Relativistic Hamiltonian Dynamics Research Articles

EMC effect, few-nucleon systems and Poincaré covariance

An approach for a Poincaré covariant description of nuclear structure and of lepton scattering off nuclei is proposed within the relativistic Hamiltonian dynamics in the light-front form. Indeed a high level of accuracy is needed for a comparison with the increasingly precise present and future experimental data at high momentum transfer. Therefore, to distinguish genuine QCD effects or effects of medium modified nucleon structure functions from conventional nuclear structure effects, the commutation rules between the Poincaré generators should be satisfied. For the first time in this paper a proper hadronic tensor for inclusive deep inelastic scattering of electrons off nuclei is derived in the impulse approximation in terms of the single nucleon hadronic tensor. Our approach is based : i) on a light-front spectral function for nuclei, obtained taking advantage of the successful non-relativistic knowledge of nuclear interaction, and ii) on the free current operator that, if defined in the Breit reference frame with the momentum transfer, , parallel to the z axis, fulfills Poincaré covariance and current conservation. Our results can be generalized : i) to exclusive processes or to semi-inclusive deep inelastic scattering processes; ii) to the case where the final state interaction is considered through a Glauber approximation; iii) to finite momentum transfer kinematics. As a first test, the hadronic tensor is applied to obtain the nuclear structure function and to evaluate the EMC effect for 3He in the Bjorken limit. Encouraging results including only the two-body part of the light-front spectral function are presented.

All classical predictions of general relativity from special relativistic Hamiltonian dynamics

Previous special relativistic calculations of gravitational redshift, light deflection and Shapiro delay are extended to include perigee advance. The three classical, order G, post-Newtonian predictions of general relativity as well as general relativistic light-speed-variation are therefore shown to be also consequences of special relativistic Newtonian mechanics in Euclidean space. The calculations are compared to general relativistic ones based on the Schwarzschild metric equation, and related literature is critically reviewed.

Dynamics of a relativistic charge in the Penning trap.

We are interested in the motion of a classical charge within a processing chamber of a Penning trap. We examine the relativistic Lagrangian and Hamiltonian dynamics without any approximations. We show that the radial and axial motions are non-linearly coupled to each other whenever the special relativity is taken into account. As the restoring quadruple potential has the axial symmetry, the dynamics of the system can be reduced to two degrees of freedom. If all the energy of a charge belongs to the axial oscillating mode, its time evolution is described by the nonlinear equation of motion for a simple pendulum. If the whole energy is accumulated in radial oscillating mode, the dynamical system resembles a double pendulum. We demonstrate that the Hamiltonian system is not integrable in the Liouville sense in the class of functions meromorphic in coordinates and momenta. Using Poincaré sections, we show that, in spite of the non-integrability, a large part of the phase space is filled by quasi-periodic solutions that encircle some periodic solutions. We determine numerically characteristic frequencies of these periodic solutions.

Electromagnetic gauge field interpolation between the instant form and the front form of the Hamiltonian dynamics

We present the electromagnetic gauge field interpolation between the instant form and the front form of the relativistic Hamiltonian dynamics and extend our interpolation of the scattering amplitude presented in the simple scalar field theory to the case of the electromagnetic gauge field theory with the scalar fermion fields known as the sQED theory. We find that the Coulomb gauge in the instant form dynamics (IFD) and the light-front gauge in the front form dynamics, or the light-front dynamics (LFD), are naturally linked by the unified general physical gauge that interpolates between these two forms of dynamics and derive the spin-1 polarization vector for the photon that can be generally applicable for any interpolation angle. Corresponding photon propagator for an arbitrary interpolation angle is found and examined in terms of the gauge field polarization and the interpolating time ordering. Using these results, we calculate the lowest-order scattering processes for an arbitrary interpolation angle in sQED. We provide an example of breaking the reflection symmetry under the longitudinal boost, $P^z \leftrightarrow -P^z$, for the time-ordered scattering amplitude in any interpolating dynamics except the LFD and clarify the confusion in the prevailing notion of the equivalence between the infinite momentum frame (IMF) and the LFD. The particular correlation found in our previous analysis of the scattering amplitude in the simple scalar field theory, coined as the J-shaped correlation, between the total momentum of the system and the interpolation angle persists in the present analysis of the sQED scattering amplitude. We discuss the singular behavior of this correlation in conjunction with the zero-mode issue in the LFD.

