scholarly journals Gauge-Independent Theory of Symmetry. II.

1965 ◽  
Vol 18 (2) ◽  
pp. 109 ◽  
Author(s):  
HA Buchdahl ◽  
LJ Tassie
Keyword(s):  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Equation Of Motion ◽  
Symmetry Operation ◽  
Quantum Mechanical ◽  
Translation Invariant ◽  
Translation Operators ◽  
Physical Symmetry ◽  
Magnetic Translation ◽  
Quantum Mechanical Systems

This paper develops a gauge-independent symmetry theory of non-relativistic quantum mechanical systems, in line with that previously considered in the context of classical mechanics. We first discuss at length the motivation for adopting the view that the invariance of a system K under a physical symmetry operation .<I' should be taken to mean invariance of the equation of motion of K under a certain gauge-independent unitary transformation U c( .<1'). The formal development of the theory is then carried through, and some detailed examples are presented. In particular, corresponding to every direction along which a system K happens to be translation invariant there exists a gauge-independent generator of translations which leaves K invariant but which is not, in general, a component of either the canonical or the kinetic momentum. The connexion between such invariant generators of translations and the so-called magnetic translation operators is referred to.

scholarly journals Siewert solutions of transcendental equations, generalized Lambert functions and physical applications

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 232-242 ◽  
Author(s):  
Victor Barsan
Keyword(s):  
Solar Energy ◽  
Energy Conversion ◽  
Analytical Methods ◽  
Systematic Approach ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Elementary Functions ◽  
Transcendental Equations ◽  
Lambert Functions

Abstract Several classes of transcendental equations, mainly eigenvalue equations associated to non-relativistic quantum mechanical problems, are analyzed. Siewert’s systematic approach of such equations is discussed from the perspective of the new results recently obtained in the theory of generalized Lambert functions and of algebraic approximations of various special or elementary functions. Combining exact and approximate analytical methods, quite precise analytical outputs are obtained for apparently untractable problems. The results can be applied in quantum and classical mechanics, magnetism, elasticity, solar energy conversion, etc.

scholarly journals KMS, ETC.

2002 ◽  
Vol 14 (07n08) ◽  
pp. 829-871 ◽  
Author(s):  
LOTHAR BIRKE ◽  
JÜRG FRÖHLICH
Keyword(s):  
Relativistic Quantum ◽  
Symmetry Operation ◽  
Green Functions ◽  
Positive Temperature ◽  
Quantum Theories ◽  
Kms Condition ◽  
Quantum Mechanical Systems ◽  
The Relationship ◽  
Lorentz Boosts

A general form of the "Wick rotation", starting from imaginary-time Green functions of quantum-mechanical systems in thermal equilibrium at positive temperature, is established. Extending work of H. Araki, the rôle of the KMS condition and of an associated anti-unitary symmetry operation, the "modular conjugation", in constructing analytic continuations of Green functions from real- to imaginary times, and back, is clarified. The relationship between the KMS condition for the vacuum with respect to Lorentz boosts, on one hand, and the spin-statistics connection and the PCT theorem, on the other hand, in local, relativistic quantum field theory is recalled. General results on the reconstruction of local quantum theories in various non-trivial gravitational backgrounds from "Euclidian amplitudes" are presented. In particular, a general form of the KMS condition is proposed and applied, e.g., to the Unruh- and the Hawking effects.

Quantum information entropy and squeezing of 𝒫𝒯-symmetric potential

2021 ◽  
Vol 36 (10) ◽  
pp. 2150065
Author(s):  
Aarti Sharma ◽  
Pooja Thakur ◽  
Girish Kumar ◽  
Anil Kumar
Keyword(s):  
Phase Transition ◽  
Quantum Information ◽  
Information Entropy ◽  
Momentum Space ◽  
Quantum Mechanical ◽  
Position Space ◽  
Entropy Squeezing ◽  
Information Theoretic ◽  
Symmetric Potential ◽  
Quantum Mechanical Systems

The information theoretic concepts are crucial to study the quantum mechanical systems. In this paper, the information densities of [Formula: see text]-symmetric potential have been demonstrated and their properties deeply analyzed. The position space and momentum space information entropy is obtained and Bialynicki-Birula–Mycielski inequality is saturated for different parameters of the potential. Some interesting features of information entropy have been discussed. The variation in these entropies is described which gets saturated for specific values of the parameter. These have also been analyzed for the [Formula: see text]-symmetry breaking case. Further, the entropy squeezing phenomenon has been investigated in position space as well as momentum space. Interestingly, [Formula: see text] phase transition conjectures the entropy squeezing in position space and momentum space.

