The problem with trying to marry quantum mechanics to einsteins special theory of relativity is the fact that the relativistic energy of a free particle of mass and momentum, is given by. Notes on relativistic quantum mechanics module 4 of refresher. In order to do this, we solve the dirac and kleingordon equations analytically and discuss the influence of this background, which is. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum. We compare the solutions and the energy spectra obtained with the corresponding ones from the dirac equation for a spin onehalf relativistic particle. We explore kleingordon equation in the new framework of quasihermitian quantum mechanics. Does this also apply for solutions of kleingordon equation or dirac equation or other relativistic wave equations. Relativistic mechanics, science concerned with the motion of bodies whose relative velocities approach the speed of light c, or whose kinetic energies are comparable with the product of their masses m and the square of the velocity of light, or mc2. Relativistic quantum mechanics video course course outline dirac and kleingordon equations, lorentz and poincare groups, fundamental processes of quantum electrodynamics. Dirac equation derivation and introduction youtube. The kleingordon equation can be generalized to describe a field in some potential v. Of course people attempted to generate equations for relativistic theories soon after schrodinger wrote down his equation. Youd have to use qed, the kleingordon and freedirac fields dont account for electromagnetic interactions, well the latter can if you apply minimal coupling but without quantum field theory one can only account for first order interactions. The klein gordon equation and relativistic quantum mechanics 1.
If not, then how do we get something that can be experimentally measured from the solutions of relativistic wave equations. As we know that this spin of electron was not explained by klein gordan and was the. Appendix a contains some mathematical results concerning the theory of linear transports along maps required for the present investigation. The kleingordon equation is a relativistic wave equation, related to the schrodinger equation. Relativistic quantum mechanics in this chapter we will address the issue that the laws of physics must be formulated in a form which is lorentzinvariant, i. In addition, diracs theory is the basis for modern quantum electrodynamics, one of the most accurate quantum theories to date. Fibre bundle formulation of relativistic quantum mechanics. Journal of mathematical analysis and applications 71, 3647 1979 on the nonrelativistic limits of the kleingordon and dirac equations andrew y. Out of this analysis will emerge the kleingordon and dirac equations, and the concept of quantum mechanical spin.
Lax introduction in this paper we give a mathematical proof that the kleingordon and dirac equations of relativistic quantum mechanics have. Course detail module 1 klein gordon and dirac equations lecture 1 introduction, the klein gordon equation lecture 2 particles and antiparticles, two component framework. The chapters that follow introduce the dirac equation, investigate its covariance properties and present various approaches to obtaining. Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from qft to relativistic quantum mechanics. Nov 16, 2017 in relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantized energy spectra. The book presents the subject in basic and easytograsp notions which will enhance the purpose of this book as a useful textbook in the area of relativistic quantum mechanics and quantum electrodynamics. Note that we have derived this equation from something that did give the right answers so. Klein gordon equation the quest for a mathematical theory of quantum mechanics began with great am bition. In its free form, or including electromagnetic interactions, it describes all spin 1. Thus i have a question on the transition from quantum mechanics to relativistic quantum mechanics. When paul dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it.
In its free form, or including electromagnetic interactions, it describes all spin 1 2 massive particles such as electrons and quarks for which parity is a symmetry. The kleingordon and dirac equations for free particles substituting the energy and momentum operators directly into the energymomentum. To illustrate this point, we solve the problem of a spin zero. Notes on relativistic quantum mechanics module 4 of. Its theoretical relevance is similar to that of the dirac equation. At the very least it should be consistent with the theory of spe cial relativity that had revolutionized classical physics. The chapters that follow introduce the dirac equation, investigate its covariance properties and present various approaches to obtaining solutions.
The attempts to generalize it to the relativistic case led to the discovery of various wave equations klein gordon, dirac, maxwell. These have to do with antiparticles, and indeed the dirac equation has historically led to the concept of the positron. The second order time derivative in the kleingordon equation leads to the negative energy solutions. Does this also apply for solutions of klein gordon equation or dirac equation or other relativistic wave equations.
