Equations Of Quantum Field Theory Research Articles

Finite element approximation in quantum theory

Many of the approaches to numerical quantum field theory which have been developed to date start from the Euclidean path integral formulation of the theory. This is because it is possible, using path integrals, to write closed form, albeit formal and difficult to evaluate, expressions for the quantities of physical interest, namely the Green’s functions. Thus, in this approach, the focus is not on finding the direct solution to the equations of quantum field theory, but rather on developing an effective and reliable method for evaluating the functional integrals representing the Green’s functions.

Projection-iteration method of solution of the equations of quantum field theory and its connection with the theory of renormalization. The equations of quantum field theory and improperly posed problems of mathematical physics

Projection-iteration method of solution of the equations of quantum field theory and its connection with the theory of renormalization. The equations of quantum field theory and improperly posed problems of mathematical physics

On distribution solutions for nonlinear differential equations: Nontriviality conditions

According to a general program for dealing with differential equations in quantum field theory, we consider a family of Cauchy problems, defining a simple model. Under the requirement that the Cauchy data be positive, the corresponding solutions are shown to converge to a nontrivial limiting point.

On some nonlinear evolution equations in quantum field theory

The field equations of a fermion field with a scalar self−interaction are studied in a three− and four−dimensional space−time. The Faedo−Galerkin method is used to prove the existence of a sequence of approximated solutions which converges in a suitable topology. In a different topology, the existence and uniqueness of a local solution

On the symmetry of dynamical equations in quantum field theory

On the symmetry of dynamical equations in quantum field theory

Operator method of solving quasipotential equations and the concept of straight-line paths at high energies

Alongside the study of the general proper t ies of solutions of quasipotential equations, for example, in the f ramework of the assumption that the local quasipotentiat is smooth [9-12], interest attaches to developing different approximate methods. In the present paper, we propose an operator method of finding approximate solutions of quasipotential equations; the formulation of this method is given in the f i rs t section. We should point out that this method is fair ly general in nature and may be applied to other equations of quantum field theory.

New Field-Theory Approach to Singular Potentials

An approach similar to the methods of renormalization of the Green's functions equations of quantum field theory is adopted to the singular potential in the Lippman-Schwinger equation. The close relation between our approach and the one used in field theory gives a method to be applied to nonrenormalizable field theories. The physical implication of this approach is discussed.

On the solution of certain singular integral equations of quantum field theory

In the study of complex phenomena involving π-mesons (e.g. simple and double photoproduction, radiative scattering, double production, etc.) one encounters singular integral equations linking the matrix elements and phase-shifts. We give here a general method of resolution of these equations which furnishes the following results :a) the simplest type is integrable by quadratures; 6) the general type is reducible to a Fredholm equation. We give also the solution of a system of coupled integral equations and of the particular one which occurs in the double production problem. This last case may be integrated by quadratures.

Singular integral equations in quantum field theory

The covariant theory of meson-nucleon scattering contains a vertex-part equation which is a singular integral equation. Because of this, there is a difficulty about the treatment of a renormalization constant. It is shown here how a consistent use of a high energy cut-off overcomes this difficulty. A related difficulty for the Bethe-Salpeter equation cannot be overcome by the same method.