Related papers: Canonical sine and cosine Transforms For Integrabl…
In this paper, we provide a concise proof of Oppenheim's double inequality relating to the cosine and sine functions. In passing, we survey this topic.
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space…
We characterize the range of the cosine transform on real Grassmannians in terms of the decomposition under the action of the special orthogonal group SO(n). Also a geometric interpretation of its image is given. The non- Archimedean…
The (in)finite dimensional symplectic group of homogeneous canonical transformations is represented on the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states.
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
We prove that the cosine law for spherical triangles and spherical tetrahedra defines integrable systems, both in the sense of multidimensional consistency and in the sense of dynamical systems.
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
In this paper, we introduce formal sine functions whose coefficients are elements of a generalized harmonic algebra and investigate their properties corresponding to the classical addition formula and Pythagorean theorem. By taking their…
We construct canonical integral transforms, analogous to the Fourier transform, that have periods six and three. The existence of such transforms is shown to arise naturally from the expectation that the Schwartz space on the real line,…
Canonical transformations using the idea of quantum generating functions are applied to construct a quantum Hamilton-Jacobi theory, based on the analogy with the classical case. An operator and a c-number forms of the time-dependent quantum…
The properties of discrete nonlinear symmetries of integrable equations are investigated. These symmetries are shown to be canonical transformations. On the basis of the considered examples, it is concluded, that the densities of the…
We introduce a new integral transform $T^\lam f$, $\lam \in C^m$, on the Stiefel manifold of orthonormal $m$-frames in $R^n$ which generalizes the $\lam$-cosine transform on the Grassmann manifold of $m$-dimensional linear subspaces of…
In this article, we give a geometric description for any invertible operator on a finite dimensional inner--product space. With the aid of such a description, we are able to decompose any given conformal transformation as a product of…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
In this paper we describe the solutions of the functional equations expressing the addition theorems for sine and cosine on commutative hypergroups.
Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
We define a canonical form for piecewise defined functions. We show that this has a wider range of application as well as better complexity properties than previous work.
We observe that, within the effective generating function formalism for the implementation of canonical transformations within wave mechanics, non-trivial canonical transformations which leave invariant the form of the Hamilton function of…
$p$-Mechanics is a consistent physical theory which describes both classical and quantum mechanics simultaneously through the representation theory of the Heisenberg group. In this paper we describe how non-linear canonical transformations…