This form of the Hamiltonian resembles that of the simple harmonic oscillator, after a canonical transformation with generating function F = ([[?
can, by a canonical transformation with the above generating function, be expressed as
A symplectic map M(t) is a canonical transformation
of a point in position-momentum phase space at initial time t = 0 to a point in position-momentum phase space at time t.
CHAPTER 13: CANONICAL TRANSFORMATION
THEORY FOR DYNAMIC CORRELATIONS IN MULTIREFERENCE PROBLEMS
We consider the canonical transformation, specified by the generating function
The longitudinal part of the reference orbit can be isolated via a canonical transformation
The (linear and higher order) dispersion can be introduced via a canonical transformation aimed at canceling the first order Hamiltonian [[?
by means of a canonical transformation specified by the generating function
Contracted Schrodinger equation topics include the purification of correlated and reduced density matrices, cumulants, extensivity and the connected formulation, generalized normal ordering, antihermitian formulations and canonical transformation
theory for dynamic correlations in multireference problems.
The authors have organized the main body of their text into ten chapters covering quantum field theory, path integral formulation, supersymmetric quantum mechanics, coherent and squeezed states, BerryAEs phase, Aharonov-Bohm, and Sagnac effects, phase space picture and canonical transformations
, and a wide variety of other related subjects.
The topics include quantum mechanics in abstract Hilbert space, symmetries, higher-order processes, and canonical transformations
for quantum systems.
Sixteen papers from the June 2006 conference present new results in normal forms of Poisson structures, deformation of Poisson structures, reduction of systems with symmetry, Kontsevich formality and its variants, and quantization of canonical transformations
via their graphs.