scholarly journals Linear Canonical Transformations in relativistic quantum physics

2021 ◽  
Vol 96 (6) ◽  
pp. 065204
Author(s):  
Ravo Tokiniaina Ranaivoson ◽  
Raoelina Andriambololona ◽  
Hanitriarivo Rakotoson ◽  
Roland Raboanary
Keyword(s):  
Quantum Physics ◽  
Relativistic Quantum ◽  
Canonical Transformations

Scattering in Classical and Quantum Physics

2021 ◽  
pp. 35-50
Author(s):  
J. Iliopoulos ◽  
T.N. Tomaras
Keyword(s):  
Particle Physics ◽  
Quantum Physics ◽  
Relativistic Quantum ◽  
Resonant Scattering ◽  
Potential Scattering ◽  
Optical Theorem ◽  
Low Energies ◽  
Scattering Lengths ◽  
Almost All ◽  
Relativistic Potential

Scattering experiments provide the main source of information on the properties of elementary particles. Here we present the theory of scattering in both classical and non-relativistic quantum physics. We introduce the basic notions of cross section and of range and strength of interactions. We work out some illustrative examples. The concept of resonant scattering, central to almost all applications in particle physics, is explained in the simple case of potential scattering, where we derive the Breit–Wigner formula. This framework of non-relativistic potential scattering turns out to be very convenient for introducing several other important concepts and results, such as the optical theorem, the partial wave amplitudes and the corresponding phase shifts and scattering lengths. The special cases of scattering at low energies, and that in the Born approximation, are studied. We also offer a first glance at the problem of the infrared divergences for the case of Coulomb scattering.

scholarly journals A Unified Scheme for Generalized Sectors Based on Selection Criteria: Order Parameters of Symmetries and of Thermality and Physical Meanings of Adjunctions

2003 ◽  
Vol 10 (03) ◽  
pp. 235-279 ◽  
Author(s):  
Izumi Ojima
Keyword(s):  
Selection Criteria ◽  
Quantum Physics ◽  
Relativistic Quantum ◽  
Order Parameters ◽  
Mathematical Framework ◽  
Mathematical Meaning ◽  
Classifying Space ◽  
Specific Domain ◽  
Geometrical Meaning ◽  
Field Algebra

A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic quantum fields in the vacuum situations with unbroken and spontaneously broken internal symmetries, through equilibrium and non-equilibrium states to some basic aspects in measurement processes. This is achieved by the help of c → q and q → c channels: the former determines the states to be selected and to be parameterized by the order parameters, and the latter provides the physical interpretations of selected states in terms of order parameters. This formulation extends the traditional range of applicability of the Doplicher-Roberts construction method for recovering the field algebra and the gauge group (of the first kind) from the data of group invariant observables to the situations with spontaneous symmetry breakdown: in use of the machinery proposed, the physical and mathematical meaning of basic structural ingredients associated with the spontaneously broken symmetry are re-examined, such as the degenerate vacua parameterized by the variables belonging to the relevant homogeneous space, the Goldstone modes and condensates, etc. The geometrical meaning of the space of order parameters is naturally understood in relation with the adjunction as the classifying space of a sector structure. As further examples of applications, some basic notions arising in the mathematical framework of quantum theory are reformulated and examined in connection with control theory.

scholarly journals Quantum simulation of relativistic quantum physics with trapped ions

2011 ◽  
Vol 264 ◽  
pp. 012020 ◽  
Author(s):  
C F Roos ◽  
R Gerritsma ◽  
G Kirchmair ◽  
F Zähringer ◽  
E Solano ◽  
...  
Keyword(s):  
Quantum Physics ◽  
Relativistic Quantum ◽  
Quantum Simulation ◽  
Trapped Ions

scholarly journals The Illusion of Quantum Mechanical Probability Waves

2020 ◽  
Vol 5 (10) ◽  
pp. 1212-1224
Author(s):  
Wim Vegt
Keyword(s):  
Wave Equation ◽  
Dirac Equation ◽  
Electromagnetic Waves ◽  
Quantum Physics ◽  
Probability Function ◽  
Relativistic Quantum ◽  
Science And Religion ◽  
Niels Bohr ◽  
Quantum Mechanical ◽  
Mechanical Probability

