Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

Electron and positron planar channeling radiation from diamond

Channeling-radiation spectra have been obtained from a diamond with ≈ 54.5 MeV electrons and positrons. Theoretical calculations are found to fit the experimental results well for electrons, but significant discrepancies exist between theoretical predictions and the positron data.     

Observation of radiation from Δn=3 transitions for planar-channeled electrons

Planar-channeled electrons make spontaneous electric-dipole transitions between states of opposite parity. Measured values for the relative intensities of radiation from Δn = 3 and Δn = 1 transitions are shown to be in reasonable agreement with calculated values for 54 MeV electrons channeled along {110} planes in silicon.