The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the generating function of a canonical transformation that maps any quantum system to a system with a vanishing Hamiltonian. A formal perturbative solution of th...

A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. Exact solutions of the transformation kernels and the phase space propagators are given for the three fundamental canonical maps as fractional-linear, gauge and contact (point) transformations. Under the nonlinear maps a phase space representation i...

A canonical formalism for Lagrangians of maximal nonlocality is established. The method is based on the familiar Legendre transformation to a new function which can be derived from the maximally nonlocal Lagrangian. The corresponding canonical equations are derived through the standard procedure in local theory and appear much like those local ones, though the implication of the equations is la...

The basic elements of the canonical formalism for description of the critical phenomena in systems isomorphic to Ising model are stated. The reduction of the eeective Hamiltonian to the canonical form and numerous consequences of such a transformation are thoroughly investigated. The shift of xed point and the critical exponents of the system are considered.

A systematic and rigorous method to construct symplectic maps near separatrix of generic Hamiltonian systems subjected to time-periodic perturbations is developed. It is based on the method of canonical transformation of variables to construct Hamiltonian maps [J. Phys. A 35, 2811 (2002)]]. Using canonical transformation of variables and the first-order approximation for the generating function...

We face the well-known gyrokinetic problem, which arises in the description of the dynamics of a charged particle subject to fast gyration for the presence of a strong electromagnetic field. The customary approach to gyrokinetic theory, using canonical variables or identifying them “a posteriori” by means of Darboux theorem, leads to potential complications and ambiguities due to the fact that ...

In a thorough paper Kuchař has examined the canonical reduction of the most general action functional describing the geometrodynamics of the maximally extended Schwarzschild geometry. This reduction yields the true degrees of freedom for (vacuum) spherically symmetric general relativity (SSGR). The essential technical ingredient in Kuchař’s analysis is a canonical transformation to a certain ch...

We consider the problem of evolving a quantum field between any two (in general, curved) Cauchy surfaces. Classically, this dynamical evolution is represented by a canonical transformation on the phase space for the field theory. We show that this canonical transformation cannot, in general, be unitarily implemented on the Fock space for free quantum fields on flat spacetimes of dimension great...