We provide a general expression and different classification schemes for the general two-dimensional canonical integral transformations that describe the propagation of coherent light through lossless first-order optical systems. Main theorems for these transformations, such as shift, scaling, derivation, etc., together with the canonical integral transforms of selected functions, are derived.

One of the main reasons why the Hamiltonian formalism is more useful than the Lagrangian formalism is that the set of coordinate transformations that leave invariant the form of the Hamilton equations is much wider than the set of coordinate transformations that leave invariant the form of the Lagrange equations. Furthermore, each of the so-called canonical transformations leaves invariant the ...

The canonical transformation theory of Yanai and Chan [J. Chem. Phys. 124, 194106 (2006)] provides a rigorously size-extensive description of dynamical correlation in multireference problems. Here we describe a new formulation of the theory based on the extended normal ordering procedure of Mukherjee and Kutzelnigg [J. Chem. Phys. 107, 432 (1997)]. On studies of the water, nitrogen, and iron ox...

Recent work on canonical transformations in quantum mechanics is applied to transform between the Moncrief metric formulation and the Witten-Carlip holonomy formulation of 2+1-dimensional quantum gravity on the torus. A nonpolynomial factor ordering of the classical canonical transformation between the metric and holonomy variables is constructed which preserves their classical modular transfor...

This paper describes a technique to support interoperable query processing when multiple heterogeneous databases are accessed. We focus on the problem of supporting query transformation transparently , so a user can pose queries locally, without any need of global knowledge about diierent data models and schemas. To support interoperable query transformation, we need to resolve the connicts (i....

The characterization and the canonical representation of order-n phase type distributions (PH(n)) is an open research problem. This problem is solved for n = 2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical representations have been introduced for the general PH distribution class so far for n > 2. In this paper we s...

We will present a consistent description of Hamiltonian dynamics on the “symplectic extended phase space” that is analogous to that of a time-independent Hamiltonian system on the conventional symplectic phase space. The extended Hamiltonian H1 and the pertaining extended symplectic structure that establish the proper canonical extension of a conventional Hamiltonian H will be derived from a ge...

We give a Bäcklund transformation connecting a generic 2D dilaton gravity theory to a generally covariant free field theory. This transformation provides an explicit canonical transformation relating both theories.

The characterization and the canonical representation of order n phase type distributions (PH(n)) is an open research problem. This problem is solved for n = 2, since the equivalence of the acyclic and the general PH distributions has been proven for a long time. However, no canonical representations have been introduced for the general PH distribution class so far for n > 2. In this paper we s...

The realizations of the Lie algebra corresponding to the dynamical symmetry group SO(2, 1) of the Kepler and oscillator potentials are q-deformed. The q-canonical transformation connecting two realizations is given and a general definition for q-canonical transformation is deduced. q-Schrödinger equation for a Kepler like potential is obtained from the q-oscillator Schrödinger equation. Energy ...