Related papers: Canonical transformations in three-dimensional pha…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
The general uncertainty principle applied to gravity can be implemented as a set of modified Poisson brackets in the canonical formalism. As such, the theory is not canonical and the resulting equations of motion do not lead to a covariant…
We consider n-linear Nambu brackets in dimension N higher than n. Starting from a Hamiltonian system with a Poisson bracket and K Casimir invariants defined in the phase space of dimension N = K+2M, where M is the number of effective…
We construct and characterize quantum Garnier systems in two variables including degenerate cases by certain holomorphic properties under the quantum canonical transformations.
Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum…
The canonical formalism for expanding metrics scenarios is presented. Non-unitary time evolution implied by expanding geometry is described as a trajectory over unitarily inequivalent representations at different times of the canonical…
A preferred form for the path integral discretization is suggested that allows the implementation of canonical transformations in quantum theory.
Quantization of gauge fields by the BRST method requires sources in addition to fields, and a bilinear anti-bracket defined in terms of them. This bracket is a sort of generalization of a Poisson bracket in classical mechanics. Canonical…
Homogeneous and isotropic cosmological models whose Hamilton-Jacobi equation is separable are deparametrized by turning their action functional into that of an ordinary gauge system. Canonical gauge conditions imposed on the gauge system…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
We introduce the notion of a `canonical' splitting over Z or ZxZ for a finitely generated group G. We show that when G happens to be the fundamental group of an orientable Haken manifold M with incompressible boundary, then the…
An affine Cartan calculus is developed. The concepts of special affine bundles and special affine duality are introduced. The canonical isomorphisms, fundamental for Lagrangian and Hamiltonian formulations of the dynamics in the affine…
The various phase spaces involved in the dynamics of parametrized nonrelativistic Hamiltonian systems are displayed by using Crnkovic and Witten's covariant canonical formalism. It is also pointed out that in Dirac's canonical formalism…
A careful study of the induced transformations on spatial quantities due to 4-dimensional spacetime diffeomorphisms in the canonical formulation of general relativity is undertaken. Use of a general formalism, which indicates the role of…
We introduce canonical coordinates on minimal time-like surfaces in the n-dimensional Minkowski space and prove the existence and the uniqueness of these parameters. With respect to these coordinates the coefficients of the first…
Phase Space is the framework best suited for quantizing superintegrable systems, naturally preserving the symmetry algebras of the respective hamiltonian invariants. The power and simplicity of the method is fully illustrated through new…
An effective method for generating linear equations of maximal symmetry in their much general normal form is obtained. In the said normal form, the coefficients of the equation are differential functions of the coefficient of the term of…
We consider a general symplectic transformation (also known as linear canonical transformation) of quantum-mechanical observables in a quantized version of a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q}…
Quantum canonical transformations corresponding to the action of the unitary operator $e^{i\epsilon(t)\sqrt{f(x)}p\sqrt{f(x)}}$ is studied. It is shown that for $f(x)=x$, the effect of this transformation is to rescale the position and…