Group Theory
Early and
sustaining
interests include Group Theory and is application to Physics,
particularly Quantum Mechanics. Here are some of the
early efforts to cvontribute to this field.
R. Gilmore,
On the Properties of Coherent States,
Revista Mexicana de Fisica 23 143-187 (1973).
R. Gilmore,
On the Properties of Coherent States,
Revista Mexicana de Fisica 23 143-187 (1973).
R. Gilmore,
Q and Prepresentatives for spherical tensors,
Journal of Physics: Math and General A9 L65-L66 (1976).
R. Gilmore,
Q and Prepresentatives for spherical tensors,
Journal of Physics: Math and General A9 L65-L66 (1976).
R. Gilmore, Group Theory
This is a chapter on Group Theory contributed to a
book on Mathematical Methods in Physics, edited
by Michael Grinfeld and shortly to be published
by John Wiley.A9 (2014)
Ryan Wasson and Robert Gilmore,
Classical Special Functions and Lie Groups ,
Ameerican Journal of Physics (submitted) A9 (2014).
The classical orthogonal functions of mathematical physics
are closely related to Lie groups. Specifically, they are
matrix elements of, or basis vectors for, unitary
irreducible representations of low-dimensional Lie groups.
We illustrate this connection for: The Wigner functions,
spherical harmonics, and Legendre polynomials; the
Bessel functions; and the Hermite polynomials.
These functions are associated with the Lie groups:
the rotation group $SO(3)$ in three-space and its covering
group $SU(2)$; the Euclidean group in the plane $E(2)$ or
$ISO(2)$; and the Heisenberg group $H_4$.
Revision: April 10, 2014