Quantum Field Theory, 2nd Edition

Dear Colleagues,

Quantum field theory is a convincing framework used to address a variety of subatomic processes, high-energy particle reactions, and the effective physics of condensed matter systems. In particular, quantum gauge theory has acquired a prominent status. This Special Issue aims to present the latest developments in local quantum field theory, perturbatively and nonperturbatively and largely analytically describing systems of the variable spacetime dimension D=d+1 and signature, as well as field content. Examples include non-perturbative and analytical approaches to gauge theory (semi-classical approximation, non-perturbative a priori estimates) and conformal field theory in d=1,2,3, as well as approaches to quantum field theory that exploit a weak–strong coupling duality. We also welcome submissions that discuss resummation schemes of small-coupling expansions, operator product expansions, numerical approaches such as lattice gauge theory, quantum field theoretic investigations on strongly curved spacetime backgrounds and at finite temperature, and the various approaches to quantum gravity.

One of the second Special Issue’s focuses is the investigation of implications of an analytical approach to 4D Euclidean Yang–Mills thermodynamics (gauge groups SU(2) and SU(3)) developed by the editor and his collaborators. In particular, we encourage contributions that discuss the temperature dependence of ultralight Planck-scale axions by referring to matrix models on the spectrum of the Dirac operator, direct or indirect (e.g., field-strength correlator) lattice computations or effective chiral field-theory techniques. In the context of astrophysical/cosmological axion physics, we welcome numerical investigations of self-gravitating axion lumps (fuzzy dark matter) for a single axion species and/or several components either treated entirely by the Poisson–Schrödinger system or partly in terms of classical N-body components. Here, it is also highly interesting to include relativistic corrections to study the potential onset of collapse. Emulator-based and effective field theoretic approaches to the non-linear growth of small-scale structure are important tools to learn about the nature of dark matter (possibly in the framework of fuzzy dark matter based on ultralight axions), and we welcome submissions in this field.

The Special Issue would also benefit from contributions that target the process of thermalization and mixing of several Yang–Mills theories subject to hierarchical Yang–Mills scales.  To this end, a revisit of big-bang nucleosynthesis and the investigation of a partial photon-induced disintegration of already formed light elements due to a Hagedorn transition at a temperature of ~10 keV would be insightful. On the basis of the Yang–Mills theory, this topic is tightly connected to understanding why electroweak symmetry breaking is so effectively and successfully realized in the Standard Model. It also touches upon issues of plasma instabilities in terrestrial nuclear-fusion experiments for both inertial and magnetic confinement.

There are interesting questions to be addressed concerning the ranking of multi-loop diagrams in deconfining SU(2) Yang–Mills thermodynamics, and it would be useful if sharper tools than those that already exist could be developed in this regard. 

The editor hopes that the quantum thermodynamics of Yang–Mills theory could shed more light on how quantum gravitational processes work within black-hole thermodynamics when studying the microscopic interplay of both ingredients. Here, we particularly welcome speculative ideas. 

Finally, we encourage authors that specialize in 2D strongly correlated electrons to contribute to this Special Issue in elucidating the non-local electronic properties (e.g. spin-charge separation and long-range magnetic correlations).

Dr. Ralf Hofmann
Guest Editor

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• ultralight axions
• Peccei–Quinn at finite temperature
• spectral densities
• mixing of Yang–Mills theories
• electroweak symmetry breaking
• coarse-graining of Euclidean field theory gradient flow cooling