There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

https://www.physi.uni-heidelberg.de/~fschney/2008SS-Preseminar/buballarev.pdf

NJL-model analysis of dense quark matter

The current status of theoretical studies on the quantum chromodynamics (QCD) phase diagram at finite temperature and baryon chemical potential is reviewed with special emphasis on the origin of various phases and their symmetry breaking patterns. Topics include quark deconfinement, chiral symmetry restoration, order of the phase transitions, QCD critical point(s), colour superconductivity, various inhomogeneous states and implications from QCD-like theories.

https://iopscience.iop.org/article/10.1088/0034-4885/74/1/014001/pdf

The phase diagram of dense QCD

Strange quark matter and compact stars

Inhomogeneous chiral condensates

We study the phase diagram of dense, locally neutral three-flavor quark matter within the framework of the Nambu--Jona-Lasinio model. In the analysis, dynamically generated quark masses are taken into account self-consistently. The phase diagram in the plane of temperature and quark chemical potential is presented. The results for two qualitatively different regimes, intermediate and strong diquark coupling strength, are presented. It is shown that the role of gapless phases diminishes with increasing diquark coupling strength.

Phase diagram of neutral quark matter: Self-consistent treatment of quark masses

Neutron stars and the transition to color superconducting quark matter

We investigate the role of the isoscalar-vector interaction and the dynamics of the Polyakov loop on inhomogeneous phases in the phase diagram of the two-flavor Nambu-Jona-Lasinio model. Thereby we concentrate on inhomogeneous phases with a one-dimensional modulation, explicitly domain-wall solitons and, for comparison, the chiral spiral. While the inclusion of the Polyakov loop merely leads to quantitative changes compared to the original Nambu-Jona-Lasinio model, the inclusion of a repulsive vector-channel interaction has significant qualitative effects: Whereas for homogeneous phases the first-order phase transition gets weakened and eventually turns into a second-order transition or a crossover, the domain of inhomogeneous phases is less affected. In particular the location of the Lifshitz point in terms of temperature and density is not modified. Consequently, the critical point disappears from the phase diagram and only a Lifshitz point (showing a different critical behavior) remains. In particular, susceptibilities remain finite.

/pdf/influence-of-vector-interaction-and-polyakov-loop-dynamics-2ygugcqmq7.pdf

Michael Buballa

Papers

NJL-model analysis of dense quark matter

Inhomogeneous chiral condensates

Phase diagram of neutral quark matter: Self-consistent treatment of quark masses

Neutron stars and the transition to color superconducting quark matter

Influence of vector interaction and Polyakov loop dynamics on inhomogeneous chiral symmetry breaking phases