Dyson-Schwinger Equations: Density, Temperature and Continuum Strong QCD

Abstract

Continuum strong QCD is the application of models and continuum quantum field theory to the study of phenomena in hadronic physics, which includes; e.g., the spectrum of QCD bound states and their interactions; and the transition to, and properties of, a quark gluon plasma. We provide a contemporary perspective, couched primarily in terms of the Dyson-Schwinger equations but also making comparisons with other approaches and models. Our discourse provides a practitioners' guide to features of the Dyson-Schwinger equations [such as confinement and dynamical chiral symmetry breaking] and canvasses phenomenological applications to light meson and baryon properties in cold, sparse QCD. These provide the foundation for an extension to hot, dense QCD, which is probed via the introduction of the intensive thermodynamic variables: chemical potential and temperature. We describe order parameters whose evolution signals deconfinement and chiral symmetry restoration, and chronicle their use in demarcating the quark gluon plasma phase boundary and characterising the plasma's properties. Hadron traits change in an equilibrated plasma. We exemplify this and discuss putative signals of the effects. Finally, since plasma formation is not an equilibrium process, we discuss recent developments in kinetic theory and its application to describing the evolution from a relativistic heavy ion collision to an equilibrated quark gluon plasma.

103 Pages, LaTeX, epsfig. To appear in Progress in Particle and Nuclear Physics, Vol. 45

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• Perturbative gauge theory in a background
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• Constraining the Hadron-Quark Phase Transition Chemical Potential via Astronomical Observation
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• Schwinger-Dyson type equations for some QFT models
• Physics-informed neural networks viewpoint for solving the Dyson-Schwinger equations of quantum electrodynamics
• Quark cluster expansion model for interpreting finite-T lattice QCD thermodynamics
• Some Analytical Aspects in Field Theories with Dynamical Mass Generation
• Superconductivity with deformed Fermi surfaces and compact stars
• On the Consistency of the Ladder Approximation and the Rainbow Approximation of Dyson-Schwinger Equation of QCD
• Impact of isospin asymmetric nuclear medium on pseudoscalar and vector $B$ mesons
• Analysis of mass difference of the $\pi$ and $\rho$ with Bethe-Salpeter equation
• Gluons, quarks and deconfinement at high density
• nonlocal quark condensate from Dyson-Schwinger Equation and its contributions to the gluon vacuum polarization based on OPE approach
• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory
• Baryon and meson masses in the Nambu--Jona-Lasinio model: A Bayesian approach
• Equilibration in an Interacting Field Theory
• Finite temperature QCD crossover at non-zero chemical potential: A Dyson-Schwinger approach