108 research outputs found
A Variational Fock-Space Treatment of Quarkonium
The variational method and the Hamiltonian formalism of QCD are used to
derive relativistic, momentum space integral equations for a quark-antiquark
system with an arbitrary number of gluons present. As a first step, the
resulting infinite chain of coupled equations is solved in the nonrelativistic
limit by an approximate decoupling method. Comparison with experiment allows us
to fix the quark mass and coupling constant, allowing for the calculation of
the spectra of massive systems such as charmonium and bottomonium. Studying the
results with and without the nonAbelian terms, we find that the presence of the
nonAbelian factors yields better agreement with the experimental spectra.Comment: TEX, no figure
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
Some exact solutions of reduced scalar Yukawa theory
The scalar Yukawa model, in which a complex scalar field interact via a real
scalar field, is reduced by using covariant Green functions. It is shown that
exact few-particle eigenstates of the truncated QFT Hamiltonian can be obtained
in the Feshbach-Villars formulation if an unorthodox "empty" vacuum state is
used. Analytic solutions for the two-body case are obtained for massless chion
exchange in 3+1 dimensions and for massive chion exchange in 1+1 dimensions.
Comparison is made to ladder Bethe-Salpeter, Feynman-Schwinger and
quasipotential results for massive chion exchange in 3+1. Equations for the
three-body case are also obtained.Comment: 19 pages, TEX, to appear in Can. J. Phy
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
Inter-particle potentials in a scalar QFT with a Higgs-like mediating field
We study the inter-particle potentials for few-particle systems in a scalar
theory with a non-linear mediating field of the Higgs type. We use the
variational method, in a reformulated Hamiltonian formalism of QFT, to derive
relativistic three and four particle wave equations for stationary states of
these systems. We show that the cubic and quartic non-linear terms modify the
attractive Yukawa potentials but do not change the attractive nature of the
interaction if the mediating fields are massive.Comment: 22 pages, 8 figures, 3 appendice
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
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 ,
and . Our calculations are carried out in the explicitly covariant
Feynman gauge.Comment: 26 page
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