Scattering Amplitudes Interpolating Between Instant Form and Front Form of Relativistic Dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. Using the method of interpolation between the instant form and the front form, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. We discuss the rationale for using front form dynamics, nowadays known as light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that LFD uniquely can offer from first-principles quantum chromodynamics. In particular, model-independent constraints are provided for the analyses of deuteron form factors and the N Δ transition form factors at large momentum transfer squared Q2. The swap of helicity amplitudes between the collinear and non-collinear kinematics is also discussed in deeply virtual Compton scattering.

MODEL INDEPENDENT CONSTRAINTS ON HADRON FORM FACTORS AT LARGE Q2 IN LIGHT-FRONT QCD

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the front form has the largest number of kinematic generators. This distinction provides useful consequences in the analysis of physical observables in hadron physics. We discuss a rationale for using the front form dynamics, known nowadays as the light-front dynamics (LFD), and present a few explicit examples of hadron phenomenology that the front form uniquely can offer from the first principle QCD. In particular, model independent constraints are provided for the analyses of deuteron form factors and the NΔ transition form factors at large momentum transfer square Q2.

Interpolating scattering amplitudes between the instant form and the front form of relativistic dynamics

Among the three forms of relativistic Hamiltonian dynamics proposed by Dirac in 1949, the instant form and the front form can be interpolated by introducing an interpolation angle between the ordinary time $t$ and the light-front time $(t+z/c)/\sqrt{2}$. Using this method, we introduce the interpolating scattering amplitude that links the corresponding time-ordered amplitudes between the two forms of dynamics and provide the physical meaning of the kinematic transformations as they allow the invariance of each individual time-ordered amplitude for an arbitrary interpolation angle. In particular, it exhibits that the longitudinal boost is kinematical only in the front form dynamics, or the light-front dynamics (LFD), but not in any other interpolation angle dynamics. It also shows that the disappearance of the connected contributions to the current arising from the vacuum occurs when the interpolation angle is taken to yield the LFD. Since it doesn't require the infinite momentum frame (IMF) to show this disappearance and the proof is independent of reference frames, it resolves the confusion between the LFD and the IMF. The well-known utility of IMF usually discussed in the instant form dynamics is now also extended to any other interpolation angle dynamics using our interpolating scattering amplitudes.

Pion generalized parton distributions with covariant and light-front constituent quark models

We investigate the model dependence of no-helicity flip generalized parton distribution of the pion upon different approaches for the quark-hadron and quark-photon vertices, in the spacelike region. In order to obtain information on contributions from both the valence and the nonvalence regions, we compare results for spacelike momentum transfers obtained from (i) an analytic covariant model with a bare quark-photon vertex, (ii) a light-front approach with a quark-photon vertex dressed through a microscopic vector-meson model, and (iii) a light-front approach based on the relativistic Hamiltonian dynamics. Our comparisons lead us to infer the same dynamical mechanism, the one-gluon-exchange dominance at short distances, as a source of both the electromagnetic form factor at large momentum transfer and the parton distribution close to the end points. The expected collinear behavior of the generalized parton distributions at high-momentum transfer, i.e. a maximum for x{approx}1, is also illustrated, independently of the different approaches. Finally, a comparison with recent lattice calculations of the gravitational form factors is presented.

Relativistic Hamiltonian dynamics and few-nucleon systems

We present a preliminary calculation of the electromagnetic form factors of 3He and 3H, performed within the light-front Hamiltonian dynamics. Relativistic effects show their relevance even at the static limit, increasing at higher values of momentum transfer, as expected.

