Related papers: Wavelets as basis functions in canonical quantizat…
The description of the electron wavefunctions in atoms is generalized to the fractional Fourier series. This method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the…
The monochromatic Dirac and polychromatic Titulaer-Glauber quantized field theories (QFTs) of electromagnetism are derived from a photon-energy wave function in much the same way that one derives QFT for electrons, that is, by quantization…
Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary…
The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The result for real-valued systems are simplified and a pair of basis functions is found. These bases are a…
An inconsistency of quantum field theory, regarding the signs of vacuum energy and vacuum pressure of elementary fields versus non-elementary fields (like e.g. phonon fields), is pointed out. An improved law for the canonical quantization…
In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density…
We present a framework for quantization of electromagnetic field in the presence of dielectric media with time-varying optical properties. Considering a microscopic model for the dielectric as a collection of matter fields interacting with…
Quantization is studied from a viewpoint of field extension. If the dynamical fields and their action have a periodicity, the space of wave functions should be algebraically extended `a la Galois, so that it may be consistent with the…
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
The 3+1 (canonical) decomposition of all geometries admitting two-dimensional space-like surfaces is exhibited. A proposal consisting of a specific re-normalization {\bf Assumption} and an accompanying {\bf Requirement} is put forward,…
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…
It is shown how the Canonical Function approach can be used to obtain accurate solutions for the distorted wave problem taking account of direct static and polarisation potentials and exact non-local exchange. Calculations are made for…
Canonical quantization relies on Cartesian, canonical, phase-space coordinates to promote to Hermitian operators, which also become the principal ingredients in the quantum Hamiltonian. While generally appropriate, this procedure can also…
The Hamilton-Jacobi method of constrained systems is discussed. The equations of motion of a singular system with time dependent constraints are obtained as total differential equations in many variables. The integrability conditions for…
The representation of solutions of Maxwell's equations as superpositions of scalar wavelets with vector coefficients developed earlier is generalized to wavelets with polarization, which are matrix-valued. The construction proceeds in four…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
We discuss the construction of wave packets resulting from the solutions of a class of Wheeler-DeWitt equations in Robertson-Walker type cosmologies, for arbitrary curvature. We show that there always exists a ``canonical initial slope" for…
In quantum communications, quantum states are employed for the transmission of information between remote parties. This usually requires sharing knowledge of the measurement bases through a classical public channel in the sifting phase of…
A canonical basis in the sense of Lusztig is a basis of a free module over a ring of Laurent polynomials that is invariant under a certain semilinear involution and is obtained from a fixed "standard basis" through a triangular base change…
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen,…