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

Comment on the equivalence of Bakamjian-Thomas mass operators in different forms of dynamics

We discuss the scattering equivalence of the generalized Bakamjian-Thomas construction of dynamical representations of the Poincar\'e group in all of Dirac's forms of dynamics. The equivalence was established by Sokolov in the context of proving that the equivalence holds for models that satisfy cluster separability. The generalized Bakamjian Thomas construction is used in most applications, even though it only satisfies cluster properties for systems of less than four particles. Different forms of dynamics are related by unitary transformations that remove interactions from some infinitesimal generators and introduce them to other generators. These unitary transformation must be interaction dependent, because they can be applied to a non-interacting generator and produce an interacting generator. This suggests that these transformations can generate complex many-body forces when used in many-body problems. It turns out that this is not the case. In all cases of interest the result of applying the unitary scattering equivalence results in representations that have simple relations, even though the unitary transformations are dynamical. This applies to many-body models as well as models with particle production. In all cases no new many-body operators are generated by the unitary scattering equivalences relating the different forms of dynamics. This makes it clear that the various calculations used in applications that emphasize one form of the dynamics over another are equivalent. Furthermore, explicit representations of the equivalent dynamical models in any form of dynamics are easily constructed. Where differences do appear is when electromagnetic probes are treated in the one-photon exchange approximation. This approximation is different in each of Dirac's forms of dynamics.Comment: 6 pages, no figure

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

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

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

Vacuum Structures in Hamiltonian Light-Front Dynamics

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light-front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure.Comment: 16 pages, report \# ANL-PHY-7524-TH-93, (Latex

Quantitative Relativistic Effects in the Three-Nucleon Problem

The quantitative impact of the requirement of relativistic invariance in the three-nucleon problem is examined within the framework of Poincar\'e invariant quantum mechanics. In the case of the bound state, and for a wide variety of model implementations and reasonable interactions, most of the quantitative effects come from kinematic factors that can easily be incorporated within a non-relativistic momentum-space three-body code.Comment: 15 pages, 15 figure

Constraints of cluster separability and covariance on current operators

Realistic models of hadronic systems should be defined by a dynamical unitary representation of the Poincare group that is also consistent with cluster properties and a spectral condition. All three of these requirements constrain the structure of the interactions. These conditions can be satisfied in light-front quantum mechanics, maintaining the advantage of having a kinematic subgroup of boosts and translations tangent to a light front. The most straightforward construction of dynamical unitary representations of the Poincare group due to Bakamjian and Thomas fails to satisfy the cluster condition for more than two particles. Cluster properties can be restored, at significant computational expense, using a recursive method due to Sokolov. In this work we report on an investigation of the size of the corrections needed to restore cluster properties in Bakamjian-Thomas models with a light-front kinematic symmetry. Our results suggest that for models based on nucleon and meson degrees of freedom these corrections are too small to be experimentally observed.Comment: Contribution to Light Cone 2011, Dallas TX, 4 pages, 2 figure

Relativity and the low energy nd Ay puzzle

We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon interaction that is exactly on-shell equivalent to the high precision CDBonn NN interaction. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator. We find that for neutron laboratory energies above 20 MeV relativistic effects on Ay are negligible. For energies below 20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by 2% and Wigner rotations lower it further up to 10 % increasing thus disagreement between data and theory. This indicates that three-nucleon forces must provide an even larger increase of the Ay maximum than expected up to now.Comment: 29 pages, 2 ps figure