Covariant Hamiltonian dynamics with negative-energy states

A relativistic quantum mechanics is studied for bound hadronic systems in the framework of the point form relativistic Hamiltonian dynamics. Negative-energy states are introduced taking into account the restrictions imposed by a correct definition of the Poincaré group generators. We obtain nonpathological, manifestly covariant wave equations that dynamically contain the contributions of the negative-energy states. Auxiliary negative-energy states are also introduced, specially for studying the interactions of the hadronic systems with external probes.

Deuteron tensor polarization componentT20(Q2)as a crucial test for deuteron wave functions

The deuteron tensor polarization component ${T}_{20}({Q}^{2})$ is calculated by the relativistic Hamiltonian dynamics approach. It is shown that in the range of momentum transfers available with current experiments, relativistic effects, meson exchange currents, and the choice of nucleon electromagnetic form factors almost do not influence the value of ${T}_{20}({Q}^{2})$. However, this value depends strongly on the actual form of the deuteron wave function, that is, on the model of the $\mathit{NN}$ interaction in the deuteron. So the existing data for ${T}_{20}({Q}^{2})$ provide a crucial test for deuteron wave functions.

TWISTORS, SPECIAL RELATIVITY, CONFORMAL SYMMETRY AND MINIMAL COUPLING — A REVIEW

An approach to special relativistic dynamics using the language of spinors and twistors is presented. Exploiting the natural conformally invariant symplectic structure of the twistor space, a model is constructed which describes a relativistic massive, spinning and charged particle, minimally coupled to an external electro-magnetic field. On the two-twistor phase space the relativistic Hamiltonian dynamics is generated by a Poincaré scalar function obtained from the classical limit (appropriately defined by us) of the second order, to an external electro-magnetic field minimally coupled Dirac operator. In the so defined relativistic classical limit there are no Grassman variables. Besides, the arising equation that describes dynamics of the relativistic spin differs significantly from the so-called Thomas Bergman Michel Telegdi equation.

Construction of form factors of composite systems by a generalized Wigner-Eckart theorem for the Poincaré group

The relativistic approach to electroweak properties of two-particle composite systems developed previously is generalized here to the case of nonzero spin. This approach is based on the instant form of relativistic Hamiltonian dynamics. A special mathematical technique is used for the parametrization of matrix elements of electroweak current operators in terms of form factors. The parametrization is a realization of the generalized Wigner--Eckart theorem on the Poincar\'e group, form factors are corresponding reduced matrix elements and they have the sense of distributions (generalized functions). The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of electromagnetic current it also automatically satisfies the conservation law.

First Integrals and Integral Invariants of Relativistic Birkhoffian Systems**The project supported by National Natural Science Foundation of China under Grant No. 19972010, the Natural Science Foundation of Henan Province under Grant Nos. 934060800, 984053100, and 998040080, and the Scientific Research Foundation of Eduction Bureau of Hunan Province under Grant No. 02C033

For a relativistic Birkhoffian system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfect differential method. Secondly, the equations of nonsimultaneous variation of the system are established by using the relation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the first integral and the integral invariant of the system is studied, and it is proved that, using a first integral, we can construct an integral invariant of the system. Finally, the relation between the relativistic Birkhoffian dynamics and the relativistic Hamiltonian dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltonian system are obtained. Two examples are given to illustrate the application of the results.

Extraction of the neutron charge form factor Gn E(Q2) from the charge form factor of deuteron Gd C(Q2)

We extract the neutron charge form factor from the charge form factor of deuteron obtained from $T_{20}(Q^2)$ data at $0\le Q^2\le$ 1.717 (GeV$^2$). The extraction is based on the relativistic impulse approximation in the instant form of the relativistic Hamiltonian dynamics. Our results (12 new points) are compatible with existing values of the neutron charge form factor of other authors. We propose a fit for the whole set (35 points) taking into account the data for the slope of the form factor at $Q^2 = 0$.