An important milestone in quantum physics has been reached by the publication of the Relativistic Quantum Mechanical Dirac Equation in 1928. However, the Dirac equation represents a 1-Dimensional quantum mechanical equation which is unable to describe the 4-Dimensional Physical Reality. In this article the 4-Dimensional Relativistic Quantum Mechanical Dirac Equation expressed in the vector probability functions  and the complex conjugated vector probability function  will be published. To realize this, the classical boundaries of physics has to be changed. It is necessary to go back in time 300 years ago. More than 200 years ago before the Dirac Equation had been published. A Return to the Inception of Physics. The time of Isaac Newton who published in 1687 in the “Philosophiae Naturalis Principia Mathematica” a Universal Fundamental Principle in Physics which was in Harmony with Science and Religion. The Universal Path, the Leitmotiv, the Universal Concept in Physics. Newton found the concept of “Universal Equilibrium” which he formulated in his famous third equation Action = - Reaction. This article presents a New Kind of Physics based on this Universal Fundamental Concept in Physics which results in a New Approach in Quantum Physics and General Relativity. The physical concept of quantum mechanical probability waves has been created during the famous 1927 5th Solvay Conference. During that period there were several circumstances which came together and made it possible to create an unique idea of material waves being complex (partly real and partly imaginary) and describing the probability of the appearance of a physical object (elementary particle). The idea of complex probability waves was new in the beginning of the 20th century. Since then the New Concept has been protected carefully within the Copenhagen Interpretation. When Schrödinger published his famous material wave equation in 1926, he found spherical and elliptical solutions for the presence of the electron within the atom. The first idea of the material waves in Schrödinger’s wave equation was the concept of confined Electromagnetic Waves. But according to Maxwell this was impossible. According to Maxwell’s equations Electromagnetic Waves can only propagate along straight lines and it is impossible that Light (Electromagnetic Waves) could confine with the surface of a sphere or an ellipse. For that reason, these material waves in Schrödinger’s wave equation could only be of a different origin than Electromagnetic Waves. Niels Bohr introduced the concept of “Probability Waves” as the origin of the material waves in Schrödinger’s wave equation. And defined the New Concept that the electron was still a particle but the physical presence of the electron in the Atom was equally divided by a spherical probability function. In the New Theory it will be demonstrated that because of a mistake in the Maxwell Equations, in 1927 Confined Electromagnetic waves could not be considered to be the material waves expressed in Schrödinger's wave equation. The New Theory presents a new equation describing electromagnetic field configurations which are also solutions of the Schrodinger's wave equation and the relativistic quantum mechanical Dirac Equation and carry mass, electric charge and magnetic spin at discrete values.

Processual Thinking in the Ontological and Epistemological context of Quantum Mechanics

2019 ◽  
Vol 62 (7) ◽  
pp. 21-36 ◽  
Author(s):  
Vladimir I. Arshinov ◽  
Vladimir G. Budanov
Keyword(s):  
Quantum Mechanics ◽  
Quantum Physics ◽  
Biological Diversity ◽  
Relativistic Quantum ◽  
Foundations Of Quantum Mechanics ◽  
Natural Environments ◽  
Cultural Codes ◽  
Problems Of Translation ◽  
Different Cultures ◽  
Cognitive Niches

The problem of commensurability/incommensurability of different cultural codes is a key problem of modern civilizational development. This is the problem of the search for communicative unity in the world of cultural and biological diversity, which has to be protected, and the search for the cohesion of different Umwelten, of semiotically-defined artificial and natural environments, of ecological and cognitive niches, taking into account that each of them has their own identity and uniqueness. The purpose of the article is to draw attention to the fact that the question of the so-called incommensurability of different conceptual schemes, paradigms, language consciousnesses is widely discussed not only in cross-cultural studies and philosophical problems of translation but also in connection with the problems of incommensurability (untranslatability) between the language of classical physics and the language of relativistic quantum physics. Attention is drawn to the problem of the incommensurability and correlation of different languages that are used in debates about the foundations of quantum mechanics, its interpretation, comprehension and ontology. Two approaches stand out in this debate. The first approach is based on the language of the formed being, on the language of things localized in time and on the logic of Aristotle. The second approach is based on the language of the becoming, process and nonlocality, on the search for various processual-oriented temporal logics. In this regard, we discuss the processual approach to understanding quantum mechanics, proposed in the philosophical and physical works of D. Bohm. The authors argue that (a) the experience of constructive understanding of the metaproblems of the interpretation of quantum mechanics, (b) the critical reception of the legacy of such philosophers of the process as Peirce, Bergson and Whitehead, (c) the deep reflection on the problems of commensurability/ incommensurability of linguistic consciousnesses of different cultures – will eventually create a common synergetic-interdisciplinary space of cooperation for the solutions of the above-mentioned issues.

scholarly journals Detectors for probing relativistic quantum physics beyond perturbation theory

2013 ◽  
Vol 87 (8) ◽  
Author(s):  
Eric G. Brown ◽  
Eduardo Martín-Martínez ◽  
Nicolas C. Menicucci ◽  
Robert B. Mann
Keyword(s):  
Perturbation Theory ◽  
Quantum Physics ◽  
Relativistic Quantum
Sign in / Sign up

Export Citation Format

Share Document