Happy birthday Dr. Dirac: A look at our recent papers inspired by his work

By Phil Brown on August 8, 2017

Here at IOP Publishing we would like to celebrate the birthday of Paul Dirac by highlighting some of the recent papers in Journal of Physics A: Mathematical and Theoretical that were influenced by his work across many areas of theoretical physics.

Dr. Paul Dirac By Nobel Foundation [Public domain], via Wikimedia Commons

Paul Dirac was born on 8th August 1902 in Bristol, UK; the same fair city as IOP Publishing is based. Dirac made world changing contributions to quantum mechanics and theoretical physics. He was a pioneer of quantum field theory and most famed across physics lecture halls the world over for the equation which would come to bear his name, that which described the relativistic motion of the electron. He was the Lucasian Professor of Mathematics at the University of Cambridge and later in life moved to Florida, where he worked at the Center for Theoretical Studies at the University of Miami, and at Florida State University. Dirac was awarded the Nobel Prize in Physics for 1933, which he shared with Erwin Schrodinger, “for the discovery of new productive forms of atomic theory”.

Today, JPhys+ would like to celebrate the contribution of this remarkable physicist across many fields by highlighting a few recent papers where many of the discoveries, theories and equations that bear his name are still topics of fundamental and groundbreaking importance.

More on the rainbow chain: entanglement, space-time geometry and thermal states

As part of our special issue celebrating John Cardy’s 70th birthday, researchers from Universidad Nacional de Educación a Distancia (UNED) and UAM-CSIC in Spain, CNRS and Université de Lorraine in France, Universidad de San Carlos de Guatemala in Guatemala and SISSA and INFN in Italy show that the universal scaling features of the rainbow chain model are captured by a massless Dirac fermion in a curved space-time.

The rainbow chain is an inhomogenous exactly solvable local spin model that, in its ground state, displays a half-chain entanglement entropy growing linearly with the system size. Although many exact results about the rainbow chain are known, the structure of the underlying quantum field theory has not yet been unraveled.

Electron interaction with the spin angular momentum of the electromagnetic field

Robert O’Connell at Louisiana State University gives a simple derivation and expansion of a recently proposed new relativistic interaction between the electron and the spin angular momentum of the electromagnetic field in quantum electrodynamics (QED).

Our derivation is based on the work of Møller, who pointed out that, in special relativity, a particle with spin must always have a finite extension. After generalizing Møller’s classical result to include both rotation and quantum effects, we show that it leads to a new contribution to the energy, which is the special relativistic interaction term. In addition, we go on to show that all relativistic terms involving spin terms arising from the Dirac equation may be obtained by this method.

Introduction to the thermodynamic Bethe ansatz

In this recent topical review Stijn van Tongeren of Humboldt University, Berlin gives a pedagogical introduction to the thermodynamic Bethe ansatz, a method that allows us to describe the thermodynamics of integrable models whose spectrum is found via the (asymptotic) Bethe ansatz.

We set the stage by deriving the Fermi–Dirac distribution and associated free energy of free electrons, and then in a similar though technically more complicated fashion treat the thermodynamics of integrable models, focusing first on the one-dimensional Bose gas with delta function interaction as a clean pedagogical example, secondly the XXX spin chain as an elementary (lattice) model with prototypical complicating features in the form of bound states, and finally the SU(2) chiral Gross–Neveu model as a field theory example.

The Dirac oscillator from theory to experiment

This Viewpoint by Christiane Quesne of Universite Libre de Bruxelles discusses the Dirac oscillator and relates to an article by Moshinsky and Szczepaniak (1989 J. Phys. A: Math. Gen. 22 L817) and was published as part of a series of Viewpoints celebrating some of the most influential papers published in JPhysA, as part of the celebrations of our JPhys50 anniversary.

The harmonic oscillator has been a basic tool in physics for many centuries. Its utmost importance in the development of theoretical physics became apparent with the birth of quantum mechanics because it was one the first problems to which quantization rules were applied.

In an attempt to reconcile quantum mechanics to relativity, Dirac proposed to linearise the free-particle Klein–Gordon equation, based on the quadratic relativistic relation between energy and momentum, and he obtained an equation describing a particle of spin 1/2, such as the electron. Introducing then the electromagnetic potentials in the equation, he arrived at a relativistic treatment of the hydrogen atom.

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