##
Special Issue on "Investigations on Hermitian and Skew-Hermitian

Systems"

## Information

Dear colleagues,

In all applications of quantum mechanics in physics and chemistry, we ultimately want to understand things that we measure in the lab. The result of any measurement is always a real number. This means that we need to be sure that the procedures we develop for quantum calculations always give us correspondingly real answers.

In quantum mechanics [Schrödinger approaches], the classical quantities are replaced by operators chosen to be compatible with a property that quantum mechanical operators satisfy, namely the Hermicity, i.e. cj*=cj, Aˆ=Aˆ†. This requirement has several important, valuable, useful consequences. The most important of these is that thereby the eigenvalues are always real numbers.

As long as such a topic is very important in energetic investigations of systems, we will try to investigate all the confusions, difficulties that have a link with this topic from near or far.

Dr. Ilyas Haouam

Guest Editor

## Topics

- Symmetry in physics;
- PT symmetry;
- Symmetry violation;
- Symmetrical Modelling;
- Hermticity; Hermitian operator; Hermitian Hamiltonian; Hermitian manifold; Hermitian conjugate;
- Skew-Hermitian operator; Anti-Hermitian operator; Self-adjoint operator;

## Lead Guest Editor(s)

Dr. Ilyas Haouam

Laboratory of applied and theoretical physics, University of Tébessa, Algeria

Email: ujpr2021@gmail.com

## Import Dates

**Submission Deadline: **December 31, 2022

**Review Results: **January 31, 2023

**Deadline for Revision: **March 01, 2023

**Notification of Final Decision: **March 30, 2023

**Approximate Publication Date: **April 30, 2023

## Submit

**Dr. Ilyas Haouam**(ujpr2021@gmail.com)

## Published Papers(4)

## Role of Skew-Symmetric Differential Forms in Mathematical Physics and Field Theory

*Universal Journal of Physics Research*

**2022**, 1(1), 32-47. DOI: 10.31586/ujpr.2022.345

(This article belongs to the Special Issue Investigations on Hermitian and Skew-Hermitian

Systems)

**Abstract**

## Quantum Properties of Coherently Driven Three-Level Atom Coupled to Vacuum Reservoir

*Universal Journal of Physics Research*

**2022**, 1(1), 48-62. DOI: 10.31586/ujpr.2022.277

(This article belongs to the Special Issue Investigations on Hermitian and Skew-Hermitian

Systems)

**Abstract**

**a**is greater than the mean photon number for two-mode cavity light. As a result, for the two-mode cavity light, the maximum quadrature squeezing is 43.42 percent.Full article

## The c-equivalence principle and its implications for physics

*Universal Journal of Physics Research*

**2022**, 1(1), 63-76. DOI: 10.31586/ujpr.2022.420

(This article belongs to the Special Issue Investigations on Hermitian and Skew-Hermitian

Systems)

**Abstract**

## Relativistic Radial Density Theory (RRDT)

*Universal Journal of Physics Research*

**2022**, 1(1), 77-87. DOI: 10.31586/ujpr.2022.500

(This article belongs to the Special Issue Investigations on Hermitian and Skew-Hermitian

Systems)

**Abstract**

*RRDT*). In this theory, the Planck and gravitational parameters can be described as the functions of the radial mass (energy) density value. This density is maximal at the minimal radius and minimal at the maximal radius. This conclusion

*RRDT*). In this theory, the Planck and gravitational parameters can be described as the functions of the radial mass (energy) density value. This density is maximal at the minimal radius and minimal at the maximal radius. This conclusion is based on the fact that the ratio of Planck mass and Planck length (radius) is constant. These radiuses can be described as the function of the energy conservation constant

*κ*. Using

*RRD*

*T*, it is possible to develop the connections between Planck’s and gravitational parameters as function of the maximal and minimal radial mass (energy) density values. In that sense, the gravitational length, time, energy and temperature can be presented as the function of the Planck length, time, energy and temperature, respectively. This opens possibility to merge of Quantum Field Theory (

*QFT*) and the General Theory of Relativity (

*GTR*) at the quantum scale in gravitational field. The existence of the maximal radial mass (energy) density value at the minimal radius in gravitational field means that no singularity in that field. Further, the existence of the minimal radial mass (energy) density value at the maximal radius in gravitational field means that no infinity in that field. It follows the postulation: the most minimal radius in a gravitational field belongs to the minimal mass (energy). Since the Planck mass is not the minimal mass in space-time, the Planck length/radius is not the minimal length/radius in the space-time. If the calculated minimal (or maximal) radius is the bigger than the related official radius it means that there exists a dark matter in this object. In that sense, the black holes are presenting the state of the matter at the minimal radius where we have the maximal radial mass (energy) density value. Further, the maximal possible radius of the matter is presenting the state with the minimal radial mass (energy) density value. Thus, the maximal and minimal radial mass (energy) density values are constants and conserved items. Now the question is: do motion of the Universe follows the

*RRD*

*T*?Full article