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The method presented in the first part of this work is applied to the superalgebra B (0,2). Two families of irreducible ∗‐representations of this superalgebra and its real form osp(1,4) are constructed explicitly in terms of differential operators on the Hilbert space L 2 ( M ̃ )⊗C N of N...
Using the theory of self‐adjoint extensions of symmetric operators the precise mathematical definition of the quantum Hamiltonian describing a finite number of δ interactions with supports on concentric spheres is given. Its resolvent is also derived, its spectral properties are described, and...
It is shown that for any local Lie group G of transformations in R × R n there exist differential systems of the form x ( m = f ( t , x ,..., x ( m −1 ), which are symmetrical under G . The order m ̱ of these systems is related to r ̱ , the number of essential parameters of G .
The set M ∞ of infinite matrices and the set Q ∞ of squarable matrices are considered as partial ∗‐algebras. The connection between Q ∞ and two partial ∗‐algebras of closed operators is studied. Conditions for a matrix representation in ‘‘von Neumann’s sense’’ of a family...
The relation between the Nambu–Goto string in D dimensions and the two‐dimensional σ model defined on the Grassmannian manifold SO( D −1,1)/SO( D −2)×SO(1,1) is investigated. For D =3 and D =4 the Nambu–Goto string is identified with a definite sector of the Grassmannian σ model. For...
Exact continuous solutions to the Einstein field equations are determined under the assumption that the subspaces of space‐time spanned by the variables X A ( A =1,2) admit the three‐dimensional group of motions of a two‐plane, and the Ricci tensor R A B ( A , B =1,2) vanishes. The...
The equation for the horizontal transport of a liquid in an unsaturated scale‐heterogeneous porous medium is ∂θ/∂ t =λ( x )∂/∂ x C (θ)∂θ/∂ x −λ′( x ) E (θ)∂θ/∂ x −λ″( x )∫( C + E ) d θ. A systematic search for Lie–Bäcklund symmetries leads to the...
The large mass asymptotics of the quantum evolution problem for a system of charged particles that mutually interact through scalar fields and couple to an arbitrary time‐varying external electromagnetic field is rigorously described. If K ( x , t ; y , s ; m ) denotes the coordinate space...
Natural generalizations of the quaternion algebra called quaternionlike algebras (ql algebras) are considered. The notion of a Lie algebra induced by a ql algebra is introduced and a classification of such Lie algebras is presented. It is shown that local Lie groups defined by Lie algebras...
A set of generators for the modular group of a surface with boundary, both in the orientable and nonorientable cases is given. All inequivalent pin structures are constructed and their transformations under these generators are computed.
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