Relativistic instant-form approach to the structure of two-body composite systems

An approach to the electroweak properties of two-particle composite systems is developed. The approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The main feature of this approach is the method of construction of the matrix element of the electroweak current operator. The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of the electromagnetic current also the conservation law automatically. The properties of the system as well as the approximations are formulated in terms of form factors. The approach makes it possible to formulate relativistic impulse approximation in such a way that the Lorentz covariance of the current is ensured. In the electromagnetic case the current conservation law is also ensured. Our approach gives good results for the pion electromagnetic form factor in the whole range of momentum transfers available for experiments at present time, as well as for the lepton decay constant of pions.

Is Minkowski Space-Time Compatible with Quantum Mechanics?

In quantum relativistic Hamiltonian dynamics, the time evolution of interacting particles is described by the Hamiltonian with an interaction-dependent term (potential energy). Boost operators are responsible for (Lorentz) transformations of observables between different moving inertial frames of reference. Relativistic invariance requires that interaction-dependent terms (potential boosts) are present also in the boost operators and therefore Lorentz transformations depend on the interaction acting in the system. This fact is ignored in special relativity, which postulates the universality of Lorentz transformations and their independence of interactions. Taking into account potential boosts in Lorentz transformations allows us to resolve the “no-interaction” paradox formulated by Currie, Jordan, and Sudarshan [Rev. Mod. Phys.35, 350 (1963)] and to predict a number of potentially observable effects contradicting special relativity. In particular, we demonstrate that the longitudinal electric field (Coulomb potential) of a moving charge propagates instantaneously. We show that this effect as well as superluminal spreading of localized particle states is in full agreement with causality in all inertial frames of reference. Formulas relating time and position of events in interacting systems reduce to the usual Lorentz transformations only in the classical limit (ħ→0) and for weak interactions. Therefore, the concept of Minkowski space-time is just an approximation which should be avoided in rigorous theoretical constructions.

On a possible estimation of the constituent-quark parameters from Jefferson Lab experiments on the pion form factor

The charge form factor of the pion is calculated for the momentum transfer range of the Jefferson Lab experiments. The approach is based on the instant form of the relativistic Hamiltonian dynamics. It is shown that the form-factor dependence on the choice of the model for the quark wave function in the pion is weak, while the dependence on the constituent-quark mass is rather significant. It is possible to estimate the mass of the constituent quark and the sum of the anomalous magnetic moments of the u- and $\bar d$ -quarks from the JLab experiments.

Isgur–Wise function in a relativistic model of constituent quarks

The integral representation for Isgur–Wise function (IWF) is obtained in the framework of instant-form relativistic Hamiltonian dynamics for mesons with one heavy quark. The upper and lower limits are calculated for the slope parameter of IWF ρ 2 by the model independent way. IWF is calculated for different wave functions of quarks in the meson. The difference between the limits of ρ 2 equals 1/3. The constraint on the slope parameter is in a good agreement with experiments. The weak dependence of IWF on the choice of wave functions is found.

Poincaré covariant current operator and elastic electron-deuteron scattering in the front-form Hamiltonian dynamics

The deuteron electromagnetic form factors, $A(Q^2)$ and $B(Q^2)$, and the tensor polarization $T_{20}(Q^2)$, are unambiguously calculated within the front-form relativistic Hamiltonian dynamics, by using a novel current, built up from one-body terms, which fulfills Poincar\'e, parity and time reversal covariance, together with Hermiticity and the continuity equation. A simultaneous description of the experimental data for the three deuteron form factors is achieved up to $Q^2 < 0.4 (GeV/c)^2$. At higher momentum transfer, different nucleon-nucleon interactions strongly affect $A(Q^2)$, $B(Q^2)$, and $T_{20}(Q^2)$ and the effects of the interactions can be related to $S$-state kinetic energy in the deuteron. Different nucleon form factor models have huge effects on $A(Q^2)$, smaller effects on $B(Q^2)$ and essentially none on $T_{20}(Q^2)$.