Probability in relativistic quantum mechanics and foliation of spacetime

The conserved probability densities (attributed to the conserved currents derived from relativistic wave equations) should be non-negative and the integral of them over an entire hypersurface should be equal to one. To satisfy these requirements in a covariant manner, the foliation of spacetime must be such that each integral curve of the current crosses each hypersurface of the foliation once and only once. In some cases, it is necessary to use hypersurfaces that are not spacelike everywhere. The generalization to the many-particle case is also possible.Comment: 9 pages, 3 figures, revised, new references, to appear in Int. J. Mod. Phys.

On the non-vanishing of the Collins mechanism for single spin asymmetries

The Collins mechanism provides a non-perturbative explanation for the large single spin asymmetries found in hard semi-inclusive reactions involving a transversely polarized nucleon. However, there are seemingly convincing reasons to suspect that the mechanism vanishes, and indeed it does vanish in the naive parton model where a quark is regarded as an essentially 'free' particle. We give an intuitive analysis which highlights the difference between the naive picture and the realistic one, and shows how the Collins mechanism arises when the quark is described as an off-shell particle by a field in interaction. A typographical error is corrected in this version.Comment: 15 pages, 2 figure

Octonionic Version of Dirac Equations

It is shown that a simple continuity condition in the algebra of split octonions suffices to formulate a system of differential equations that are equivalent to the standard Dirac equations. In our approach the particle mass and electro-magnetic potentials are part of an octonionic gradient function together with the space-time derivatives. As distinct from previous attempts to translate the Dirac equations into different number systems here the wave functions are real split octonions and not bi-spinors. To formulate positively defined probability amplitudes four different split octonions (transforming into each other by discrete transformations) are necessary, rather then two complex wave functions which correspond to particles and antiparticles in usual Dirac theory.Comment: Version accepted by Int. J Mod. Phy

Contribution of spin 1/2 and 3/2 resonances to two-photon exchange effects in elastic electron-proton scattering

We calculate contributions of hadron resonances to two-photon exchange effects in electron-proton scattering. In addition to the nucleon and P33 resonance, the following heavier resonances are included as intermediate states in the two-photon exchange diagrams: D13, D33, P11, S11 and S31. We show that the corrections due to the heavier resonances are smaller that the dominant nucleon and P33 contributions. We also find that there is a partial cancellation between the contributions from the spin 1/2 and spin 3/2 resonances, which results in a further suppression of their aggregate two-photon exchange effect.Comment: 6 pages, 1 figure; additional comparison with data, results unchanged; to be published in Phys. Rev.

The Biedenharn Approach to Relativistic Coulomb-type Problems

The approach developped by Biedeharn in the sixties for the relativistic Coulomb problem is reviewed and applied to various physical problems.Comment: 16 pages, 4 figure

PT-Symmetric Representations of Fermionic Algebras

A recent paper by Jones-Smith and Mathur extends PT-symmetric quantum mechanics from bosonic systems (systems for which $T^2=1$) to fermionic systems (systems for which $T^2=-1$). The current paper shows how the formalism developed by Jones-Smith and Mathur can be used to construct PT-symmetric matrix representations for operator algebras of the form $\eta^2=0$, $\bar{\eta}^2=0$, $\eta\bar{\eta}+\bar {\eta} =\alpha 1$, where $\bar{eta}=\eta^{PT} =PT \eta T^{-1}P^{-1}$. It is easy to construct matrix representations for the Grassmann algebra ($\alpha=0$). However, one can only construct matrix representations for the fermionic operator algebra ($\alpha\neq0$) if $\alpha= -1$; a matrix representation does not exist for the conventional value $\alpha=1$.Comment: 5 pages, 2 figure

Pion-Exchange and Fermi-Motion Effects on the Proton-Deuteron Drell-Yan Process

Within a nuclear model that the deuteron has NN and \pi NN components, we derive convolution formula for investigating the Drell-Yan process in proton-deuteron (pd) reactions. The contribution from the \pi NN component is expressed in terms of a pion momentum distribution that depends sensitively on the \pi NN form factor. With a \pi NN form factor determined by fitting the \pi N scattering data up to invariant mass W = 1.3 GeV, we find that the pion-exchange and nucleon Fermi-motion effects can change significantly the ratios between the proton-deuteron and proton-proton Drell-Yan cross sections, R_{pd/pp} = \sigma^{pd}/(2\sigma^{pp}), in the region where the partons emitted from the target deuteron are in the Bjorken x_2 > 0.4 region. The calculated ratios R_{pd/pp} at 800 GeV agree with the available data. Predictions at 120 GeV for analyzing the forthcoming data from Fermilab are presented.Comment: 27 pages, 10 figures. A couple of new numerical results are added. arXiv admin note: substantial text overlap with arXiv:1106.556

Nucleus-Nucleus Bremsstrahlung from Ultrarelativistic Collisions

The bremsstrahlung produced when heavy nuclei collide is estimated for central collisions at the Relativistic Heavy Ion Collider. Soft photons can be used to infer the rapidity distribution of the outgoing charge. An experimental design is outlined.Comment: 12 pages, 7 figures, uses revte

Branching Ratio and CP-asymmetry for B-> 1^{1}P_{1}gamma decays

We calculate the branching ratios for B_{d}^{0}->(b_{1},h_{1})gamma at next-to-leading order (NLO) of alpha_{s} where b_{1} and h_{1} are the corresponding radially excited axial vector mesons of rho and omega respectively. Using the SU(3)symmetry for the form factor, the branching ratio for B_{d}^{0}->(b_{1},h_{1})gamma is expressed in terms of the branching ratio of the B_{d}^{0}-> K_{1}gamma and it is found to be B(B_{d}^{0}->b_{1}gamma)=0.71* 10^{-6} and B(B_{d}^{0}-> h_{1}gamma) =0.74*10^{-6}. We also calculate direct CP asymmetry for these decays and find, in confirmity with the observations made in the literature, that the hard spectator contributions significantely reduces the asymmetry arising from the vertex corrections alone. The value of CP-asymmetry is 10% and is negative like rho and omega in the Standard Model.Comment: 10 pages, 2 figure