The dirac equation relativistic spectrum is, however, easily recovered if the. The quest for a mathematical theory of quantum mechanics began with great am bition. The first chapter deals with the klein gordon equation and its properties a. Mar 03, 2008 more properly, one should really say that the kleingordon and dirac equations are invariant, and that the schrodinger equation is not, but this is not the dominant usage. Its solutions include a quantum scalar or pseudoscalar field, a field whose.
The chapters that follow introduce the dirac equation, investigate its covariance. In the context of quantum field theory qft, the equations determine the dynamics of quantum fields. How to use the einstein energymomentum relation to derive the klein gordon wave equation. Both kleingordon and dirac equations admit negative energies.
It gives a thorough analysis of the kleingordon and dirac equations highlighting their properties. Proof of existence of spin of electron using dirac. The first chapter deals with the kleingordon equation and its properties and applications. Introduction to relativistic quantum mechanics 249 1. Readers who want to get to rqm quickly, without studying its foundation in special relativity can skip the. Wave equations concentrates mainly on the wave equations for spin0 and spin12 particles. Is there supersymmetry between dirac and klein gordon. It provides valuable insights into the underlying physics. Relativisticquantum mechanics 1 university of oxford. Relativistic quantum mechanics book chapter iopscience. This introduction prepares the way for the construction of relativistic quantum. In addition, dirac s theory is the basis for modern quantum electrodynamics, one of the most accurate quantum theories to date. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one and threedimensional box using the kleingordon equation in the feshbachvillars formalism.
The problem with trying to marry quantum mechanics to einsteins special theory of relativity is the fact that the relativistic energy of a. This approach lacks mathematical rigor, but is more intuitive. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, firstorder hamiltonian and momentum constraints that lead to emergent features of temporal and spatial translations. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one and threedimensional box using the klein gordon. The dirac equation and the prediction of antimatter. Kleingordon equation the quest for a mathematical theory of quantum mechanics began with great am bition. Both klein gordon and dirac equations admit negative energies. We treat space and time as bona fide quantum degrees of freedom on an equal footing in hilbert space. Lecture 22 relativistic quantum mechanics theory of condensed.
Chapter 1 deals with the klein gordon equation and its properties and appli. It is a quantized version of the relativistic energymomentum relation. Early attempts to merge quantum mechanics with special relativity involved the replacement of the schrodinger equation with a covariant equation such as the kleingordon equation or the dirac equation. Lecture notes wave equations of relativistic quantum mechanics. We will present an overview of special relativity, relativistic kleingordon and dirac wave equations and the convention in this book for dirac spinors, and a selfcontained discussion of representation theory of the rotation and lorentz groups. These fundamental physical constants reflect special relativity and quantum mechanics, respectively. It is consistent with both the principles of quantum mechanics and the theory of special relativity. Introduction, the klein gordon equation particles and antiparticles, two component framework coupling to electromagnetism, solution of the coulomb problem bohrsommerfeld semiclassical solution of the coulomb problem, the dirac equation and the clifford algebra dirac matrices, covariant form of the dirac equation, equations of motion, spin. In order to avoid this problem, dirac tried to find an equation.
Contains a thorough analysis of the kleingordon and dirac equations highlighting their properties. It is secondorder in space and time and manifestly lorentzcovariant. Furthermore, in quantum field theory, every component of every quantum field must satisfy the free kleingordon equation, making the equation a generic expression of quantum fields. We will come back to the question what it actually describes later on. The first chapter deals with the kleingordon equation and. The nonrelativistic limit of the dirac equation one important requirement for the dirac equation is that it reproduces what we know from nonrelativistic quantum mechanics. It gives a thorough analysis of the klein gordon and dirac equations highlighting their properties. We can play around with the interpretation of the wavefunctions in relativistic quantum mechanics but. Relativistic quantum mechanics wave equations concentrates mainly on the wave equations for spin0 and spin12 particles. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their.
