## 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