Related papers: Linear Canonical Transform On Boehmian Space
We argue that the conventional construction for quantum fields in curved spacetime has a grave drawback: It involves an uncountable set of physical field systems which are nonequivalent with respect to the Bogolubov transformations, and…
he octonion offset linear canonical transform can be defined as a time shifted and frequency modulated version of the octonion linear canonical transform, a more general framework of most existing signal processing tools. In this paper, we…
There is a canonical unitary transformation from $L^2(\R)$ onto the Fock space $F^2$, called the Bargmann transform. The purpose of this article is to translate some important results and operators from the context of $L^2(\R)$ to that of…
A method for constructing Lagrangians for the Lie transformation groups is explained. As examples, the Lagrangians for real plane rotations and affine transformations of the real line are constructed.
This paper is concentrated on the classification of permutation matrix with the permutation similarity relation, mainly about the canonical form of a permutational similar equivalence class, the cycle matrix decomposition of a permutation…
Let $\C$ be a sequence of multisets of subspaces of a vector space $\F_q^k$. We describe a practical algorithm which computes a canonical form and the stabilizer of $\C$ under the group action of the general semilinear group. It allows us…
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle…
We devise a method that reduces the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings. Canonical matrices of (i) bilinear or sesquilinear forms, (ii) pairs of symmetric,…
This is a survey on the ongoing development of a descriptive theory of represented spaces, which is intended as an extension of both classical and effective descriptive set theory to deal with both sets and functions between represented…
Base on some simple facts of Hadamard product, characterizations of positive definite preserving linear transformations on real symmetric matrix spaces with an additional assumption "$\ra T(E_{ii})=1, i=1,2,..., n$" or "$T(A)>0\to A> 0$",…
The offset linear canonical transform encompassing the numerous integral transforms, is a promising tool for analyzing non-stationary signals with more degrees of freedom. In this paper, we generalize the windowed offset linear canonical…
The purpose of this paper is to introduce an algebraic cohomology and formal deformation theory of left alternative algebras. Connections to some other algebraic structures are given also.
A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation…
We investigate the 2D quaternion windowed linear canonical transform(QWLCT) in this paper. Firstly, we propose the new definition of the QWLCT, and then several important properties of newly defined QWLCT, such as bounded, shift,…
In this paper, we present an algebraic approach to idempotent functional analysis, which is an abstract version of idempotent analysis. The basic concepts and results are expressed in purely algebraic terms. We consider idempotent versions…
We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
We construct a modification of the Poisson bracket which is suitable for a canonical analysis of space-time noncommutative field theories. We show that this bracket satisfies the Jacobi identities and generates equations of motion. In this…
We obtain a characterisation of the Fourier transform on the space of Schwartz class functions on $\mathbb{R}^n.$ The result states that any appropriately additive bijection of the Schwartz space onto itself, which interchanges convolution…
We construct and characterize quantum Garnier systems in two variables including degenerate cases by certain holomorphic properties under the quantum canonical transformations.