A generalized field theory. II. Linearized field equations

A thorough examination of the generalized field theory, formulated by the same authors in a previous paper, is being carried out in the absence of feedback effects. The results obtained are found to be in complete agreement with those of linear field theories of gravity and electromagnetism. Strict functions, which serve as indicators of the strength of the two fields, are being identified. This study reveals also two interesting results: the first is the classification of tetrad vector fields used, the second is the definite appearance of a mutual interaction between gravitational and electromagnetic fields.     

A generalized reggeon field theory incorporating hard scattering effects

Guided by the parton interpretation of RFT and by QCD, we propose an RFT where the pomeron field depends both onb and onQ ², the bare propagator describing an inhomogenous random walk inb and in lnQ ². Here,Q ² measures the virtuality of the inelastic processes which generate the pomeron exchange amplitude as their shadow. The asymptotic behaviour of such a theory should be different from that of standard RFT, at and above the critical point. Arguments are given in favour of a supercritical pomeron.     

When is a field theory a generalized free field?

We show within a scalar relativistic quantum field theory that if either some even truncatedn-point-function vanishes or some multiple commutator of the field operators is a c-number then the field is necessarily a generalized free field.     

A generalized self-dual Chern-Simons Higgs theory

In the recently discovered Chern-Simons model, the reduction to a Bogomol'nyi bound or self-duality depends crucially on the specific form of the Higgs potential energy function, which is characterized by a ⁶ type self-interaction. The purpose of this paper is to show that a much wider class of Higgs self-interaction may be allowed to achieve self-duality provided that the kinetic energy term of the Higgs scalar is suitably modified. The existence of topological multivortex solutions is also established. Furthermore, it is remarked that the Meissner effect may occur in the model.     

The generalized Fényes-Nelson model for free scalar field theory

The generalized Fényes-Nelson model of quantum mechanics is applied to the free scalar field. The resulting Markov field is equivalent to the Euclidean Markov field with the times scaled by a common factor which depends on the diffusion parameter. This result is consistent with Guerra's earlier work on stochastic quantization of scalar fields. It suggests a deep connection between Euclidean field theory and the stochastic interpretation of quantum mechanics. The question of Lorentz covariance is also discussed.     

A holomorphic field theory

Starting from conformal kinematics we show that the complex Minkowski space as a model of time-space is as good as the real one. A holomorphic field theory is constructed on and it is shown that real field theory is a linear approximation of the holomorphic one.     

A finite-action solution to generalized Yang-Mills-Higgs theory

We study the seven-dimensional generalized Yang-Mills-Higgs theory which results by dimensional reduction from eight-dimensional generalized SO(8) Yang-Mills theory. Using an SO(7)-symmetric ansatz, we prove the existence of a weak topologically nontrival finite-action solution.     

A cosmological exact solution of generalized Brans-Dicke theory with complex scalar field and its phenomenological implications

When the Brans-Dicke theory is formulated in terms of the Jordan scalar field φ, the amount of dark energy is related to the mass of this field. We investigate a solution which is relevant to the late universe. We show that if φ is taken to be a complex scalar field, then an exact solution to the vacuum equations requires that the Friedmann equation possesses both a constant term and one which is proportional to the inverse sixth power of the scale factor. Possible interpretations and phenomenological implications of this result are discussed.     

Topological particle field theory,general coordinate invariance and generalized Chern-Simons actions

We show that recently proposed generalized Chern-Simons action can be identified with the field theory action of a topological point particle. We find the crucial correspondence which makes it possible to derive the field theory actions from a special version of the generalized Chern-Simons actions. We provide arguments that the general coordinate invariance in the target space and the flat connection condition as a topological field theory can be accommodated in a very natural way. We propose series of new gauge invariant observables.     

