23 research outputs found
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
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
Higgs particles interacting via a scalar Dark Matter field
We study a system of two Higgs bound state, interacting via a real scalar
Dark Matter mediating field, without imposing symmetry on the DM sector
of the postulated Lagrangian. The variational method in the Hamiltonian
formalism of QFT is used to derive relativistic wave equations for the
two-Higgs system, using a truncated Fock-space trial state. Approximate
solutions of the 2-body relativistic coupled integral equations are presented,
and conditions for the existence of Higgs bound states is examined in a broad
parameter space of DM mass and coupling constants
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
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