Hamiltonization of theories with degenerate coordinates

We consider a class of Lagrangian theories where part of the coordinates does not have any time derivatives in the Lagrange function (we call such coordinates degenerate). We advocate that it is reasonable to reconsider the conventional definition of singularity based on the usual Hessian and, moreover, to simplify the conventional hamiltonization procedure. In particular, in such a procedure, it is not necessary to complete the degenerate coordinates with the corresponding conjugate momenta.     

New nonlinear σ-model with N=4 extended supersymmetry

A new nonlinear -model with N=4 supersymmetry in d=2 is constructed in terms of a N=2 tensor multiplet in d=4. Four equivalent formulations of the theory in superspace are obtained. The component structure of the model is considered by means of the Legendre transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1987.     

Heterocyclization of 1,1-dicyano-2-(trifluoromethyl)ethylenes with 1,3,3-trimethyl-3,4-dihydroisoquinoline and its derivatives

1,3,3-Trimethyl-3,4-dihydroisoquinolines react with 1,1-dicyano-2,2-bis(trifluoromethyl)ethylene to give 4-amino-6,6-dimethyl-2,2-bis(trifluoromethyl)-3-cyano-6,7-dihydro-2H-benzo[a]quinolizines. The reaction of 3,3-dimethyl-1-cyanomethylidene-1,2,3,4-tetrahydroisoquinoline and the methyl ester of 3,3-dicyano-2-(trifluoromethyl)acrylic acid leads to 5,5-dimethyl-3-oxo-2-(trifluoromethyl)-2-(dicyanomethyl)-2,3,5,6-tetrahydropyrrolo[2,1-a]isoquinoline.A. N. Nesmeyanov Institute of Heteroorganic Compounds, Russian Academy of Sciences, 117813 Moscow. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 8, pp. 1888–1892, August, 1992.     

Generalized oscillator representations for generalized Calogero Hamiltonians

We construct generalized oscillator representations for all generalized Calogero Hamiltonians with the potential V (x) = g ₁ /x ² + g ₂ x ² , g ₁ ≥ ?1/4, g ₂ > 0. These representations are generically nonunique, but for each Hamiltonian, there exists an optimum representation explicitly determining the ground state and its energy. For generalized Calogero Hamiltonians with coupling constants g ₁ < ?1/4 or g ₂ < 0, generalized oscillator representations do not exist, which agrees with the fact that the corresponding Hamiltonians are not bounded from below.     

Space-time locality in theSp(2)-symmetric Lagrangian formalism

The existence of a local solution to the Sp(2) master equation for the gauge field theory is proved in the perturbation theory under standard regularity assumptions for the action. The arbitrariness of solutions to the Sp(2) master equation is described, provided they are proper. The effective action can be chosen to be Sp(2) invariant and (under the additional assumption that the gauge transformation generators are Lorentz tensors) Lorentz invariant. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 115. No. 3, pp. 373–388, June, 1998.     

Short Envelope Solitons in Nonconservative Media

We consider the dynamics of short envelope solitons within the framework of the third-order nonlinear Schrödinger equation with allowance for both linear losses and pumping by an external wave field. An equation for the soliton amplitude is derived. The stationary value of the soliton amplitude is found.     

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.