Hot or Dense Matter ∗

I review some of the properties of hot and/or dense relativistic matter. I've been asked to review hot and/or dense matter. As a general rule, most particle physicists aren't that familiar with the behavior of quantum field theory at finite temperature and density. We've all been introduced to how to think about systems of a few relativistic particles with given energies, and how to describe such systems with quantum field theory, but most of us haven't had occasion to develop comparable experience and intuition about systems of many particles at finite temperature or density. I am therefore going to forgo attempting a comprehensive review of recent results. Instead, I will try to give a primer on relativistic hot or dense matter , with a perhaps somewhat quirky choice of topics dictated by my own areas of competence. To begin, let me define some terms. Matter will mean gauge theories (coupled to fermions and so forth). As far as gauge theories go, I'll restrict my attention to QCD and electroweak theory. Hot or dense will mean relativistically, and even ultra-relativistically, hot or dense. Ultra-relativistically hot QCD matter is matter at high density: if there weren't any initially, they'd instantly appear due to pair creating collisions of photons or gluons or whatever. However, in this field, the adjective " dense " is used instead as a codeword to mean " non-zero chemical potential µ. " More specifically, dense typically refers to non-zero chemical potential µ B for baryon number. So dense QCD refers to the case where the numbers of quarks and anti-quarks are significantly different. I'll begin by focusing just on hot matter, by which I mean µ = 0 or close to it (µ ≪ T). This is the situation of relevance to the early Universe at temperatures above the QCD scale, when the asymmetry between the number of quarks and anti-quarks was very small. One example of a situation where the physics of hot (but not " dense ") gauge * Talk given at DPF2000.