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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...
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...
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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