Showing papers in "Reports on Mathematical Physics in 1974"

TL;DR: In this paper, a unified framework for the construction of symplectic manifolds from systems with symmetries is presented, including rotationally invariant systems, the rigid body, fluid flow, and general relativity.

TL;DR: In this article, it was shown that a necessary and sufficient condition for the Wigner quasi-probability density to be a true density is that the corresponding Schrodinger state function be the exponential of a quadratic polynomial.

TL;DR: The homomorphism of a special kind between the ring of symmetric polynomials and the center of the symmetric group ring is established in this article, where the proper values of the images are the values of corresponding symmetric polynomials with the variables substituted by the set of integers found from the corresponding Young diagram.

TL;DR: In this paper, it was shown that for a given 3-dimensional hyperplane Q, generated by two space-like and one time-like vector, one can construct three operators: x1Q, x2Q, tQ. The operator tQ is used to formulate the realistic interpretation of the uncertainty relation Δt · ΔE ⩾ ħ/2.

TL;DR: In this article, the authors present an effective method which allows to verify whether a given superoperator Λ ∈ L (A 1, A 2) is a positive map.

TL;DR: In this article, a concept related to the entropy is studied, where A and B are two density matrices, with eigenvalues a1, a2,… and b1, b2, etc, arranged in decreasing order and repeated according to multiplicity.

TL;DR: In this paper, up to a conjugation of connected subgroups of the Poincare group P, a number of general theorems on inhomogeneous Lie algebras and useful properties are proved.

TL;DR: In this paper, the system of coherent states for complex bounded homogeneous domains is constructed and the properties of the coherent states are investigated, and the question of selecting complete subsystems connected with discrete subgroups of the motion groups of Hermitian symmetric spaces is also studied.

TL;DR: In this article, a general notion of a selfpolar form is introduced and investigated, and it turns out that self-polar forms are distinguished by a sort of maximum principle.

TL;DR: In this paper, the geometric structure of systems which are invariant under the 15-parameter conformal group of the Minkowski space is investigated and the notion of causality in the context of a conformally invariant world is investigated.

TL;DR: In this paper, the authors derived explicit rigorous bounds for the variation of energy bands with the potential and for the radii of convergence of the kp perturbation theory in terms of the potential.

TL;DR: In this article, an isomorphism between certain subspaces of the Hilbert spaces of symmetric and antisymmetric n-point functions is described, and the functional representation for the anticommuntation relations is derived.

TL;DR: Using the spectral resolution for the operators Adagger;kAk, it was shown in this article that |TrA1…An|≤∑i=1mΦi = 1nα(k)i.

TL;DR: In this paper, a heuristic quantum mechanical path integral formula with paths in phase space is given a precise mathematical meaning, and a quantum quantum path integral model with path integral formulas with path integrals in phase spaces is presented.

TL;DR: A Poisson bracket definition for the local type functionals on a space-like surface in the classical field theory is given in the language of the multisymplectic geometry.

TL;DR: In this article, the Minkowski space M4 is considered as a local chart of a compact differentiable manifold M4c, on which the whole conformal group O(2, 4) Z 2 acts continuously.

TL;DR: In this article, the irreducible representations of the generalized Clifford groups Gmn in the case where m is a prime number, are extended to the case when m is any integer.

TL;DR: In this paper, it was shown that all conditions for quantum dynamical semigroups, which were accepted recently by Kossakowski as postulates, can be derived from Mackey's axiomatics of quantum mechanics.

TL;DR: In this paper, the stationary Schrodinger operator H of a many-body system M with two-body rotation invariant interactions is reduced with respect to the symmetries of permutation of identical particles, rotations and reflections, into a direct sum of operators H τ, where τ is an index of the irreducible representations of the symmetry group of the system.

TL;DR: In this article, the reduced p-particle matrix (p⩽N) corresponding to a 2-temperature equilibrium state of a system of N coupled oscillators (the two temperatures Ttr and Tre1 relating to the translational and relative motion of the latter) was proved.

TL;DR: In this article, an axiomatic basis for non-relativistic quantum theory is proposed, which consists of five axioms involving only the probability p(A, α, E) that measurement of an observable A in a state α will lead to a value in a Borel set E.

TL;DR: In this article, the nonlocal multiplication of phase space functions is generalized to functions over locally compact Abelian groups or over homogeneous spaces of such groups, and it is shown that such nonlocal algebras of functions are closely related to the ray-representations of the corresponding dual groups.

TL;DR: In this paper, the notion of generalized invariant transformations of variational problems in Lagrangian formulation is discussed in the framework of the variational theory in fibred manifolds, and necessary and sufficient conditions for generators of one-parameter groups of such transformations are derived, completing thus some previous results of A. Trautman on the theory of transformations.

TL;DR: In this paper, a concept of contraction of Lie-groups is defined and its relation to the concept of Lie algebras is studied, and some general theorems are asserted for simple contractions are asserted.

TL;DR: The Gelfand-Graev horospheric approach to the Fourier transform on SO ( n, 1) is confined to Class I representations; as mentioned in this paper extend their method to the regular representation of the group SL(2, R ).

TL;DR: For the general situation without a mass gap current generated global charges are shown to possess symmetric extensions to the dense domain D QL of all quasi local states as mentioned in this paper, i.e. they admit at least one self-adjoint extension.

TL;DR: In this article, the Clebsch-Gordan coefficients for the Weyl group W (i.e., Poincare group extended by dilatations) are derived using Mackey's theory of induced representations.

TL;DR: In this paper, the authors extend the Gelfand-Helgason theory of horospheric transformations to the regular representation of an arbitrary connected semi-simple Lie group, and show that the measure required for the most continuous series of a group of real-rank unity is the square of the Plancherel measure for G ; and at the double poles of this the residues are precisely the contributions of the remaining principal series.

TL;DR: Theorem 9.2 as discussed by the authors states that there exists a class of functions which contains all functions of the q and functions of p and all momentum observables and which is closed with respect to any linear canonical transformation L ; a rule Λ assigning a unique self-adjoint operator to each function f ; a unitary operator W L corresponding to L and an equation Λ(f∘L)=W -1 L ΛƒW L.

TL;DR: In this article, the tensor product of an arbitrary irreducible representation of U ( n ) of signature α with its contragredient was considered. And it was shown that the irreducedible representation (1, 0, 0/0/0, 1/1/1) occurs in this product with multiplicity equal to the number of distinct components of signatureα diminished by one.