Препринти Iнституту фiзики конденсованих систем НАН України розповсюджуються серед наукових та iнформацiйних установ. Вони також доступнi по електроннiй комп'ютернiй мережi на WWW-сер-верi iнституту за адресою http://www.icmp.lviv.ua/ Анотацiя. Розглядаються узагальнення моделi Вiка-Куткоського з нелiнiйним полем-посередником. Шляхом розкладу за параметром нелiнiйности та вилученням поля-посередника з допомогою кова-рiянтної функцiї Ґрiна отримано лаґранжiян iз часо-нелокальними багато-точковими членами взаємодiї. У нижчих наближеннях теорiї ϕ 3 отримано звичнi дво-струмовi взаємодiї та три-струмову взаємо-дiю типу конфайнменту. Цей же результат отримано точно для версiї дипольної моделi. При гамiльтонiзацiї та канонiчному квантуваннi наближено враховано часову нелокальнiсть. Релятивiстичнi дво-та три-частинковi хвильовi рiвняння отримано варiяцiйним методом iз застосуванням багато-частинкових пробних станiв у просторi Фока. Отримано нерелятивiстичнi границi цих рiвнянь, аналiзуються та коротко обговорюються їх властивостi.
On confinement interactions in nonlinear generalizations of the Wick-Cutkosky model
Yu.W.Darewych, A.DuviryakAbstract. We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky model. Using an expansion in the nonlinearity parameter and eliminating the mediating field by means of the covariant Green function we derive a Lagrangian with many-point time-nonlocal interaction terms. In low-order approximations of ϕ 3 theory we obtain the usual twocurrent interaction and a three-current confining one. The same result is obtained exactly for a version of the dipole model. The Hamiltonization and canonical quantization is performed with time non-locality taken into account approximately. Relativistic two-and three-particle wave equations are derived variationally by using many-particle Fock space trial states. The non-relativistic limits of these equations are obtained and their properties are analyzed and discussed briefly.
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.
Abelian potentials of pointlike moving sources are obtained from the nonstandard theory of Yang-Mills field. They are used for the construction of the time-symmetric and time-asymmetric Fokker-type action integrals describing the dynamics of two-particle system with confinement interaction. The timeasymmetric model is reformulated in the framework of the Hamiltonian formalism. The corresponding two-body problem is reduced to quadratures. The behaviour of Regge trajectories is estimated within the semiclassical consideration.
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