دانلود کتاب On Relativistic Angular Momentum Theory

This is four papers of P. Winternitz and co-authors which link separation of variables in differential equations with its symmetry group. Here ii abstract of these papers:On Relativistic Angular Momentum TheoryP. Winternitz, Ya. A. Smorodinskii, and M. UhlirSoviet Journal of Nuclear Physics: Volume 1, Number 1, July 1965(J. Nucl. Phys. (U.S.S.R.) 1, 163-172 January, 1965)The components of the relativistic angular momentum are given explicitly in four coordinate systems in the Lobachevskii space of relativistic velocities. Complete sets of commuting operators are found which define these systems. We consider the classical quantities corresponding to the invariants of subgroups of the Lorentz group, and the electromagnetic fields in which they are integrals of the motion.Invariant Expansions of Relativistic Amplitudes and Subgroups of the Proper Lorentz GroupP. Winternitz and I. FrisSoviet Journal of Nuclear Physics, Volume 1, Number 5, November 1965(J. Nucl. Phys. (USSR) 1, 889—901, May, 1965)All the conjugate classes of continuous subgroups of the proper Lorentz group are found; their invariants are investigated and the relation of these subgroups to the coordinate systems in which the Laplace equation is separable in Lobachevskii space is considered. To make clear the group properties of elliptical coordinates, the simpler case of euclidean motions of the plane is treated.Quantum Numbers in the Little Groups of the Poincare GroupWinternitz, I. Lukac, and Ya. A. SmorodinskiiSoviet Journal of Nuclear Physics: Volume 7, Number 1, July 1968(J_ Yad. Fiz. 7, 192-201 January, 1968)The integrals of motion and the problem of the introduction of quantum numbers in the groups o(3), o(2,1), and E2 are considered. It is shown that to any system of coordinates admitting a separation of variables in the Laplace equation there corresponds an integral of motion which is a homogeneous Hermitian polynomial quadratic in the generators of the corresponding group. Any operator of the type considered is equivalent to one of the polynomials.Poincare and Lorentz-invariant expansions of relativistic amplitudesP. Winternitz, Ya. A. Smorodinskii, and M. B. SheftelSoviet Journal of Nuclear Physics: Volume 7, Number 6, December 1968(Yad. Fiz. 7, 1325—1338, June, 1968)A discussion is presented of the double expansions of relativistic amplitudes in terms of the irreducible representations of the homogeneous Lorentz group, suggested recently for arbitrary values of the kinematic variables s and t. The relation of these expansions to the relativistic phase shift analysis in terms of representations of various little groups of the Poincare group is studied.