Ultralocal spinor field models

Ultralocal spinor (fermion) field theories are distinguished by the independent temporal development of the field at each spacial point. For a wide class of models explicit operator constructions are given, in a positive definite Hilbert space, for the interacting field, the Hamiltonian, and several other operators. Not only do the fermion field operators fail to fulfill canonical anticommutation relations but associated ultralocal boson fields are required for their realization giving rise to both fermion and boson type excitations. Construction of the Hamiltonian from the field, as well as the transition from the interacting to the noninteracting theories entails various infinite renormalizations that are made explicit. The formulation and solution of these models is based solely on symmetry arguments and general principles, and makes no use whatsoever of cutoffs or perturbation theory.     

Exact hypersurface-homogeneous scalar field models

A mechanism is presented for obtaining exact solutions of the Einstein equations for hypersurface-homogeneous scalar fields which unifies and generalizes recent results for inflaton fields in the spatially homogeneous case and for thick domain walls in the timelike-homogeneous case.     

Conformally invariant scalar field in charge-asymmetric cosmological models

Within a statistical approach to the general theory of relativity, we have constructed isotropic-charge-asymmetric cosmological models with an ultrarelativistic mixture of baryons and antibaryons and a conformally invariant scalar field. We have determined the role of the scalar field in the models obtained. We have investigated the evolution of small perturbations on the background of the spatially flat nonsingular model.Donets Polytechnical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 71–75, January, 1994.     

Ultralocal quantum field theory in terms of currents

The paper considers the possibility of constructing ultralocal theories, whose Hamiltonians contain no gradient terms and are therefore diagonal in position space, entirely in terms of currents with an equal time current algebra replacing the canonical commutation relations. It is shown that the free current theory can be defined in terms of a certain representation of the current algebra related to the group,S L(2,R). This representation is then constructed by using certain results of Araki and in the process a new infinitely divisible state on the universal covering group ofSL(2,R) is displayed. An ultralocal free theory can also be constructed for the canonical fields, and its relation to the free current theory is shown to involve a certain renormalization procedure reminiscent of the thermodynamic limit.Research sponsored by the Air Force Office of Scientific Research under Contract No. F 44620-71-C-0108 and Contract No. AF 49(638) 1545.     

Nonsingular cosmological models: the massive scalar field case

The nonminimal coupling of a massive self-interacting scalar field with a gravitational field is studied. Spontaneous symmetry breaking occurs in the open universe even when the sign on the mass term is positive. In contrast to grand unified theories, symmetry breakdown is more important for the early universe and it is restored only in the limit of an infinite expansion. Symmetry breakdown is shown to occur in flat and closed universes when the mass term carries a wrong sign. The model has a naturally defined effective gravitational coupling coefficient which is rendered time-dependent due to the novel symmetry breakdown. It changes sign below a critical value of the cosmic scale factor indicating the onset of a repulsive field. The presence of the mass term severely alters the behaviour of ordinary matter and radiation in the early universe. The total energy density becomes negative in a certain domain. These features make possible a nonsingular cosmological model for an open universe. The model is also free from the horizon and the flatness problems.     

Cosmological perturbations in SFT inspired non-local scalar field models

We clearly and consistently supersymmetrize the celebrated horizontality condition to derive the off-shell nilpotent and absolutely anticommuting Becchi?CRouet?CStora?CTyutin (BRST) and anti-BRST symmetry transformations for the supersymmetric system of a free spinning relativistic particle within the framework of superfield approach to BRST formalism. For the precise determination of the proper (anti-)BRST symmetry transformations for all the bosonic and fermionic dynamical variables of our system, we consider the present theory on a (1,2)-dimensional supermanifold parameterized by an even (bosonic) variable (??) and a pair of odd (fermionic) variables ?? and $\bar{\theta}$ (with $\theta^{2} = \bar{\theta}^{2} = 0$ , $\theta\bar{\theta}+ \bar{\theta}\theta= 0$ ) of the Grassmann algebra. One of the most important and novel features of our present investigation is the derivation of (anti-)BRST invariant Curci?CFerrari type restriction which turns out to be responsible for the absolute anticommutativity of the (anti-)BRST transformations and existence of the coupled (but equivalent) Lagrangians for the present theory of a supersymmetric system. These observations are completely new results for this model.     

Inflationary stages in cosmological models with a scalar field

Homogeneous isotropic cosmological models with a massive scalar field are studied. It is shown that inflationary stages of evolution are characteristic of most solutions in these models.     

Inflation in cosmological models with a non-minimally coupled, massless scalar field

A homogeneous, spatially flat cosmological model induced by a massless scalar field is investigated. The parameter ξ of coupling of the field with the curvature can take any value. It is shown that the range of values of ξ is divided into three regions, ξ<0, 0<ξ<1/6, and ξ>1/6, each of which is characterized by the behavior of the scale factor in it. The points ξ=0 and ξ=1/6 are singular. Stages with exponential and power-law inflation are found in the ranges 0<ξ<1/6 and ξ>1/6. An exponential inflationary stage with acceptable cosmological consequences can occur for small positive ξ. Kazan’ State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 53–57, March, 1997.     

Kinklike structures in scalar field theories: From one-field to two-field models

In this Letter we study the possibility of constructing two-field models from one-field models. The idea is to start with a given one-field model and use the deformation procedure to generate another one-field model, and then couple the two one-field models nontrivially, to get to a two-field model, together with some explicit topological solutions. We show with several distinct examples that the procedure works nicely and can be used generically.     

Interacting tachyonic scalar field

We discuss the coupling between dark energy and matter by considering a homogeneous tachyonic scalar field as a candidate for dark energy.We obtained the functional form of scale factor by assuming that the coupling strength depends linearly on the Hubble parameter and energy density.We also estimated the cosmic age of the Universe for different values of coupling constant.     

Symmetric space scalar field theory

Some quantum field theories, such as the chiral SU(2) ? SU(2) theory, can have a dynamics invariant under a group $\text{G}$ that is realized on a vacuum which is invariant only under a subgroup $\text{H}$ of $\text{G}$. These theories may be defined by scalar fields which are coordinates for the coset manifold $\text{G}$/$\text{H}$. They are thus non-polynomial theories on a symmetric space, with the group motions in this space described by a set of Killing vectors. We show how the Lagrange function may be constructed entirely from the Killing vectors. In particular, all physical quantities may be expressed in terms of the currents formed out of the Killing vectors. The current correlation functions do not exhibit the spurious wave function renormalizations which are encountered if ordinary Green's functions are computed. We illustrate the general method by calculating one-loop counter terms in a completely invariant fashion. An Appendix describes in simple terms the general theory of symmetric spaces, which should prove useful in other contexts.     

Oscillating universe and scalar field

In order to obtain models of the homogeneous Isotropic universe that can oscillate without going through a singular state, a cosmic field is introduced that produces a negative pressure, following the work of Pachner. One is led to single out a particular form for this field. If one adds to the Einstein field equations an expression corresponding to this field, taking into account the existence of a cosmic time, one obtains theC-field of Hoyle and Narlikar for the case of conservation of matter.