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A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalised to many variables, and permits the simultaneous existence of coherent states, and the transposition of…
The Lagrangian mechanical consideration of the dynamics of ideal incompressible hydrodynamic, magnetohydrodynamic, and Hall magnetohydrodynamic media, which are formulated as dynamical systems in appropriate Lie groups equipped with…
Photons propagating in Laguerre-Gaussian modes have characteristic orbital angular momentums, which are fundamental optical degrees of freedom. The orbital angular momentum of light has potential application in high capacity optical…
The Hermite polynomials are ubiquitous but can be difficult to work with due to their unwieldy definition in terms of derivatives. To remedy this, we showcase an underappreciated Gaussian integral formula for the Hermite polynomials, which…
One of the central concepts in modern theoretical physics, gauge symmetry, is typically realised by lifting a finite-dimensional global symmetry group of a given functional to an infinite-dimensional local one by extending the functional to…
A common approach to digital system design involves transforming a continuous-time (s-domain) transfer function into the discrete-time (z-domain) using methods such as Euler or Tustin. These transformations are shown to be specific cases of…
This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…
We construct new composite Higgs/gauge-Higgs unification (GHU) models in flat space that overcome all the difficulties found in the past in attempting to construct models of this sort. The key ingredient is the introduction of large…
When light is passed through aberrated optical systems, the resulting degradation in amplitude and phase has deleterious effects, for example, on resolution in imaging, spot sizes in focussing, and the beam quality factor of the output…
We theoretically describe the quantum properties of a large Fresnel number degenerate optical parametric oscillator with spherical mirrors that is pumped by a Gaussian beam. The resonator is tuned so that the resonance frequency of a given…
With the emergence of the field of quantum communications, the appropriate choice of photonic degrees of freedom used for encoding information is of paramount importance. Highly precise techniques for measuring the polarisation, frequency,…
We have found an exact formula expressing a general correlation function containing both products and ratios of characteristic polynomials of random Hermitian matrices. The answer is given in the form of a determinant. An essential…
By employing x-Bohm theory and p-Bohm theory, we construct the position and momentum trajectories of single-mode and superposed-mode Laguerre-Gaussian (LG) beams. The dependence of divergence velocity and rotation velocity on the initial…
The linear canonical transform (LCT) was extended to complex-valued parameters, called complex LCT, to describe the complex amplitude propagation through lossy or lossless optical systems. Bargmann transform is a special case of the complex…
We consider gaugeon formulations which discuss the quantum gauge freedom covariantly in the framework of generalized BRST transformation for the Yang-Mills theory as well as the BRST invariant Higgs model. We generalize the BRST symmetries…
Some multiple hypergeometric transformation formulas arising from the balanced du- ality transformation formula are discussed through the symmetry. Derivations of some transformation formulas with different dimensions are given by taking…
Multiple-degrees-of-freedom free-space communication combining polarization and high-order spatial modes promises high-capacity communication channel. While high-order spatial modes have been widely exploited for dense coding and…
Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this…
The crossed channels of generalized reaction \gamma N - \gamma N have been considered. The transformation coefficients from the independent helicity amplitudes to the invariant functions are calculated. The explicit expressions for…
We develop a new point of view to introduce families of functions, which can be identified as generalization of the ordinary trigonometric or hyperbolic functions. They are defined using a procedure based on umbral methods, inspired to the…