Variational Derivation of Relativistic Fermion-Antifermion Wave Equations in QED

We present a variational method for deriving relativistic two-fermion wave equations in a Hamiltonian formulation of QED. A reformulation of QED is performed, in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. The reformulation permits one to use a simple Fock-space variational trial state to derive relativistic fermion-antifermion wave equations from the corresponding quantum field theory. We verify that the energy eigenvalues obtained from the wave equation agree with known results for positronium.Comment: 25 pages, accepted in Journal of Mathematical Physics (2004

Bound-State Variational Wave Equation For Fermion Systems In QED

We present a formulation of the Hamiltonian variational method for QED which enables the derivation of relativistic few-fermion wave equation that can account, at least in principle, for interactions to any order of the coupling constant. We derive a relativistic two-fermion wave equation using this approach. The interaction kernel of the equation is shown to be the generalized invariant M-matrix including all orders of Feynman diagrams. The result is obtained rigorously from the underlying QFT for arbitrary mass ratio of the two fermions. Our approach is based on three key points: a reformulation of QED, the variational method, and adiabatic hypothesis. As an application we calculate the one-loop contribution of radiative corrections to the two-fermion binding energy for singlet states with arbitrary principal quantum number $n$, and $l =J=0$. Our calculations are carried out in the explicitly covariant Feynman gauge.Comment: 26 page

Exact spinor-scalar bound states in a QFT with scalar interactions

We study two-particle systems in a model quantum field theory, in which scalar particles and spinor particles interact via a mediating scalar field. The Lagrangian of the model is reformulated by using covariant Green's functions to solve for the mediating field in terms of the particle fields. This results in a Hamiltonian in which the mediating-field propagator appears directly in the interaction term. It is shown that exact two-particle eigenstates of the Hamiltonian can be determined. The resulting relativistic fermion-boson equation is shown to have Dirac and Klein-Gordon one-particle limits. Analytic solutions for the bound state energy spectrum are obtained for the case of massless mediating fields.Comment: 12 pages, RevTeX, 1 figur

Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model

We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky model. Using an iterative approach and eliminating the mediating field by means of the covariant Green function we arrive at a Lagrangian density containing many-point time-nonlocal interaction terms. In low-order approximations of $\phi^3{+}\phi^4$ theory we obtain the usual two-current interaction as well as a three-current interaction of a confining type. The same result is obtained without approximation for a version of the dipole model. The transition to the Hamiltonian formalism and subsequent canonical quantization is performed with time non-locality taken into account approximately. A relativistic three-particle wave equation is derived variationally by using a three-particle Fock space trial state. The non-relativistic limit of this equation is obtained and its properties are analyzed and discussed.Comment: 15 pages, 1 figure, LaTe

Exact two-particle eigenstates in partially reduced QED

We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be obtained in the canonical equal-time formalism for the case where there are no free photons. These eigenstates lead to two- and three-body Dirac-like equations with electromagnetic interactions. Perturbative and some numerical solutions of the two-body equations are presented for positronium and muonium-like systems, for various strengths of the coupling.Comment: 33 pages, LaTex 2.09, 4 figures in EPS forma

Variational Two Fermion Wave Equations in QED: Muonium Like Systems

We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. The resulting modified Hamiltonian contains the photon propagator directly. A simple Fock-state variational trial function is used to derive relativistic two-fermion equations variationally from the expectation value of the Hamiltonian of the field theory. The interaction kernel of the equation is shown to be, in essence, the invariant M-matrix in lowest order. Solutions of the two-body equations are presented for muonium like system for small coupling strengths. The results compare well with the observed muonium spectrum, as well as that for hydrogen and muonic hydrogen. Anomalous magnetic moment effects are discussed

Analysis of inter-quark interactions in classical chromodynamics

The QCD gluon equation of motion is solved approximately by means of the Green function. This solution is used to reformulate the Lagrangian of QCD such that the gluon propagator appears directly in the interaction terms of the Lagrangian. The nature of the interactions is discussed. Their coordinate-space form is presented and analyzed in the static, non-relativistic case.Comment: 10 pages, 1 figure, LaTex2

Strange Decays of Nonstrange Baryons

The strong decays of excited nonstrange baryons into the final states Lambda K, Sigma K, and for the first time into Lambda(1405) K, Lambda(1520) K, Sigma(1385) K, Lambda K*, and Sigma K*, are examined in a relativized quark pair creation model. The wave functions and parameters of the model are fixed by previous calculations of N pi and N pi pi, etc., decays. Our results show that it should be possible to discover several new negative parity excited baryons and confirm the discovery of several others by analyzing these final states in kaon production experiments. We also establish clear predictions for the relative strengths of certain states to decay to Lambda(1405) K and Lambda(1520) K, which can be tested to determine if a three-quark model of the Lambda(1405) K is valid. Our results compare favorably with the results of partial wave analyses of the limited existing data for the Lambda K and Sigma K channels. We do not find large Sigma K decay amplitudes for a substantial group of predicted and weakly established negative-parity states, in contrast to the only previous work to consider decays of these states into the strange final states Lambda K and Sigma K.Comment: 25 pages, 8 figures, RevTe

Two fermion relativistic bound states: hyperfine shifts

We discuss the hyperfine shifts of the Positronium levels in a relativistic framework, starting from a two fermion wave equation where, in addition to the Coulomb potential, the magnetic interaction between spins is described by a Breit term. We write the system of four first order differential equations describing this model. We discuss its mathematical features, mainly in relation to possible singularities that may appear at finite values of the radial coordinate. We solve the boundary value problems both in the singular and non singular cases and we develop a perturbation scheme, well suited for numerical computations, that allows to calculate the hyperfine shifts for any level, according to well established physical arguments that the Breit term must be treated at the first perturbative order. We discuss our results, comparing them with the corresponding values obtained from semi-classical expansions.Comment: 16 page

The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach

The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum of the field system is asymmetrical. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for a part of the aforementioned region. Besides, for the bosonic equivalent to the massive Schwinger model, the masses of the one boson and two-boson bound states agree with the recent second-order results of a fermion-mass perturbation calculation when the fermion mass is small.Comment: Latex, 11 pages, 8 figures (EPS files