Relativistic velocity addition from the geometry of momentum space

With the goal of developing didactic tools, we consider the geometrization of the addition of velocities in special relativity by using Minkowski diagrams in momentum space. For the case of collinear velocities, we describe two ruler-and-compass constructions that provide simple graphical solutions working with the mass-shell hyperbola in a 1+1-dimensional energy-momentum plane. In the spirit of dimensional scaffolding, we use those results to build a generalization in 1+2 dimensions for the case of non-collinear velocities, providing in particular a graphical illustration of how the velocity transverse to a boost changes while the momentum remains fixed. We supplement the discussion with a number of interactive applets that implement the diagrammatic constructions and constitute a visual tool that should be useful for students to improve their understanding of the subtleties of special relativity.

General Properties of Higher-Spin Fermion Interaction Currents and Their Test in πN-Scattering

The currents of higher-spin fermion interactions with zero- and half-spin particles are derived. They can be used for the N*(J) ↔ Nπ-transitions (N*(J) is thenucleon resonance with the J spin). In accordance with the theorem on currents and fields, the spin-tensors of these currents are traceless, and their products with the γ-matrices and the higher-spin fermion momentum vanish, similarly to the field spin-tensors. Such currents are derived explicitly for J=3/2and 5/2. It is shown that, in the present approach, the scale dimension of a higher spin fermion propagator equals to –1 for any J ≥ 1/2. The calculations indicate that the off-mass-shell N* contributions to the s-channel amplitudes correspond to J = JπN only ( JπN is the total angular momentum of the πN-system). As contrast, in the usually exploited approaches, such non-zero amplitudes correspond to 1/2 ≤ JπN ≤ J. In particular, the usually exploited approaches give non-zero off-mass-shell contributions of the ∆(1232)-resonance to the amplitudes S31, P31( JπN = 1/2) and P33, D33(JπN = 3/2), but our approach – to P33 and D33 only. The comparison of these results with the data of the partial wave analysis on the S31-amplitude in the ∆(1232)-region shows the better agreement for the present approach.

On the coupling of relativistic particle to gravity and Wheeler–DeWitt quantization

A system consisting of a point particle coupled to gravity is investigated. The set of constraints is derived. It was found that a suitable superposition of those constraints is the generator of the infinitesimal transformations of the time coordinate [Formula: see text] and serves as the Hamiltonian which gives the correct equations of motion. Besides that, the system satisfies the mass shell constraint, [Formula: see text], which is the generator of the worldline reparametrizations, where the momenta [Formula: see text], [Formula: see text], generate infinitesimal changes of the particle’s position [Formula: see text] in spacetime. Consequently, the Hamiltonian contains [Formula: see text], which upon quantization becomes the operator [Formula: see text], occurring on the right-hand side of the Wheeler–DeWitt equation. Here, the role of time has the particle coordinate [Formula: see text], which is a distinct concept than the spacetime coordinate [Formula: see text]. It is also shown how the ordering ambiguities can be avoided if a quadratic form of the momenta is cast into the form that instead of the metric contains the basis vectors.

Planar generalized electrodynamics for one-loop amplitude in the Heisenberg picture

We examine the generalized quantum electrodynamics as a natural extension of the Maxwell electrodynamics to cure the one-loop divergence. We establish a precise scenario to discuss the underlying features between photon and fermion where the perturbative Maxwell electrodynamics fails. Our quantum model combines stability, unitarity, and gauge invariance as the central properties. To interpret the quantum fluctuations without suffering from the physical conflicts proved by Haag’s theorem, we construct the covariant quantization in the Heisenberg picture instead of the Interaction one. Furthermore, we discuss the absence of anomalous magnetic moment and mass-shell singularity.

Threefold spin helicity as possible origin of SU(3) gauge symmetry

In this paper, the notion of spin helicity is generalized into threefold spin helicity. It appears to be a useful means to extend the standard Dirac equation to describe coloured fermions. The threefold generalization of helicity is derived from the mass shell condition, spin, and kinetic helicity in a natural way. It is found that the three different types of helicities are associated with the rotation degrees of freedom in 3-D coordinate space. Moreover, threefold helicity can by unitary transformation be connected with the empirical SU(3) colour symmetry of the quarks, and thus be brought into the mathematical form of the SU(3) Yang–Mills gauge theory of the standard model. This offers an alternative picture of the physical origin of quark symmetry in compliance with the Coleman–Mandula theorem.

Strong CP violation in spin-1/2 singly charmed baryons

We report on the calculation of the CP-violating form factor F3 and the corresponding electric dipole moment for charmed baryons in the spin-1/2 sector generated by the QCD θ-term. We work in the framework of covariant baryon chiral perturbation theory within the extended-on-mass-shell renormalization scheme up to next-to-leading order in the chiral expansion.

Bundles of Quantum States

A brief introduction to Frölicher's notion of smoothness (F-smoothness) leads to a natural definition of a distributional bundle, that is a bundle whose fibers are distributional spaces constituted of generalised sections of 2-fibered classical bundles. Indeed the essential notions of finite-dimensional differential geometry can be seamlessly extended to such bundles. The case when the underlying classical bundle is a vector bundle over a mass-shell bundle yields the bundle of quantum states of a multi-particle system.

Off-shell Nucleons in Intermediate Energy Physics

I discuss some issues pertaining to vertices involving virtual (i.e. off-mass-shell) nucleons, namely, in which processes off-shell vertices appear, their transformation properties under field redefinitions, and the attempts that have been made to esti- mate their effects in electromagnetic processes at intermediate energies.