Theory of the scattering of pions from nuclei

A nonrelativistic quantum field theoretic formulation of pion-nucleus scattering is presented. A nonrelativistic boson-complex-target Low equation is developed, in which the coupling between the incident boson and target constituent particles is completely general. This development is then particularized to the case where the bosons are pions and the target is a nucleus of A nucleons. Special detailed attention is paid to the case where the pion-nucleon coupling is linear. The pion-nucleus Low equation is decomposed into a finite series of A terms, referred to as a spectator expansion, of which the first term involves one active particle and (A-1) spectators and the higher terms involve an increasingly larger number of active target particles. Within the framework of the nonrelativistic pion-nucleus Low equation, a formal definition of the pion-nucleus optical potential is also given.     

Current density in relativistic quantum mechanics

We extend to relativistic theories the concepts of probability density and probability current density of nonrelativistic quantum mechanics, together with the charge and current densities that are used as sources of the electromagnetic field in the semi-classical theory of radiation. There are some limitations in the procedure, especially in the case of several particles.     

Induced electron capture in field-assisted energetic atomic collisions

We present model considerations for the process of the electron capture in energetic nonrelativstic collisions of light atomic particles in the presence of a relatively weak low-frequency external electromagnetic field. The field is treated as an elliptically polarized quantum single-mode field. Establishing validity of the dipole approximation to the electron transfer (where the total momentum of all emitted or absorbed photons can be well above the typical inneratomic momenta of an electron in the initial and final states) and neglecting the Doppler and aberration effects, we give a fully nonrelativistic treatment for the field-assisted collisions and show that the capture cross section is invariant with respect to the Galilean transformations. The model consideration suggests that the field can substantially influence the capture dynamics and considerably change the capture cross section compared to the field-free collisions. This is especially the case if the “resonance” conditions nω≈±v ²/2 are satisfied, with nω being the energy transferred to or absorbed from the electromagnetic field and v the collision velocity.     

Space-time trajectories of quantum particles

The concept of trajectory is extended theoretically from classical mechanics through nonrelativistic and relativistic quantum mechanics. Forced motion of the particle as might be caused by an electromagnetic field is included in the equations. A new interpretation of the electromagnetic potential and the gauge transformation is presented. Using this formal structure, the problem of collecting particles into packets using trajectories is studied for both quantum mechanics and classical mechanics. Quantum mechanical trajectories are found to be significantly more restricted than those allowed by classical physics. The uncertainty principle comes from the second-order nature of the field equation without recourse to statistical arguments. The trajectories of particles in a quantum state can be calculated explicitly from the wave function (also see article in Volume 20, Number 6).     

Nonlinear Schrödinger mechanics and the law of gravity

This paper is a study of the consequences that follow from modeling a nonlinear and nonrelativistic quantum theory for gravitating particles. At present there exists no relativistic generalizations that do not sacrifice certain assumptions which are standard in covariant field theories.     

Macroscopic Quantum Electrodynamics of a Plasma Model: Derivation of the Vlasov Kinetics

We derive the large-scale Vlasov kinetics of a plasma model from its underlying quantum electrodynamics. The model comprises a system of nonrelativistic electrons, coupled to a quantised electromagnetic field and to a passive, positively charged, neutralising background.     

Relativistic shell models and meson-exchange currents

We discuss the connection between nonrelativistic pair exchange currents and relativistic mean field theories. Heavy mesons, especially the σ-meson, are shown to yield strong enhancements to the matrix element of “odd” Dirac operators, such as γ and γ₄γ₅, in complete analogy to the strong enhancements obtained in relativistic mean field theories. For isoscalar operators, there is a cancelling contribution from ω-pair diagrams, called “backflow” in relativistic theories, but for isovector operators the equivalent ρ-pair diagram is very weak. Agreement between traditional nonrelativistic calculations and experiment is worsened by the introduction of heavy-meson pair diagrams. The situation can be improved on adding vertex form factors and short-range correlation functions that reduce the heavy-meson pair contribution by about a factor of two. The differences between the two approaches are emphasized and experimental tests are discussed.     

Partons and gravitation: Some puzzling questions

The rather general belief in the theory of gravitation according to which neutral massive bodies with zero electric and magnetic moments are surrounded by a null electromagnetic field is analyzed from a critical viewpoint. Beginning the analysis at an atomic level, it is not difficult to see that neutral atoms are surrounded by a nonnull electromagnetic field generated by their peripheral electrons and by their nuclei even though their overall charge is zero. The data emerging from recent deep inelastic e-p scattering experiments clearly indicate that nucleons are composed by a number of charged constituents, often called partons, in a highly dynamical behavior.Consequently, nucleons and nuclei can also be a rather relevant source of electromagnetic field, in view of the presumed large number of partons, which is produced not only by their overall charges, but more properly by the charges of their individual constituents. Summing up the contributions from a large number of atoms, the possibility of a seizable electromagnetic field surrounding any neutral massive body emerges. Three assumptions, termed standard, weak, and strong according to which the energy-momentum tensor of the electromagnetic field generated by the matter constituents does not contribute, or partially contribute, or is entirely responsible of the gravitational field, are introduced. In order to assess the physical relevance of each of the above assumptions, a simple bound state model of the π⁰ particle is introduced in terms of two charged valence partons in a ¹S state. Some models of the electromagnetic field produced by the π⁰ charged constituents are derived as a ground for further extension to the case of nucleons, nuclei, and entire atoms. The gravitational field equations for the π⁰ particle according to the standard assumption are recalled and the ones according to the weak and strong assumptions are introduced. The puzzling implications of our analysis clearly cast shadows on the standard assumption, leaving as possible alternative for an exact formulation a selection between the weak and the strong assumptions. Some implications of the latter assumptions are discussed; the restrictions for the exterior case are derived using the framework of the “already unified theory”; some inconsistency with the gravitational wave theory is briefly discussed; and it is emphasized that the strong assumption implies a fully geometrical unification of gravitational and electromagnetic fields since the gravitational field is identified with a particular form, or “mutation,” of the electromagnetic field originated primarily in the nuclear, but also in the atomic structure. The admissibility of both the weak and the strong assumptions on the basis of our present knowledge is discussed and the feasibility of some experiments aiming at the proper selection as well as the ultimate physical assessment of the new assumptions is briefly analyzed.     

