Relativistic Quantum Dynamics of Many-Body Systems

Relativistic quantum dynamics requires a unitary representation of the Poincare group on the Hilbert space of states. The dynamics of many-body systems must satisfy cluster separability requirements. In this paper we formulate an abstract framework of four dimensional Euclidean Green functions that can be used to construct relativistic quantum dynamics of N-particle systems consistent with these requirements. This approach should be useful in bridging the gap between few-body dynamics based on phenomenological mass operators and on quantum field theory.Comment: Latex, 9 Pages, Submitted to World Scientific - 50 Years of Quantum Many-Body Theory - A Conference in Honor of the 65-th Birthdays of John W. Clark, Alpo J. Kallio, Manfred L. Ristig, and Sergio Rosat

From Light Nuclei to Nuclear Matter. The Role of Relativity?

The success of non-relativistic quantum dynamics in accounting for the binding energies and spectra of light nuclei with masses up to A=10 raises the question whether the same dynamics applied to infinite nuclear matter agrees with the empirical saturation properties of large nuclei.The simple unambiguous relation between few-nucleon and many-nucleon Hamiltonians is directly related to the Galilean covariance of nonrelativistic dynamics. Relations between the irreducible unitary representations of the Galilei and Poincare groups indicate thatthe ``nonrelativistic'' nuclear Hamiltonians may provide sufficiently accurate approximations to Poincare invariant mass operators. In relativistic nuclear dynamics based on suitable Lagrangeans the intrinsic nucleon parity is an explicit, dynamically relevant, degree of freedom and the emphasis is on properties of nuclear matter. The success of this approach suggests the question how it might account for the spectral properties of light nuclei.Comment: conference proceedings "The 11th International Conference on Recent Progress in Many-Body Theories" to be published by World Scientifi

Scaling of Hadronic Form Factors in Point Form Kinematics

The general features of baryon form factors calculated with point form kinematics are derived. With point form kinematics and spectator currents hadronic form factors are functions of $\eta:={1\over 4}(v_{out}-v_{in})^2$ and, over a range of $\eta$ values are insensitive to unitary scale transformations of the model wave functions when the extent of the wave function is small compared to the scale defined by the constituent mass, $<r^2 > \ll 1/m^2$. The form factors are sensitive to the shape of such compact wave functions. Simple 3-quark proton wave functions are employed to illustrate these features. Rational and algebraic model wave functions lead to a reasonable representation of the empirical form factors, while Gaussian wave functions fail. For large values of $\eta$ point form kinematics with spectator currents leads to power law behavior of the wave functions

Relativistic Quantum Mechanics - Particle Production and Cluster Properties

This paper constructs relativistic quantum mechanical models of particles satisfying cluster properties and the spectral condition which do not conserve particle number. The treatment of particle production is limited to systems with a bounded number of bare-particle degrees of freedom. The focus of this paper is about the realization of cluster properties in these theories.Comment: 36 pages, Late

Axial Transition Form Factors and Pion Decay of Baryon Resonances

The pion decay constants of the lowest orbitally excited states of the nucleon and the $\Delta(1232)$ along with the corresponding axial transition form factors are calculated with Poincar\'e covariant constituent-quark models with instant, point and front forms of relativistic kinematics. The model wave functions are chosen such that the calculated electromagnetic and axial form factors of the nucleon represent the empirical values in all three forms of kinematics, when calculated with single-constituent currents. The pion decay widths calculated with the three forms of kinematics are smaller than the empirical values. Front and instant form kinematics provide a similar description, with a slight preference for front form, while the point form values are significantly smaller in the case of the lowest positive parity resonances.Comment: 18 pages, 5 figures. Slightly revised, accepted in Phys. Rev.

Melosh rotation: source of the proton's missing spin

It is shown that the observed small value of the integrated spin structure function for protons could be naturally understood within the naive quark model by considering the effect from Melosh rotation. The key to this problem lies in the fact that the deep inelastic process probes the light-cone quarks rather than the instant-form quarks, and that the spin of the proton is the sum of the Melosh rotated light-cone spin of the individual quarks rather than simply the sum of the light-cone spin of the quarks directly.Comment: 5 latex page

Comparison of Relativistic Nucleon-Nucleon Interactions

We investigate the difference between those relativistic models based on interpreting a realistic nucleon-nucleon interaction as a perturbation of the square of a relativistic mass operator and those models that use the method of Kamada and Gl\"ockle to construct an equivalent interaction to add to the relativistic mass operator. Although both models reproduce the phase shifts and binding energy of the corresponding non-relativistic model, they are not scattering equivalent. The example of elastic electron-deuteron scattering in the one-photon-exchange approximation is used to study the sensitivity of three-body observables to these choices. Our conclusion is that the differences in the predictions of the two models can be understood in terms of the different ways in which the relativistic and non-relativistic $S$-matrices are related. We argue that the mass squared method is consistent with conventional procedures used to fit the Lorentz-invariant cross section as a function of the laboratory energy.Comment: Revtex 13 pages, 5 figures, corrected some typo