To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

Neutron Stars 1: Equation of State and Structure

We calculate the number density, energy density, transverse pressure, longitudinal pressure, and magnetization of an ensemble of spin one-half particles in the presence of a homogenous background magnetic field. The magnetic field direction breaks spherical symmetry causing the pressure transverse to the magnetic field direction to be different than the pressure parallel to it. We present explicit formulas appropriate at zero and finite temperature for both charged and uncharged particles including the effect of the anomalous magnetic moment. We demonstrate that the resulting expressions satisfy the canonical relations $\ensuremath{\Omega}=\ensuremath{-}{P}_{\ensuremath{\parallel}}$ and ${P}_{\ensuremath{\perp}}={P}_{\ensuremath{\parallel}}\ensuremath{-}MB$, with $M=\ensuremath{-}\ensuremath{\partial}\ensuremath{\Omega}/\ensuremath{\partial}B$ being the magnetization of the system. We numerically calculate the resulting pressure anisotropy for a gas of protons and a gas of neutrons and demonstrate that the inclusion of the anomalous magnetic increases the level of pressure anisotropy in both cases.

https://cupola.gettysburg.edu/cgi/viewcontent.cgi?article=1071&context=physfac

Bulk Properties of a Fermi Gas in a Magnetic Field

We study the effects of high magnetic fields on the particle population and equation of state of hybrid stars using an extended hadronic and quark SU(3) non-linear realization of the sigma model. In this model the degrees of freedom change naturally from hadrons to quarks as the density and/or temperature increases. The effects of high magnetic fields and anomalous magnetic moment are visible in the macroscopic properties of the star, such as mass, adiabatic index, moment of inertia, and cooling curves. Moreover, at the same time that the magnetic fields become high enough to modify those properties, they make the star anisotropic.

Hybrid stars in a strong magnetic field

We study the effect of strong magnetic fields on the structure of neutronstar. We find that if the interior field is on the same order as the surface fieldcurrently observed, then the influences of the field on the star's mass and radius arenegligible; if the field is as large as that estimated from the scalar virial theorem,then considerable effects will be induced. The maximum mass of the star will beincreased substantially while the central density is greatly reduced. The radius ofa magnetic star can be larger by about 10% ～ 20% than a nonmagnetic star of thesame mass.

https://iopscience.iop.org/article/10.1088/1009-9271/3/4/359/pdf

A Study of Neutron Star Structure in Strong Magnetic Fields that includes Anomalous Magnetic Moments

We study the effects of strong magnetic fields on the neutron star structure. If the interior field of a star is on the same order of the surface field currently observed, the influences of the magnetic field on the star mass and radius are negligible. If one assumes that the internal magnetic field can be as large as that estimated from the scalar virial theorem, considerable effects can be induced. The maximum mass of stars is arisen substantially while the central density is largely suppressed. For two equal-mass stars the radius of the magnetic star can be larger by about 10% $\sim$ 20% than the nonmagnetic star.

Guangjun Mao

Papers

A Study of Neutron Star Structure in Strong Magnetic Fields that includes Anomalous Magnetic Moments

Study of the neutron star structure in strong magnetic fields including the anomalous magnetic moments

Effects of Strong Magnetic Fields on the Neutron Star Structure