60 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
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
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
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
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 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
Variational two-particle wave equation in scalar quantum field theory
We study two-particle systems in a model quantum field theory, in which
scalar particles of different mass interact via a mediating scalar field. The
Lagrangian of the model is reformulated 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. The variational method, with a simple Fock-state trial
state, is used to derive a relativistic momentum-space two-particle wave
equation. Non-relativistic and one-particle limits of the equation are determined and discussed brieflyМи вивчаємо двочастинкові системи в модельній квантовій теорії поля, в якій скалярні частинки різної маси взаємодіють через посередкове скалярне поле. Використовуючи коваріантні функції Ґріна для
розв’язку посередкового поля в термінах частинкових полів, переформульовано ляґранжіян моделі. В результаті в гамільтоніяні виникає пропагатор посередкового поля прямо в члені, який описує
взаємодію. Варіяційна метода з простим пробним фоковим станом
використовується для того, щоб вивести релятивістичне двочастинкове хвильове рівняння в імпульс-просторі. Одержуються і обговорюються нерелятивістичні і одночастинкові границі цього рівняння
FEW-PARTICLE EIGENSTATES IN THE YUKAWA MODEL
Розглядається переформулювання моделі Юкави, у якій ферміони
взаємодіють через посередництво (масивного або безмасового)
скалярного поля. За допомогою коваріянтних функцій Ґріна поле, що
переносить взаємодію, виражено у термінах ферміонних полів. Результуючий гамільтоніян теорії містить член, що описує взаємодію, у
який явно входить пропагатор поля — носія взаємодії. Показано, що
коли можна знехтувати процесами, що включають випромінювання фізичних квантів поля-носія, то з використанням нестандартного
означення вакуумного стану можна отримати у рамках канонічного
одночасового формалізму точні власні стани результуючого гамільтоніяну для декількох ферміонів. Ці власні стани приводять до двота тричастинкових рівнянь Діракового типу із скалярними взаємодіями. Числовим розв’язуванням рівняння на власні значення отримано двоферміонні зв’язані стани для J = 0 . Проведено порівняння із
стандартним розглядом цієї моделі.We consider a reformulation of the Yukawa model, in which fermions interact via a mediating (massive or massless) scalar field. Covariant Green
functions are used express the mediating field in terms of the fermion
fields. The resulting Hamiltonian of the theory has an interaction term in
which the propagator of the mediating field appears directly. We show that
if processes involving emission of physical mediating field quanta can be
ignored and an unconventional empty vacuum is used, then exact few-
fermion eigenstates of the resulting truncated Hamiltonian can be obtained
in the canonical equal-time formalism. These eigenstates lead to two- and
three-body Dirac-like equations with scalar interactions. Two-fermion bound states are obtained by the numerical solution of the eigenvalue equation for J = 0 states. Comparison is made with conventional treatments of
this model
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