Quantum Field Formalism for the Electromagnetic Interaction of Composite Particles in a Nonrelativistic Gauge Model

A classical nonrelativistic U(1) × U(1) gauge field model for the electromagnetic interaction of composite particles is proposed and the quantum formalism is constructed. This gauge model containing a Chern–Simons U(1) field and the electromagnetic U(1) field can be coupled to both a bosonic or a fermionic matter field. We explicitly consider the second case, a composite fermion system in the presence of an electromagnetic field, and we carry out the canonical quantization by the Dirac method. The path integral approach is developed and the Feynman rules are established. A simplified model is considered. As an alternative path integral method, the BRST formalism for this gauge model is also treated.     

Gauge invariance,lorentz covariance and the observer

We discuss a number of questions related to the role of the observer in classical and quantum theories of fields, in particular electrodynamics. We find the gauge-independent parts of the electromagnetic potential, which are classical observables, both in a non-covariant manner and in a Lorentz covariant, observer-dependent way. We present an analysis of the probabilistic interpretation of relativistic quantum mechanics, similar to that of the nonrelativistic theory, and discuss the gauge invariance of the corresponding probability amplitudes.     

Quantum States of a Trapped Dirac Particle in a Pseudoscalar Potential

We obtain the quantum states of a trapped Dirac particle in the presence of a pseudoscalar potential. A change in the geometrical boundary condition can cause an effective electromagnetic field which can act on the trapped object. The nonrelativistic limit is discussed.     

Radiation Reaction of a Nonrelativistic Quantum Charged Particle

An alternative approach to analyze the nonrelativistic quantum dynamics of a rigid and extended charged particle taking into account the radiation reaction is discussed with detail. Interpretation of the field operators as annihilation and creation ones, theory of perturbations and renormalization are not used. The analysis is carried out in the Heisenberg picture with the electromagnetic field expanded in a complete orthogonal basis set of functions which allows the electromagnetic field to satisfy arbitrary boundary conditions. The corresponding coefficients are the field operators which satisfy the usual commutation relations. A nonlinear equation of motion for the charged particle is obtained. A careful consideration of the quantum effects allows the derivation of a linear equation of motion which is free of both runaway solutions and preacceleration, even for a point charge. Also, the electromagnetic mass, which is defined as the coefficient of the acceleration operator, vanishes for a point particle. However, this does not mean that the results are free of ambiguities which are exhibited and discussed.     

A Generalization of the Bargmann’s Theory of Ray Representations

The paper contains a complete theory of factors for ray representations acting in a Hilbert bundle, which is a generalization of the known Bargmanns theory. With its help, we have reformulated the standard quantum theory so that the gauge freedom emerges naturally from the very nature of quantum laws. The theory is of primary importance in the investigations of covariance (in contradistinction to symmetry) of a quantum theory which possesses a nontrivial gauge freedom. In that case the group in question is not any symmetry group but a covariance group only – the case not yet investigated in depth. It is shown that the factor of a covariance group representation depends on space and time when the system in question possesses gauge freedom. In nonrelativistic theories, the factor depends on time only. In relativistic theory, the Hilbert bundle is built over spacetime while in the nonrelativistic case-over time. We explain two applications of this generalization: in the theory of a quantum particle in gravitational field in the nonrelativistic limit, and in quantum electrodynamics.     

Nonrelativistic Quantum Mechanics with Spin in the Framework of a Classical Subquantum Kinetics

Recently it has been shown that the spinless one-particle quantum mechanics can be obtained in the framework of entirely classical subquantum kinetics. In the present paper we argue that, within the same scheme and without any extra assumption, it is possible to obtain both the nonrelativistic quantum mechanics with spin, in the presence of an arbitrary external electromagnetic field, as well as the nonlinear quantum mechanics.     

Near-threshold amplitude of pion-deuteron scattering: One-loop contributions

The one-loop expression for the absorptive correction to the πd scattering length is discussed. Relevant Feynman diagrams are calculated both in the relativistic and in the nonrelativistic formalism. A simple expression is obtained for the one-loop correction that arises in the πd scattering length owing to the Fermi motion of the nucleons in the deuteron. This correction includes absorption effects. Fulfillment of the unitarity relation is verified explicitly.