2023-02-06T04:39:45Zhttps://keep.lib.asu.edu/oai/requestoai:keep.lib.asu.edu:node-1548662021-08-30T18:21:44Zoai_pmh:alloai_pmh:repo_items154866
https://hdl.handle.net/2286/R.I.40221
http://rightsstatements.org/vocab/InC/1.0/
All Rights Reserved
2016
vii, 140 pages : illustrations
Doctoral Dissertation
Academic theses
Text
eng
Lanfear, Nathan A
Suslov, Sergei
Kotschwar, Brett
Platte, Rodrigo
Matyushov, Dmitry
Kuiper, Hendrik
Gardner, Carl
Arizona State University
Partial requirement for: Ph.D., Arizona State University, 2016
Includes bibliographical references (pages 125-140)
Field of study: Applied mathematics
Chapter 1 introduces some key elements of important topics such as; quantum mechanics,<br/><br/>representation theory of the Lorentz and Poincare groups, and a review of some basic rela- ´<br/><br/>tivistic wave equations that will play an important role in the work to follow. In Chapter 2,<br/><br/>a complex covariant form of the classical Maxwell’s equations in a moving medium or at<br/><br/>rest is introduced. In addition, a compact, Lorentz invariant, form of the energy-momentum<br/><br/>tensor is derived. In chapter 3, the concept of photon helicity is critically analyzed and its<br/><br/>connection with the Pauli-Lubanski vector from the viewpoint of the complex electromag- ´<br/><br/>netic field, E+ iH. To this end, a complex covariant form of Maxwell’s equations is used.<br/><br/>Chapter 4 analyzes basic relativistic wave equations for the classical fields, such as Dirac’s<br/><br/>equation, Weyl’s two-component equation for massless neutrinos and the Proca, Maxwell<br/><br/>and Fierz-Pauli equations, from the viewpoint of the Pauli-Lubanski vector and the Casimir ´<br/><br/>operators of the Poincare group. A connection between the spin of a particle/field and ´<br/><br/>consistency of the corresponding overdetermined system is emphasized in the massless<br/><br/>case. Chapter 5 focuses on the so-called generalized quantum harmonic oscillator, which<br/><br/>is a Schrodinger equation with a time-varying quadratic Hamiltonian operator. The time ¨<br/><br/>evolution of exact wave functions of the generalized harmonic oscillators is determined<br/><br/>in terms of the solutions of certain Ermakov and Riccati-type systems. In addition, it is<br/><br/>shown that the classical Arnold transform is naturally connected with Ehrenfest’s theorem<br/><br/>for generalized harmonic oscillators. In Chapter 6, as an example of the usefulness of the<br/><br/>methods introduced in Chapter 5 a model for the quantization of an electromagnetic field<br/><br/>in a variable media is analyzed. The concept of quantization of an electromagnetic field<br/><br/>in factorizable media is discussed via the Caldirola-Kanai Hamiltonian. A single mode<br/><br/>of radiation for this model is used to find time-dependent photon amplitudes in relation<br/><br/>to Fock states. A multi-parameter family of the squeezed states, photon statistics, and the<br/><br/>uncertainty relation, are explicitly given in terms of the Ermakov-type system.
Applied Mathematics
Theoretical Physics
Electrodynamics
Pauli-Lubanski Pseudo-Vector
Quantization
Quantum Field Theory
Quantum Mechanics
Schrödinger equation
Mathematics
Physics--Philosophy.
The Pauli-Lubanski Vector in a Group-Theoretical Approach to Relativistic Wave Equations