Lagrangian formulation of irreducible massive fields of arbitrary spin in (2+1) dimensions

The Lagrangian formulation for free massive fields corresponding to arbitrary integer and half-integer spin-irreducible representations of the Poincaré group in three-dimensional space-time is presented. The relationship of the theory under consideration to the self-duality equations in four dimensions is discussed. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 113, No. 1, pp. 45–57, October, 1997.     

True BRST symmetry algebra and the theory of its representations

A simple treatment of BRST symmetry is proposed. From the physical point of view, it expresses a symmetry between ghosts and spurions; from the mathematical point of view, the symmetry operations are linear transformations in the superspaceC _1,1. From this it follows that the true BRST symmetry algebra isl(1, 1), the Lie superalgebra of all linear endomorphisms ofC _1,1, which extends the usual BRST algebra of the generatorsQ andQ _c with two new generatorsK=Q ^* andR={Q,Q ^*}. The theory of the representations ofl(1, 1) is developed systematically. The sets of automorphisms and involutions ofl(1, 1) are described. Decompositions into irreducible and indecomposable components are constructed for large classes of representations, both finite-and infinite-dimensional. Particular attention is devoted to the analysis of the indecomposable representations (in particular, a connection between them and subspaces of the continuous spectrum of the generators is found) and also of the metric properties of the indefinite spaces of the representations. A class of physical representations is identified and described in detail.V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 3–16, April, 1992.     

Nonperturbative quantization of models of massive non-Abelian gauge fields with spontaneously broken symmetry

We propose a new method for uniquely quantizing models of massive non-Abelian gauge fields with spontaneously broken symmetry applicable outside the framework of a perturbation theory in the coupling constant.     

Equivalence of Lagrangian and HamiltonianSp(2)-symmetric BRST quantizations

The existence of a local solution to the quantum Sp(2) master equation and the equivalence of the Lagrangian and Hamiltonian Sp(2) quantizations are proved in the framework of perturbation theory. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 1, pp. 137–148, January, 1997.     

Quantization of model of antisymmetric tensor field in the framework of extended BRST symmetry

The model of an antisymmetric second-rank tensor field is quantized in both the Lagrangian and the Hamiltonian forms of extended BRST quantization. It is shown that the Lagrangian quantization leads to a unitaryS matrix.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 3, pp. 420–428, September, 1995.     

Coupling of general Lagrangian systems

This work is devoted to the coupling of two fluid models, such as two Euler systems in Lagrangian coordinates, at a fixed interface. We define coupling conditions which can be expressed in terms of continuity of some well chosen variables and then solve the coupled Riemann problem. In the present setting where the interface is characteristic, a particular choice of dependent variables which are transmitted ensures the overall conservativity.

     

Exact sets of test uncharged massive spin 3/2 fields in general relativity

A theorem giving the necessary and sufficient conditions for Penrose's exact sets of spinor fields in curved spacetimes is proved. An algorithm for augmenting a system of fields to an exact set and constructing covariant Taylor expansions for the fields of an exact set is proposed. The general approach is applied to test massive spin 3/2 fields. Two possible forms of exact sets are constructed for them on the basis of modified Dirac-Fierz-Pauli equations. The functional arbitrariness in the solutions of the equations for exact sets is determined. In one of the cases, the obtained exact set can be interpreted as a system of fields of spins 3/2 and 1/2 interacting through the gravitational field.State University, Kiev. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 1, pp. 119–133, January, 1995.     

On the Lagrangian formulation of a Lane-Emden-type equation and double reduction

We classify all Noether point symmetries of the Lane-Emden-type equation x y ″ + n y ′ + x^νf (y) = 0 with respect to the standard Lagrangian L = 1/2 xⁿy ′² – x^{n +ν –1} ∫ f (y)dy for various functions f (y). We then obtain first integrals of the various cases which admit Noether point symmetries and obtain reduction to quadratures for these cases. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lagrangian formulation of the linear autonomous magnetization dynamics in spin-torque auto-oscillators

A Lagrangian formalism is used to find steady-state solution of the Landau-Lifshitz-Gilbert-Slonczewski equation corresponding to the linear autonomous dynamics of a magnetic auto-oscillatory system subject to the action of a spin-polarized electric current. In such a system, two concurrent dissipative mechanisms, arising from the positive intrinsic dissipation and the negative current-induced one, take place simultaneously and make the excitation of a steady precessional motion of the magnetization vector conceivable. The proposed formulation leads to the definition of a complex generalized non-Hermitian Eigenvalue problem, both in the case of a macrospin model and in the more general case of an ensemble of magnetic particles interacting each other through magnetostatic and exchange interactions. This method allows to identify the spin-wave normal modes which become unstable in the presence of the two competing dissipative contributions and provides an accurate estimation of the value of the excitation threshold current.     

Lagrangian formulation of domain decomposition methods: A unified theory

Domain decomposition methods based on one Lagrange multiplier have been shown to be very efficient for solving ill-conditioned problems in parallel. Several variants of these methods have been developed in the last ten years. These variants are based on an augmented Lagrangian formulation involving one or two Lagrange multipliers and on mixed type interface conditions between the sub-domains. In this paper, the Lagrangian formulations of some of these domain decomposition methods are presented both from a continuous and a discrete point of view.     

On the Eulerian–Lagrangian formulation of balance equations in porous media

The article presents a general approach to modeling the transport of extensive quantities in the case of flow of multiple multicomponent fluid phases in a deformable porous medium domain under nonisothermal conditions. The models are written in a modified Eulerian–Lagrangian formulation. In this modified formulation, the material derivatives are written in terms of modified velocities. These are the velocities at which the various phase and component variables propagate in the domain, along their respective characteristic curves. It is shown that these velocities depend on the heterogeneity of various solid matrix and fluid properties. The advantage of this formulation, with respect to the usually employed Eulerian one, is that numerical dispersion, associated with the advective fluxes of extensive quantities, are eliminated. The methodology presented in the article shows how the Eulerian–Lagrangian formulation is written in terms of the relatively small number of primary variables of a transport problem. © 1997 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 13: 505–530, 1997     

对称型插值框架的注记

通过引进新的参数,将对称型插值的一般框架作进一步推广和改进,新的插值框架包含更为丰富的插值格式;给出几种新形式的对称型有理插值格式;最后,将结果推广到向量值及矩阵值情形.