6 research outputs found
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
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
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