Space-like meson electromagnetic form factor in a relativistic quark model

The space-like electromagnetic form factor is expressed in terms of the overlap integral of the initial and final meson wave functions written as Lorentz covariant distributions of internal momenta. The meson constituents are assumed to be valence quarks and an effective vacuum-like field. The momentum of the latter represents a relativistic generalization of the potential energy of the quark system. The calculation is fully Lorentz covariant and the form factors of the charged mesons are normalized to unity at t=0. The numerical results have been obtained by freezing the transverse degrees of freedom. We found r_\pi^2=0.434 fm^2, r_{K^+}^2=0.333 fm^2, r_{K^0}^2=-0.069 fm^2 by taking m_{u,d}=430 MeV, m_s=700 MeV.Comment: 10 pages, revtex, 2 figure

Analytical solutions of a Dirac bound state equation and their field interpretation

We solve the single particle Dirac bound state equation with a particular confining potential and comment its significance from the point of view of the quantum field theory. We show that the solutions describe a complex physical system made of a free particle and of an effective field representing the confining potential.Comment: 6 pages, Late

Comments on a bound state model for a two body system

We show that in classical mechanics, as well as in nonrelativistic quantum mechanics the equation of the relative motion for a two-body bound system at rest can be replaced by individual dynamical equations of the same kind as the first one, but with different parameters. We assume that in relativistic quantum mechanics the individual equations are Dirac equations with modified parameters in agreement with the individual Schr\"odinger equations. We find that products of solutions to the individual equations with correlated arguments are the quantum analogues of the classical representation of a bound system and represent suitable models for the bound state wave functions. As validity test for the new representation of bound states we suggest to use some observable differences between this one and the representation in terms of relative coordinates.Comment: 5 pages, comments are wellcom

Relativistic covariance and the bound state wave function

We establish a relation between the solution of a relativistic bound state equation in quantum mechanics and the field representation of a bound state with the aid of creation and annihilation operators. We show that a bound system can be represented by a gas of free constituents and a classical effective field representing the countless quantum fluctuations generating the binding potential. The distribution function of the internal momenta is given by the projection of the free states on the solution of a relativistic bound state equation in the rest frame of the bound system. In this approach Lorentz covariance, mass-shell constraints and single particle normalizability of the bound state function are simultaneously and explicitly satisfied. The discussion is made for a two particle bound state and can be easily generalized to the case of three or more particles.Comment: 6 pages, Revte

A Lorentz covariant representation of bound state wave functions

We present a method enabling us to write in relativistic manner the wave function of some particular two particle bound state models in quantum mechanics. The idea is to expand the bound state wave function in terms of free states and to introduce the potential energy of the bound system by mens of the 4-momentum of an additional constituent, supposed to represent in a global way some hidden degrees of freedom. The procedure is applied to the solutions of the Dirac equation with confining potentials which are used to describe the quark antiquark bound states representing a given meson state.Comment: 6 pages, no figur

A stationary relativistic representation of the bound state

We show that a bound system in momentum space can be treated like a gas of free elementary constituents and a collective excitation of a background field which represents the countless quantum fluctuations generating the binding potential. The distribution function of the internal momenta in the bound system at rest is given by the projection of the solution of a relativistic bound state equation on the free wave functions of the elementary constituents. The 4-momentum carried by the collective excitation is the difference between the bound state 4-momentum and the sum of the free 4-momenta. This definiton ensures the explicit fulfilment of Lorentz covariance, mass-shell constraints and single particle normalizability of the bound state function. The discussion is made for a two particle bound state and can be easily generalized to the case of three or more particles.Comment: 12 page

Dynamic localization of lattice electrons under time dependent electric and magnetic fields

Applying the method of characteristics leads to wavefunctions and dynamic localization conditions for electrons on the one dimensional lattice under perpendicular time dependent electric and magnetic fields. Such conditions proceed again in terms of sums of products of Bessel functions of the first kind. However, this time one deals with both the number of magnetic flux quanta times $\pi$ and the quotients between the Bloch frequency and the ones characterizing competing fields. Tuning the phases of time dependent modulations leads to interesting frequency mixing effects providing an appreciable simplification of dynamic localization conditions one looks for. The understanding is that proceeding in this manner, the time dependent superposition mentioned above gets reduced effectively to the influence of individual ac-fields exhibiting mixed frequency quotients. Besides pure field limits and superpositions between uniform electric and time dependent magnetic fields, parity and periodicity effects have also been discussed.Comment: 10 pages. Submitted to: J.Phys. : Condens. Matte

A Lorentz covariant approach to the bound state problem

The relativistic equivalent of the Schr\"odinger equation for a two particle bound state having the total angular momentum $S$ is written in the form of a Lorentz covariant set of equations (p_1^mu+p_2^mu+Omega^mu)Psi(p_1,p_2;P) chi_S(\vec{p}_1,\vec{p}_2)=P^mu Psi(p_1,p_2;P) chi_S(\vec{p}_1,\vec{p}_2) where the operators Omega^mu are the components of a 4-vector quasipotential. The solution of this set is a stationary function representing the distribution of spins and internal momenta in a reference frame where the momentum of the bound system is P^\mu. The contribution of the operators Omega^mu to the bound state momentum is assumed to be the 4-momentum of a vacuum-like effective field entering the bound system as an independent component. It is shown that a state made of free quarks and of the effective field has definite mass and can be normalized like a single particle state. The generalization to the case of three or more particles is immediate

Generalized versus selected descriptions of quantum LC - circuits

Proofs are given that the quantum-mechanical description of the LC -circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrodinger-equation established before via F(n)=n, as well as to modified charge conservation laws. However, selected descriptions can also be done by looking for a unique derivation of the effective inductance. This leads to site independent inductances, but site dependent ones get implied by accounting for periodic solutions to F(n) in terms of Jacobian elliptic functions. Many-charge generalizations of quantum circuits, including the modified continuity equation for total charge and current densities, have also been discussed

Meson electromagnetic form factors in a relativistic quark model

The main assumption of the model is that in soft processes mesons behave like systems made of valence quarks and an effective vacuum- like field. The 4-momentum of the latter represents the relativistic generalization of the potential energy. The electromagnetic form factors are expressed in terms of the overlap integral of the initial and final wave functions written under the form of Lorentz covariant distribution of quark momenta. The calculation is fully Lorentz covariant and the form factors of the charged mesons are normalized to unity at t=0.Comment: 11 pages, LaTeX, 1 eps figure, submitted to Physics Letters