Schoene1 general motors research laboratories, warren, michigan 48090 submitted by peter d. Motivated by these problems, dirac set to find another relativistic quantum mechanical equation. Solutions to common problems with probability interpretation and inde. The development of quantum mechanics is presented from a historical perspective. Notes on relativistic quantum mechanics module 4 of refresher course conducted by indian academies of sciences st berchmans college, changanacherry, kerala, may 814, 20. Relativistic quantum mechanics online course video lectures. You mean using a relativistic field equation to predict the bound states etc. This book aims at addressing this gap by providing a lucid description of single particle relativistic dynamics at the quantum scale adapting, in a sense, the schrodinger wave equations. Relativistic quantum mechanics online course video. In particle physics, the dirac equation is a relativistic wave equation derived by british physicist. But can it only be described by relativistic quantum mechanics.
On the nonrelativistic limits of the kleingordon and. The kleingordon equation is applied in the description of mesons and corresponding fields. In physics, specifically relativistic quantum mechanics rqm and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. Quantum mechanics relativistic quantum mechanics rqm. The attempts to generalize it to the relativistic case led to the discovery of various wave equations kleingordon, dirac, maxwell. Introduction, the kleingordon equation particles and antiparticles, two component framework coupling to electromagnetism, solution of the coulomb problem bohrsommerfeld semiclassical solution of the coulomb problem, the dirac equation and the clifford algebra dirac matrices, covariant form of the dirac equation, equations of motion, spin. The dirac equation and the prediction of antimatter david vidmar. Relativistic quantum mechanics kleingordon equation dirac. Contains specific chapters on symmetry in relativistic quantum mechanics and lorentz and poincare groups. The kleingordon equation kleinfockgordon equation or sometimes kleingordon fock equation is a relativistic wave equation, related to the schrodinger equation. The kleingordon equation is a linear homogeneous secondorder partial differential equation with constant coefficients. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantized energy spectra.
Course detail module 1 kleingordon and dirac equations lecture 1 introduction, the kleingordon equation lecture 2 particles and antiparticles, two component framework. Relativistic quantum mechanics kleingordon equation. There are two such equations, one called the kleingordon and the other one called the dirac equation. It would also lead him to one of the most important and daring predictions in the history of science. Unlike the conventional treatment, we show that kleingordon and dirac equations in. Quantum space, quantum time, and relativistic quantum. Both the kleingordon equation and the dirac equation are important examples for hyperbolic partial differential equations. This relativistic quantum theory was both complicated and elegant, and would win dirac. Deriving the klein gordon equation relativistic quantum youtube. As you all know, in ordinary quantum mechanics we ignore relativity. In particle physics, the dirac equation is a relativistic wave equation derived by british physicist paul dirac in 1928. This relativistic quantum theory was both complicated and elegant, and would win dirac the nobel prize in physics in 1933.
The final formalism of dealing with the relativistic quantum equations has been developed since that time and is now called the quantum field theory. The dirac equation automatically includes spin, and thus gives a reason. To illustrate this point, we solve the problem of a spin zero relativistic particle in a one and threedimensional box using the kleingordon. For full reconciliation of quantum mechanics with special relativity, quantum. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the effect that spin has on the quantised energy spectra. Provides extended derivations of all relevant physical. Relativistic quantum mechanics video course course outline dirac and klein gordon equations, lorentz and poincare groups, fundamental processes of quantum electrodynamics. The relativistic wave equations have several interesting and new features. In the context of quantum field theory qft, the equations determine the dynamics of. Chapter 1 deals with the klein gordon equation and its properties and applications. Relativistic quantum mechanics is developed, including the kleingordon equation and up to the dirac equation. In relativistic quantum mechanics this problem allows also to highlight the implications of special relativity for quantum physics, namely the.
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