Analytic calculation of radiative-recoil corrections to muonium hyperfine splitting; Electron-line contribution

ANNALS OF PHYSICS202, 468469 (1990)

Abstracts

of Papers

to Appear

in Future

Issues

Analytic Calculation of Radiative-Recoil Correclions to Muonium Hyperfine Splitting; Electron-Line Contribution. MICHAEL I. EIDES, SAVELY G. KARSHENBOIM, AND VALERY A. SHELYUTO. D. I. Mendeleev Institute of Metrology, Moskovsky pr. 19, Leningrad 198 005, USSR.

The detailed account of analytic calculation of radiative-recoil corrections to muonium hyperline splitting, induced by electron-line radiative insertions, is presented. The consideration is performed in the framework of the effective two-particle formalism. A good deal of attention is paid to the problem of the divergence cancellation and the selection of graphs, relevant to radiative-recoil corrections. The analysis is greatly facilitated by use of the Fried-Yennie gauge for radiative photons. The obtained set of graphs turns out to be gauge-invariant and actual calculations are performed in the Feynman gauge. The main technical tricks, with the help of which we have effectively utilized the existence in the problem of the small parameter-mass ratio and managed to perform all calculations in the analytic form, are described. The main intermediate results, as well as the final answer, 6E,, = (a(Za)/a2)(m/M)EF (6((3) + 371~ In 2 + a*/2 + 17/8), are also presented.

The Functional

Integral

for

Quantum

Systems

with

Hamiltonians

Unbounded

from

Below.

M~CHEL

CARREAUAND EDWARD FARHI. Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; SAM GUTMANN. Department of Mathematics, Northeastern University, Boston, Massachusetts 02115; AND PAUL F. MENDE. Department of Mathematics and Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139. A quantum system with a self-adjoint Hamiltonian has a well-defined unitary time evolution operator even if there is no ground state. However, if the spectrum of the Hamiltonian is unbounded from below, the Brownian (or imaginary time) functional integral may diverge for all times. Working in one-dimensional non-relativistic quantum mechanics with potentials which are unbounded from below at infinity and at the origin, we show how to regulate the Brownian functional integral, analytically continue to quantum mechanical time, and then remove the cutoff to obtain the quantum Green’s function associated with any self-adjoint Hamiltonian. Our constructions illustrate the equivalence of the operator and functional integral approaches to quantum mechanics.

The Path

Integral

for

the Kepler

Problem

on the Pseudosphere.

Laboratory, Imperial College of Science, Technology London SW7, United Kingdom.

CHRISTIAN

and Medicine,

The Blackett Prince Consort Road,

GROSCHE.

The path integral for the generalized Kepler problem on the pseudosphere is calculated. As for the generalized Kepler problem we describe the potential problem I’(a) = -(Ze*/R)(coth a - 1) (a > 0, R-curvature) on the D-dimensional pseudosphere, whereas for the genuine Kepler problem this feature of the potential is only true for the four-dimensional pseudosphere. Energy spectrum and wave-functions are explicitly calculated. The result is compared with the flat-space limit (i.e., R + co) and with the free motion on the pseudosphere. The application of the result of the path integral solution of the Manning-Rosen potential plays a crucial role in the calculation.

468 OOO3-4916/90 $7.50 Copyright Q 1990 by Academic Press, Inc. All rights of reproduction m any form reserved.