TIME DELAY AND CALABI INVARIANT IN CLASSICAL SCATTERING THEORY

Transcending Classical Invariant Theory

Let SP2n(R) = SP2n = Sp be the real symplectic group of rank n. Let Sp denote the two-fold cover of Sp. There is a unitary representation, constructed by Shale [Sh] and Weil [WA], of Sp that is of considerable interest in the theory of automorphic forms. We denote this representation by wand call it the oscillator representation. The purpose of this paper is to establish about w a fact that sho...

Graph Theory and Classical Invariant Theory

Classical invariant theory has died and been resurrected many times. Its golden age in the last century was marked with the flowering of unsurpassed computational ability, and the explicit determination of the invariants of most of the elementary polynomials. The computational approach is commonly acknowledged to have been dealt a death-blow by Hilbert’s celebrated Basis Theorem, an existential...

Remarks on Classical Invariant Theory

A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra. The formulation also allows skew-symmetric as well as symmetric variables. Examples illustrate the scope of this formulation.

Standard Monomial Theory for Harmonics in Classical Invariant Theory

Resonances and adiabatic invariance in classical and quantum scattering theory

We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances, explaining a series of results recently found in non-relativistic and relativistic regimes. Further, a connection between statistical quantities like quantal reso...