On generally covariant quantum field theory and generalized causal and dynamical structures

We give an example of a generally covariant quasilocal algebra associated with the massive free field. Maximal, two-sided ideals of this algebra are algebraic representatives of external metric fields. In some sense, this algebra may be regarded as a concrete realization of Ekstein's ideas of presymmetry in quantum field theory. Using ideas from our example and from usual algebraic quantum field theory, we discuss a generalized scheme, in which maximal ideals are viewed as algebraic representatives of dynamical equations or Lagrangians. The considered frame is no quantum gravity, but may lead to further insight into the relation between quantum theory and space-time geometry.     

A conformal holomorphic field theory

A formulation of a field theory on the complex Minkowski space in terms of complex differential geometry is proposed. It is also shown that our model of field theory differs from the standard model on the real Minkowski space only in the limit of high energy.     

A solvable tensor field theory

Letters in Mathematical Physics - We solve the closed Schwinger–Dyson equation for the 2-point function of a tensor field theory with a quartic melonic interaction, in terms of...     

Currents,stress tensor and generalized unitarity in conformal invariant quantum field theory

Matrix elements of internal symmetry currents and energy momentum density tensor are constructed in Migdal Polyakov conformal invariant bootstrap field theory. Their 3-point functions satisfy Bethe Salpeter equations which determine any free coefficients that may still occur in the conformal invariant Ansatz. Ward identities are verified for alln-point functions. They imply correct equal time current commutation relations. A proof of generalized unitarity is also given. Various equivalent forms of the propagator bootstrap are discussed. Our algebraic techniques also yield an eigenvalue equation for first order correction to the exactly conformal invariant theory, assuming the latter is Gell-Mann Low large momentum asymptote of a renormalizable finite mass theory.     

A generalized spin ladder in a magnetic field

We study the phase diagram of coupled spin-1/2 chains with bilinear and (chiral) three-spin exchange interactions in a magnetic field. The model is soluble on a one-parametric line in the space of coupling constants connecting the limiting cases of a single and two decoupled Heisenberg chains with nearest neighbour exchange only. We give a complete classification of the low-energy properties of the integrable system and introduce a numerical method which allows to study the possible phases of spin ladder systems away from the soluble line in a magnetic field. Received 17 November 1998 and Received in final form 22 January 1999     

A nonperturbative stability theory of quantum field theory models

A nonperturbative method of analysis of the stability problem of quantum field theory models is proposed. The method consists in the systematic analysis of the functional dependence on boson field B of the effective boson Lagrangian S^eff(B) consisting of the fermion term S_l^F(B), constraint term S_l^FP(B) and the boson self-interaction term S_l(B). A new heat kernel representation for S_l^F(B) is derived in which counterterms are calculated in the explicit functional form by means of the analytic renormalization method. Using these results the instabillity of Yukawa₄, four-Fermi₄, and the massive Gürsey models is demonstrated.     

A self-consistent field theory of crystals

A self-consistent theory of crystals is presented. The classical phenomenological theory of crystals is derived by means of the boson transformation method.     

A local logarithmic conformal field theory

The local logarithmic conformal field theory corresponding to the triplet algebra at c = -2 is constructed. The constraints of locality and duality are explored in detail, and a consistent set of amplitudes is found. The spectrum of the corresponding theory is determined, and it is found to be modular invariant. This provides the first construction of a non-chiral rational logarithmic conformal field theory, establishing that such models can indeed define bona fide conformal field theories.     

A scalar field theory of gravitation

A scalar theory of gravitation is developed from a variational principle. The speed of light is taken to be a function of the potential of the gravitational field. The predictions of the light deflection and the advancement of the perihelion agree with those made by Einstein's theory. The gravitational (active) mass differs from the inertial (passive) mass and both are dependent on the gravitational potential.     

A question concerning unified field theory

The quantum hydrodynamics of extended particles is advanced by taking into account the gravitational field. A system of equations is obtained for relativistic nonlinear quantum unified field theory.Institute of Terrestrial Magnetism, the Ionosphere and Radiowave Propagation, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 71–76, November, 1993.