Point Form Dynamics Research Articles

Strange and nonstrange baryon spectra in the relativistic interacting quark-diquark model with a Gürsey and Radicati-inspired exchange interaction

The relativistic interacting quark-diquark model, constructed in the framework of point form dynamics, is extended to strange baryons. The strange and nonstrange baryon spectra are calculated and compared with the experimental data.

RELATIVISTIC QUARK-DIQUARK MODEL

We discuss our relativistic quark-diquark model, developed in the framework of point form dynamics. Our results for the nonstrange baryon spectrum and for the nucleon electromagnetic form factors are discussed.

Point-form dynamics of quasistable states

We present a field theoretical model of point-form dynamics which exhibits resonance scattering. In particular, we construct point-form Poincaré generators explicitly from field operators and show that in the vector spaces for the in-states and out-states (endowed with certain analyticity and topological properties suggested by the structure of the S-matrix) these operators integrate to furnish differentiable representations of the causal Poincaré semigroup, the semidirect product of the semigroup of spacetime translations into the forward lightcone and the group of Lorentz transformations. We also show that there exists a class of irreducible representations of the Poincaré semigroup defined by a complex mass and a half-integer spin. The complex mass characterizing the representation naturally appears in the construction as the square root of the pole position of the propagator. These representations provide a description of resonances in the same vein as Wigner's unitary irreducible representations of the Poincaré group provide a description of stable particles.

Relativistic quark-diquark model of baryons

A relativistic quark-diquark mass operator with direct and exchange interaction has been constructed in the framework of point form dynamics. The nonstrange baryon spectrum has been calculated and compared with experimental data.

Point-Form Hamiltonian Dynamics and Applications

This short review summarizes recent developments and results in connection with point-form dynamics of relativistic quantum systems. We discuss a Poincare invariant multichannel formalism which describes particle production and annihilation via vertex interactions that are derived from field theoretical interaction densities. We sketch how this rather general formalism can be used to derive electromagnetic form factors of confined quark-antiquark systems. As a further application it is explained how the chiral constituent quark model leads to hadronic states that can be considered as bare hadrons dressed by meson loops. Within this approach hadron resonances acquire a finite (non-perturbative) decay width. We will also discuss the point-form dynamics of quantum fields. After recalling basic facts of the free-field case we will address some quantum field theoretical problems for which canonical quantization on a space-time hyperboloid could be advantageous.

Perturbations of unitary representations of the Galilei group: Mass operators with continuous spectra

We present a systematic procedure for constructing mass operators with continuous spectra for a system of particles in a manner consistent with Galilean relativity. These mass operators can be used to construct what may be called point-form Galilean dynamics. As in the relativistic case introduced by Dirac, the point-form dynamics for the Galilean case is characterized by both the Hamiltonian and momenta being altered by interactions. An interesting property of such perturbative terms to the Hamiltonian and momentum operators is that, while having well-defined transformation properties under the Galilei group, they also satisfy Maxwell’s equations. This result is an alternative to the well-known Feynman–Dyson derivation of Maxwell’s equations from non-relativistic quantum physics.

Semigroup integrability of point-form dynamics

We study the integrability of Poincare algebras for a collection of interacting particles. Using point-form dynamics, we will explicitly construct a pair of rigged Hilbert spaces in which a subset of the Poincare algebra integrates to a differentiable representation of the causal Poincare semigroup, the semidirect product of the Lorentz group and the semigroup of spacetime translations into the forward light cone. We will also give an example of a rigged Hilbert space in which the point-form algebra integrates to a differentiable representation of the Poincare group. The representations of the Poincare semigroup provide a means of understanding relativistic resonances and decaying states by way of a unified state vector description and thereby uniquely and unambiguously defining their mass, width and lifetime.

Relativistic calculation of hard bremsstrahlungpp→ppγto discriminate among different kinds ofNNinteractions

Previous nonrelativistic calculations have demonstrated a high sensitivity of hard bremsstrahlung $pp\ensuremath{\rightarrow}pp\ensuremath{\gamma}$ at the beam energies of $350--500\phantom{\rule{0.3em}{0ex}}\text{MeV}$ to the kind of nucleon-nucleon potential (meson exchange potentials versus the Moscow one). Here, bremsstrahlung calculations are generalized by means of relativistic considerations (point form dynamics). The necessary formal technique is presented. Resulting cross sections become smaller in comparison with nonrelativistic theory and their angular dependence changes. However, the high sensitivity to the kind of potential continues to exist and is characteristic of the differential cross section even at a relatively low beam energy of ${E}_{0}=280\phantom{\rule{0.3em}{0ex}}\text{MeV}$ where corresponding experimental data do exist. Our calculations give some preliminary indication that one of the versions of the Moscow potential may be valid here.

Quantum effects in relativistic decays

By using both explicit time-dependent andS-matrix formalisms of relativistic quantum theory we calculate the decay law of a moving unstable system and show that the classical Einstein time dilation formula is not rigorously applicable in this case and quantum corrections should be taken into account. The consistency of experimental data with Einstein's time dilation formula and the absence of translation-induced decays indicate that the interactions responsible for decays belong to the Dirac instant form dynamics rather than to the point form dynamics. Our results suggest that even though the different forms of dynamics are scattering-equivalent, they are not exactly physically equivalent, as was thought before. Three different experiments with unstable particles are discussed which allow one in principle to determine the details of the interaction governing the decay.

Heavy-quark symmetry and Dirac's point form dynamics.

Dirac's point form dynamics provides a natural framework for studying the additional symmetries associated with hadrons containing a single heavy quark. The heavy-quark limit both as an approximation and as a rigorous limit can be examined within concrete models. Special attention is given to the Bakamjian-Thomas construction, and an illustrative model calculation is presented.