic radii and magnetic moment of the proton can be reproduced, while the magnetic moment of the neutron is too small. The dipole shape of the form factors, $G^p_M(Q^2)/\mu_p$ and $G^n_M(Q^2)/\mu_n,$ can be reproduced. The ratio $\mu G^p_E/G^p_M$ decreases with $Q^2,$ but too fast.Comment: 22 pages, 6 pages, accepted by J.Phys.

Generic Two-Qubit Photonic Gates Implemented by Number-Resolving Photodetection

We combine numerical optimization techniques [Uskov et al., Phys. Rev. A 79, 042326 (2009)] with symmetries of the Weyl chamber to obtain optimal implementations of generic linear-optical KLM-type two-qubit entangling gates. We find that while any two-qubit controlled-U gate, including CNOT and CS, can be implemented using only two ancilla resources with success probability S > 0.05, a generic SU(4) operation requires three unentangled ancilla photons, with success S > 0.0063. Specifically, we obtain a maximal success probability close to 0.0072 for the B gate. We show that single-shot implementation of a generic SU(4) gate offers more than an order of magnitude increase in the success probability and two-fold reduction in overhead ancilla resources compared to standard triple-CNOT and double-B gate decompositions.Comment: 5 pages, 3 figure

On the problem of interactions in quantum theory

The structure of representations describing systems of free particles in the theory with the invariance group SO(1,4) is investigated. The property of the particles to be free means as usual that the representation describing a many-particle system is the tensor product of the corresponding single-particle representations (i.e. no interaction is introduced). It is shown that the mass operator contains only continuous spectrum in the interval $(-\infty,\infty)$ and such representations are unitarily equivalent to ones describing interactions (gravitational, electromagnetic etc.). This means that there are no bound states in the theory and the Hilbert space of the many-particle system contains a subspace of states with the following property: the action of free representation operators on these states is manifested in the form of different interactions. Possible consequences of the results are discussed.Comment: 35 pages, Late

Point-Form Analysis of Elastic Deuteron Form Factors

Point-form relativistic quantum mechanics is applied to elastic electron-deuteron scattering. The deuteron is modeled using relativistic interactions that are scattering-equivalent to the nonrelativistic Argonne $v_{18}$ and Reid '93 interactions. A point-form spectator approximation (PFSA) is introduced to define a conserved covariant current in terms of single-nucleon form factors. The PFSA is shown to provide an accurate description of data up to momentum transfers of 0.5 ${\rm GeV}^2$, but falls below the data at higher momentum transfers. Results are sensitive to the nucleon form factor parameterization chosen, particularly to the neutron electric form factor.Comment: RevTex, 31 pages, 1 table, 13 figure