Sp(2) covariant quantization of models of vector and axial fields

Quantum models of vector and axial fields (U_v(N) × U_A(N)) are given within the framework of the Lagrangian version of Sp(2) formalism.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 34–37, August, 1995.     

Sp(2) BRST invariant quantization of strings: The harmonic gauge

We analyze the mixed algebra of local diffeomorphisms and Weyl transformations for bosonic strings. BRST and anti-BRST operators are then constructed keeping a manifest Sp(2) invariance. The harmonic gauge arises as a natural gauge choice. All this work is redone in the presence of a two-dimensional background metric. We manage to write down a simple action, to compute the stress tensor and to work out the critical dimensions.     

SO(4, 2)-covariant formulation of the Bargmann-Wigner equations

It is shown that the Bargmann-Wigner equations can be written in anSO(4, 2)-covariant form. As well as the Lorentz rotations, theSO(4, 2) group contains a space-inversion and a time-reflection operator (which are different from the usual ones). It also contains the Foldy-Wouthuysen and Cini-Touschek transformations. The spin-s theory for the massive and massless cases, and also a set of Bargmann-Wigner equations corresponding to space-like four-momentum, are all given by the sameSO(4, 2)-covariant equations, and their solutions can be obtained by transforming the solutions corresponding to the special gauge in which the four-momentum vanishes.     

Sp(2) renormalization

The renormalization of general gauge theories on flat and curved space–time backgrounds is considered within the Sp(2)-covariant quantization method. We assume the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Sp(2)-covariant formalism one can show that the theory possesses gauge-invariant and diffeomorphism invariant renormalizability to all orders in the loop expansion and the extended BRST-symmetry after renormalization is preserved. The advantage of the Sp(2) method compared to the standard Batalin–Vilkovisky approach is that, in reducible theories, the structure of ghosts and ghosts for ghosts and auxiliary fields is described in terms of irreducible representations of the Sp(2) group. This makes the presentation of solutions to the master equations in more simple and systematic way because they are Sp(2)-scalars.     

Space of states of the Freedman-Townsend model in the BLT-quantization scheme

Within the framework of the Lagrangian method of BLT (Batalin-Lavrov-Tyutin) quantization, we have studied the structure of a space of asymptotic states of the well-known Freedman-Townsend model (the model of an antisymmetric second-rank tensor field). We have shown that the physical unitarity condition is satisfied within the considered model. Tomsk State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 79–83, October, 1997.     

q-deformed SUSY algebra for suq(n)-covariant q-fermions

The q-deformed SUSY algebra is obtained for su_q(n)-covariant q-fermions and the Hamiltonian for them is constructed.     

Electron scattering in the microscopic Sp(3, R) model

A generating function formalism is presented for calculating the longitudinal and transverse electron scattering form factors of doubly even light nuclei in the microscopic Sp(3, R) model, and a practical computational method for carrying out the calculations is given. The method is applied to calculate the longitudinal elastic (0 → 0) and inelastic (0 → 2) form factors of ²⁰Ne in the SU(3), Sp(1, R), and S0(3) × D submodels. These results are compared with experiment and with other calculations.     

The parameter in an Sp(2N)×U(1) model

We present a model based upon the gauge group Sp(2N)×U(1) which contains the SU(2)×U(1) electroweak model as an exact subsector. The parameter in this symplectic model is calculated to leading order in 1/N. We illustrate the general dependence of upon the Higgs coupling constant λ with particular interest in th e large λ limit. Finally, the 1/N result is compared with conventional one-and two-loop expressions for in the standard model.     

Stochastic quantization and the renormalization (to first order) of the n-field model

This article is concerned with a recently developed new approach to quantum field theory, the method of stochastic quantization. This method is based on the use of the Langevin equation, which describes the non-equilibrium dynamics of a system, for the quantization of a theory [1], In this paper it is shown how the renormalization of the coupling constant for the n-field model arises in stochastic quantization. It is also shown that the renormalization does not depend on the parametrization of the n-field (to first order in the coupling constant). The Gell-Mann-Low function is obtained to first order.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–6, January, 1985.In conclusion the author is grateful to A. A. Migdal for supervising this work and to M. A. Bershadskii for useful discussions.     

Physical unitarity in the Lagrangian Sp(2)-symmetric formalism

The structure of state vector space for a general (non-anomalous) gauge theory is studied within the Lagrangian version of the Sp(2)-symmetric quantization method. The physical S-matrix unitarity conditions are formulated. The general results are illustrated on the basis of simple gauge theory models.     

From the Hamiltonian to the Lagrangean formalism for 1-reducible theories. The Freedman-Townsend model

The paper presents a possible path to the sp(3) BRST Lagrangean formalism for a 1-reducible gauge field theory starting from the Hamiltonian one. This appears to be not at all a trivial attempt and will allow explanation of the structure of generators and the form of the master equations in the Lagrangean sp(3) theories. The Freedman-Townsend model, for which a Lagrangean (covariant) sp(3) theory is important, is presented.     

Applications of a unique group embedding of internal symmetry groups andSU(2): spin-extensions for G2 and for the Sp(6)-Trion model

A recently proposed method of embeddingSU (2) and an internal symmetry groupG into a bigger groupG is applied to construct a spin extension ofG ₂ andSp (6). BecauseG ₂ andSp (6) possess a generalized quark model the embedding group can be proved to be unique and to be given bySp (14) resp.O (12) forG ₂ resp.Sp (6). For a particle classification splittings are calculated and tabulated forSp (14) ↓G ₂ xSU (2) andO (12) ↓Sp (6) xSU (2). The identification of low dimensional irreducible representations ofO (12) is quite satisfactory whereas an unreasonable number of unobserved particles are needed to fill up the supermultiplets of the spin extensionSp (14) of G₂.     

Canonical quantization of the Skyrme model

The canonical quantization of the Skyrme model is presented. Due to the complexities of the original set-up, first postulated by Rajeev, a new set of fields is found which satisfy a Lie algebra and for this reason, simplifies the study of the system. Using the new fields, the properties of the states under rotations are examined. As a result we re-derive the quantization of the coefficient of the Wess-Zumino action as an a priori consistency condition. We also find under what circumstances states with non-vanishing winding number behave like fermions.     

Semiclassical quantization of the shell model

The classical limit of the nuclear shell model is shown to be a many-dimensional hamiltonian system in which the coordinates and momenta are the coherent-state parameters of the original quantum system. Several methods for semiclassical quantization of this system are discussed, including surfaces of section and the Birkhoff-Gustavson transformation to action-angle variables. Application to a schematic three-level shell model indicates some of the new problems involved in requantizing multi-dimensional systems which are not present in one-dimensional examples. These include difficulties in finding periodic orbits and the onset of stochasticity.