Jump to ContentJump to Main Navigation

You are looking at 1-20 of 21 items

  • Keywords: Dirac equation x
Clear All Modify Search

View:

The Nahm Transform for Calorons

Benoit Charbonneau and Jacques Hurtubise

in The Many Facets of Geometry: A Tribute to Nigel Hitchin

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199534920
eISBN:
9780191716010
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199534920.003.0004
Subject:
Mathematics, Geometry / Topology

One mysterious feature of the self-duality equations on ℝ4 is the existence of a quite remarkable non-linear transform, the Nahm transform. It maps solutions to the self-duality equations on ℝ4 ... More


Quantized Dirac Fields

Carlo Giunti and Chung W. Kim

in Fundamentals of Neutrino Physics and Astrophysics

Published in print:
2007
Published Online:
January 2010
ISBN:
9780198508717
eISBN:
9780191708862
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508717.003.0002
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses the physics of quantized Dirac fields with detailed treatment of Dirac equation, representations of gamma matrices, products of gamma matrices, relativistic covariance (boosts, ... More


Relativistic wave equations

Victor Galitski, Boris Karnakov, Vladimir Kogan, and Victor Galitski, Jr.

in Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers, and Researchers

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199232710
eISBN:
9780191774973
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199232710.003.0015
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter deals with problems related to the Klein-Gordon equation and the Dirac equation.


Elementary relativistic quantum mechanics

Efstratios Manousakis

in Practical Quantum Mechanics: Modern Tools and Applications

Published in print:
2015
Published Online:
December 2015
ISBN:
9780198749349
eISBN:
9780191813474
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198749349.003.0031
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter is seeking relativistic wave equations, which are invariant under Lorentz transformations, in an attempt to obtain a quantum mechanical description of relativistic particles. First, the ... More


Relativistic square-root spaces∗

Chun Wa Wong

in Introduction to Mathematical Physics: Methods & Concepts

Published in print:
2013
Published Online:
May 2013
ISBN:
9780199641390
eISBN:
9780191747786
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199641390.003.0003
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Einstein's derivation of the Lorentz transformation between space and time coordinates is given. The resulting relativistic kinematics of £  Lorentz spacetime and momentum-energy vectors is readily ... More


Relativistic Mechanics

Oliver Johns

in Analytical Mechanics for Relativity and Quantum Mechanics

Published in print:
2005
Published Online:
January 2010
ISBN:
9780198567264
eISBN:
9780191717987
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198567264.003.0016
Subject:
Physics, Atomic, Laser, and Optical Physics

It was apparent from its beginning that special relativity developed as the invariance theory of electrodynamics would require a modification of Newton’s three laws of motion. This chapter discusses ... More


Dirac Theory of the Electron

P.J.E. Peebles

in Quantum Mechanics

Published in print:
2019
Published Online:
May 2021
ISBN:
9780691209821
eISBN:
9780691206738
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691209821.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter explores applications drawn from Dirac theory of the electron. In the treatment of electrons, it uses the following: an electron has spin 1/2; its magnetic dipole moment is very nearly ... More


Relativistic quantum mechanics

G. Barr, R. Devenish, R. Walczak, and T. Weidberg

in Particle Physics in the LHC Era

Published in print:
2016
Published Online:
March 2016
ISBN:
9780198748557
eISBN:
9780191811203
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198748557.003.0006
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter starts with a brief summary of special relativity, describing how 4-vectors and the Lorentz transformation can be represented by complex matrices. Spinors are introduced as basic ... More


From Schrödinger to Einstein and Dirac: Relativistic Effects

Jochen Autschbach

in Quantum Theory for Chemical Applications: From Basic Concepts to Advanced Topics

Published in print:
2020
Published Online:
February 2021
ISBN:
9780190920807
eISBN:
9780197508350
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780190920807.003.0024
Subject:
Chemistry, Quantum and Theoretical Chemistry

The implications of Einstein’s special relativity in chemistry are discussed. It is shown that relativistic effects on the electronic structure of an atom or molecule scales in leading order as Z2, ... More


Fermions and the Dirac equation

Michael Kachelriess

in Quantum Fields: From the Hubble to the Planck Scale

Published in print:
2017
Published Online:
February 2018
ISBN:
9780198802877
eISBN:
9780191841330
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198802877.003.0008
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

Starting from the spinor representation of the Lorentz group,Weyl spinors and their transformation properties are derived. The Dirac equation and the properties of its solutions are discussed. ... More


Spin Separation and the Modified Dirac Equation

Kenneth G. Dyall and Knut Faegri

in Introduction to Relativistic Quantum Chemistry

Published in print:
2007
Published Online:
November 2020
ISBN:
9780195140866
eISBN:
9780197561744
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195140866.003.0022
Subject:
Chemistry, Quantum and Theoretical Chemistry