scholarly journals Quantum speed limit for a relativistic electron in the noncommutative phase space

2017 ◽  
Vol 32 (23n24) ◽  
pp. 1750143 ◽  
Author(s):  
Kang Wang ◽  
Yu-Fei Zhang ◽  
Qing Wang ◽  
Zheng-Wen Long ◽  
Jian Jing
Keyword(s):  
Relativistic Electron ◽  
Uniform Magnetic Field ◽  
Lorentz Invariance ◽  
Relativistic Quantum ◽  
Quantum Mechanical ◽  
Speed Limit ◽  
Speed Of Light ◽  
Minimum Evolution ◽  
Noncommutative Phase Space ◽  
Average Speed

The influence of the noncommutativity on the average speed of a relativistic electron interacting with a uniform magnetic field within the minimum evolution time is investigated. We find that it is possible for the wave packet of the electron to travel faster than the speed of light in vacuum because of the noncommutativity. It is a clear signature of violating Lorentz invariance in the noncommutative relativistic quantum mechanical region.

scholarly journals Relativistic quantum mechanics

1932 ◽  
Vol 136 (829) ◽  
pp. 453-464 ◽  
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Classical Theory ◽  
Correspondence Principle ◽  
Relativistic Quantum ◽  
Classical Mechanics ◽  
Hamiltonian Function ◽  
Relativistic Quantum Mechanics ◽  
Classical Electrodynamics ◽  
Quantum Phenomena

The steady development of the quantum theory that has taken place during the present century was made possible only by continual reference to the Correspondence Principle of Bohr, according to which, classical theory can give valuable information about quantum phenomena in spite of the essential differences in the fundamental ideas of the two theories. A masterful advance was made by Heisenberg in 1925, who showed how equations of classical physics could be taken over in a formal way and made to apply to quantities of importance in quantum theory, thereby establishing the Correspondence Principle on a quantitative basis and laying the foundations of the new Quantum Mechanics. Heisenberg’s scheme was found to fit wonderfully well with the Hamiltonian theory of classical mechanics and enabled one to apply to quantum theory all the information that classical theory supplies, in so far as this information is consistent with the Hamiltonian form. Thus one was able to build up a satisfactory quantum mechanics for dealing with any dynamical system composed of interacting particles, provided the interaction could be expressed by means of an energy term to be added to the Hamiltonian function. This does not exhaust the sphere of usefulness of the classical theory. Classical electrodynamics, in its accurate (restricted) relativistic form, teaches us that the idea of an interaction energy between particles is only an approxi­mation and should be replaced by the idea of each particle emitting waves which travel outward with a finite velocity and influence the other particles in passing over them. We must find a way of taking over this new information into the quantum theory and must set up a relativistic quantum mechanics, before we can dispense with the Correspondence Principle.

scholarly journals An analysis on Quantum mechanical Stability of Regular Polygons on a Point Base Using Heisenberg Uncertainty Principle

2021 ◽  
Vol 9 (10) ◽  
pp. 74-79
Author(s):  
Anurag Chapagain
Keyword(s):  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stability Problem ◽  
Classical Mechanics ◽  
Quantum Mechanical ◽  
Heisenberg Uncertainty Principle ◽  
Heisenberg Uncertainty ◽  
Degree Of Stability ◽  
The Stability ◽  
Heisenberg's Uncertainty Principle

Abstract: It is a well-known fact in physics that classical mechanics describes the macro-world, and quantum mechanics describes the atomic and sub-atomic world. However, principles of quantum mechanics, such as Heisenberg’s Uncertainty Principle, can create visible real-life effects. One of the most commonly known of those effects is the stability problem, whereby a one-dimensional point base object in a gravity environment cannot remain stable beyond a time frame. This paper expands the stability question from 1- dimensional rod to 2-dimensional highly symmetrical structures, such as an even-sided polygon. Using principles of classical mechanics, and Heisenberg’s uncertainty principle, a stability equation is derived. The stability problem is discussed both quantitatively as well as qualitatively. Using the graphical analysis of the result, the relation between stability time and the number of sides of polygon is determined. In an environment with gravity forces only existing, it is determined that stability increases with the number of sides of a polygon. Using the equation to find results for circles, it was found that a circle has the highest degree of stability. These results and the numerical calculation can be utilized for architectural purposes and high-precision experiments. The result is also helpful for minimizing the perception that quantum mechanical effects have no visible effects other than in the atomic, and subatomic world. Keywords: Quantum mechanics, Heisenberg Uncertainty principle, degree of stability, polygon, the highest degree of stability

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