Nonlocal Quantum Field Theory Research Articles

Nonlocal Quark Model and Meson Decays

AbstractIn the framework of nonlocal quantum field theory we have constructed a quantized field called the virton field satisfying the conditions: the field of free virton quanta is equal identically to zero the causal function of this virton field differs from zero. We consider this virton field can be a good candidate for the description of quark confinement.It is suggested that the physical particles are described by the ordinary quantized fields but they interact with each other through the quark‐virton field only. Using the simplest form of the interaction Lagrangian invariant under transformations of the SU(3) × SUc(3) × U1 group, the mass corrections, some strong, weak and electromagnetic decays of the vector and pseudoscalar mesons are considered. A good agreement with experiment is obtained.

Confinement of quarks in nonlocal quantum field theory

The model of quarks in the frame of nonlocal quantum field theory is demonstrated. Here all basic principles of quantum theory are conserved, quarks are automatically confined and the scaling behaviour of the amplitude of an inclusive process is manifested explicitly in lower orders of perturbation theory.

A note on the axioms for a strictly nonlocal quantum field theory

The Iofa-Fainberg ([5]) formulation of a strictly nonlocal quantum field theory in terms of vacuum expectation values is reviewed in the Gelfand-Shilov ([2]) spaces to clarify that it lies just at the “boundary” of the theories considered by Constantinescu ([1]). A simple proof of holomorphy of the Laplace transformation of the relevant generalized functions (g.f.) which avoids the usual intermediate step of reduction to theorems on Laplace transforms of tempered distributions is given.

Description of Non-Polynomial Quantum Field Theories by Superpropagator Method

The description of superpropagator method and its applications to the mesodynamics, weak interaction, electrodynamics involving gravity and the chiral invariant field theory is given. The low-energy behaviour of particles is described, taking into account the loop Feynman diagrams. The renormalizations of physical quantities are finite and are expressed in terms of coupling constants. Partly this work was reported at the Third International Conference on Non-Local Quantum Field Theory in 1973 at Alushta, USSR.

A proof of the unitarity ofS-matrix in a nonlocal quantum field theory

Using the formfactors which are entire analytic functions in a momentum space, nonlocality is introduced for a wide class of interaction Lagrangians in the quantum theory of one-component scalar field φ(x). We point out a regularization procedure which possesses the following features: 1. The regularizedSδ matrix is defined and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} S^\delta = S.$$ 2. The Green positive-frequency functions which determine the operation of multiplication in\(S \cdot S^ + \mathop = \limits_{Df} S \circledast S^ + \) can be also regularized ⊛δ and there exists the limit $$\mathop {\lim }\limits_{\delta \to 0} \circledast ^\delta = \circledast \equiv .$$ 3. The operator\(J(\delta _1 ,\delta _2 ,\delta _3 ) = S^{\delta _1 } \circledast ^{\delta _2 } S^{\delta _3 + } \) is continuous at the point δ1=δ2=δ3=0. 4. $$S^\delta \circledast ^\delta S^{\delta + } \equiv 1at\delta > 0.$$ Consequently, theS-matrix is unitary, i.e. $$S \circledast S^ + = S \cdot S^ + = 1.$$

Quantized De Sitter space, the connection to the Pauli principle and an application to Feynman's relativistic quark theory II

A continuation of a previous paper, in which a model of a quantized space-time theory has been investigated, considers further problems of a quantized De Sitter space. There will be shown that a De Sitter space is a very useful starting point to a non-local relativistic quantum field theory, containing the Pauli principle, for the theory of elementary particles, as a connection to Feynman's relativistic quark theory, where the groupSU(3) has a particular importance, will be discussed. This method offers the possibility of treating weak local differences from a space with De Sitter metric as a perturbation. Therefore the problem of a fundamental elementary lengthlo must be considered in connection with the general theory of relativity.

Quantised De Sitter space and the connection to the Pauli principle

It will be shown that the introduction of a fundamental lengthlo permits the definition of commutator rules between different observation systems, represented by the Poincare groups. This fact leads to the model of a quantized De Sitter space, and the formulation of a non-local quantum field theory will be obtained. The Dirac spinors will be derived from the invariance of the quadratic form, defining De Sitter groups, and a connection to Pauli's exclusion principle can be understood by the same reason of a quantised space. A description of the structure of elementary particles involves a particular importance of the groupSU(3).

II Международное совещание по нелокальной квантовой теории поля (Азау, 15—24 марта 1970 г.)

II Международное совещание по нелокальной квантовой теории поля (Азау, 15—24 марта 1970 г.)

Composite bosons in nonlocal quantum field theory withZ 3≈1

Composite bosons in nonlocal quantum field theory withZ 3≈1

Nonlocal quantum field theory, nonlinear interaction lagrangians, and the convergence of the perturbation-theory series

Thus, for a definite class of significantly nonlinear interaction Lagrangians, we were able to construct, within the framework of nonlocal quantum field theory, the S-matrix of the theory in the form of a convergent perturbation-theory series in the Euclidean formulation of the theory. It was shown earlier that after a continuation into the physical domain, the S-matrix will be unitary in every order of perturbation theory. The next problem is the study of the behavior of the amplitudes of physical processes within the framework of the complete converging series which represents the total S-matrix of the theory.

Нелокальная квантовая теория поля

Нелокальная квантовая теория поля