In the preceding chapters, the theory for calculations based on the Dirac equation has been laid out in some detail. The discussion of the methods included a comparison with equivalent ... More


Relativistic Wave Equations

Michael E. Peskin

in Concepts of Elementary Particle Physics

Published in print:
2019
Published Online:
November 2019
ISBN:
9780198812180
eISBN:
9780191850301
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198812180.003.0003
Subject:
Physics, Particle Physics / Astrophysics / Cosmology, Theoretical, Computational, and Statistical Physics

This chapter presents the wave equations that govern the behavior of quantum mechanical particles with spin 0, 1/2, and 1 in relativistic theories. These equations are the Klein-Gordon equation, the ... More


Quantum Lattice Boltzmann (QLB)

Sauro Succi

in The Lattice Boltzmann Equation: For Complex States of Flowing Matter

Published in print:
2018
Published Online:
June 2018
ISBN:
9780199592357
eISBN:
9780191847967
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780199592357.003.0032
Subject:
Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The Lattice Boltzmann concepts and applications described so far refer to classical, i.e., non-quantum physics. However, the LB formalism is not restricted to classical Newtonian mechanics and indeed ... More


The Schrödinger Equation in the Presence of Fields

Stephan P. A. Sauer

in Molecular Electromagnetism: A Computational Chemistry Approach

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199575398
eISBN:
9780191775109
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199575398.003.0002
Subject:
Physics, Atomic, Laser, and Optical Physics

This chapter derives the Hamiltonian for the electronic Schrödinger equation of a molecule in the presence of external and internal static electric or magnetic fields. It starts off with the ... More


Gauge Field Theory and Gravitation

Daniel Canarutto

in Gauge Field Theory in Natural Geometric Language: A revisitation of mathematical notions of quantum physics

Published in print:
2020
Published Online:
December 2020
ISBN:
9780198861492
eISBN:
9780191894374
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198861492.003.0006
Subject:
Mathematics, Applied Mathematics, Mathematical Physics

The notion of 2-spinor soldering form allows a neat formulation, called the ‘tetrad-affine setting’, of a theory of matter and gauge fields interacting with the gravitational field. The latter is ... More


Density Functional Approaches to Relativistic Quantum Mechanics

Kenneth G. Dyall and Knut Faegri

in Introduction to Relativistic Quantum Chemistry

Published in print:
2007
Published Online:
November 2020
ISBN:
9780195140866
eISBN:
9780197561744
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780195140866.003.0020
Subject:
Chemistry, Quantum and Theoretical Chemistry

The wave function is an elusive and somewhat mysterious object. Nobody has ever observed the wave function directly: rather, its existence is inferred from the various experiments whose outcome is ... More


Particle Physics in the LHC Era

Giles Barr, Robin Devenish, Roman Walczak, and Tony Weidberg

Published in print:
2016
Published Online:
March 2016
ISBN:
9780198748557
eISBN:
9780191811203
Item type:
book
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198748557.001.0001
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This book gives a modern introduction to particle physics. The main mathematical tools required for the rest of the book are developed in Chapter 2. A quantitative introduction to accelerator physics ... More


Graphene

Norman J. Morgenstern Horing

in Quantum Statistical Field Theory: An Introduction to Schwinger's Variational Method with Green's Function Nanoapplications, Graphene and Superconductivity

Published in print:
2017
Published Online:
January 2018
ISBN:
9780198791942
eISBN:
9780191834165
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198791942.003.0012
Subject:
Physics, Theoretical, Computational, and Statistical Physics

Chapter 12 introduces Graphene, which is a two-dimensional “Dirac-like” material in the sense that its energy spectrum resembles that of a relativistic electron/positron (hole) described by the Dirac ... More


Time reversal

George Jaroszkiewicz

in Images of Time: Mind, Science, Reality

Published in print:
2016
Published Online:
January 2016
ISBN:
9780198718062
eISBN:
9780191787553
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198718062.003.0026
Subject:
Physics, Particle Physics / Astrophysics / Cosmology

This chapter discusses time reversal, starting from basic Newtonian mechanics and ending with quantum field theory. The chapter explains the meaning of time reversal in experimental physics, step by ... More


Fermionic Formulation of the Ising Model

Giuseppe Mussardo

in Statistical Field Theory: An Introduction to Exactly Solved Models in Statistical Physics

Published in print:
2020
Published Online:
May 2020
ISBN:
9780198788102
eISBN:
9780191830082
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198788102.003.0009
Subject:
Physics, Theoretical, Computational, and Statistical Physics

A crucial aspect of the Ising model is its fermionic nature and this chapter is devoted to this property of the model. In the continuum limit, a Dirac equation for neutral Majorana fermions emerges. ... More


View: