Galaxies appear on the sky as huge clouds of light, thousands of light-years across: see the illustrations in Section 1.3 below. Each contains anywhere from a million stars up to a million million (1012); gravity binds the stars together, so they do not wander freely through space. This introductory chapter gives the astronomical information that we will need to understand how galaxies are put together.

Almost all the light of galaxies comes from their stars. Our opening section attempts to summarize what we know about stars, how we think we know it, and where we might be wrong. We discuss basic observational data, and we describe the life histories of the stars according to the theory of stellar evolution. Even the nearest stars appear faint by terrestrial standards. Measuring their light accurately requires care, and often elaborate equipment and procedures. We devote the final pages of this section to the arcana of stellar photometry: the magnitude system, filter bandpasses, and colors.

In Section 1.2 we introduce our own Galaxy, the Milky Way, with its characteristic ‘flying saucer’ shape: a flat disk with a central bulge. In addition to their stars, our Galaxy and others contain gas and dust; we review the ways in which these make their presence known.

Stars travel around the Galaxy, and galaxies orbit within their groups and clusters, under the force of gravity. Stars are so much denser than the interstellar gas through which they move that neither gas pressure nor the forces from embedded magnetic fields can deflect them from their paths. If we know how mass is distributed, we can find the resulting gravitational force, and from this we can calculate how the positions and velocities of stars and galaxies will change over time.

But we can also use the stellar motions to tell us where the mass is. As we discovered in Chapter 2, much of the matter in the Milky Way cannot be seen directly. Its radiation may be absorbed, as happens for the visible light of stars in the dusty disk. Some material simply emits too weakly: dense clouds of cold gas do not show up easily in radio-telescope maps. The infamous dark matter still remains invisibly mysterious. But, since the orbits of stars take them through different regions of the galaxies they inhabit, their motions at the time we observe them have been affected by the gravitational fields through which they have travelled earlier. So we can use the equations for motion under gravity to infer from observed motions how mass is distributed in those parts of galaxies that we cannot see directly.

The Local Group contains roughly three dozen galaxies within a sphere about a megaparsec in radius, centred between the Milky Way and our nearest large neighbor, the Andromeda galaxy M31. Figure 4.1 shows the brighter members. The three most prominent are M31, the Milky Way, and M33; according to the classification of Section 1.3, these are all spiral galaxies. M31 is about 50% more luminous than the Milky Way, while M33 is only 20% as luminous. Between them, these three galaxies emit 90% of the visible light of the Local Group. The only elliptical galaxy is M32, a satellite to M31. The remaining systems are irregular galaxies, or the even less luminous dwarf irregulars, dwarf ellipticals, and dwarf spheroidals. Many of these smaller galaxies are in orbit either around the Milky Way or around M31.

Table 4.1 lists known and probable members of the Local Group within a megaparsec of the Sun. The apparent brightness of each member is generally known to within 10%, except for the Milky Way, where our location within the disk presents special problems. Distances to Local Group galaxies are derived by picking out individual stars, measuring their apparent brightness, and estimating their true luminosity, using methods such as the period–luminosity relation for Cepheid variables. In this way, distances to the ten or so brightest galaxies can be measured to within 10%.

Elliptical galaxies look like simple objects; but they are not. As their name implies, they appear round on the sky; the light is smoothly distributed, and they lack the bright clumps of young blue stars and patches of obscuring dust which are such obvious features of spiral galaxies. Ellipticals are almost devoid of cool gas, except at the very center; in contrast to S0 systems, they have no prominent disk. Their smooth appearance suggests that, like the molecules of air in a room, their stars have had time to reach a well-mixed equilibrium state. As with stars on the main sequence, we would expect the properties of elliptical galaxies to reflect the most probable state of a fairly simple system, with 'no surprises'.

Instead, detailed studies reveal a bewildering complexity. Elliptical galaxies cover a huge range of luminosity and of light concentration. Some ellipticals rotate fast, others hardly at all. Some appear to be oblate (grapefruit shaped), while others have a triaxial shape with three unequal axes, like a squashed (American or rugby) football. These properties are interlinked: luminous ellipticals are more likely to be triaxial, slowly rotating, and also strong X-ray sources, while the less luminous systems are oblate and relatively rapidly rotating, and have dense stellar cusps at their centers.

On learning that a new text on quantum field theory has appeared, one is surely tempted to respond with Isidor Rabi's famous comment about the muon: “Who ordered that?” After all, many excellent textbooks on quantum field theory are already available. I, for example, would not want to be without my well-worn copies of Quantum Field Theory by Lowell S. Brown (Cambridge 1994), Aspects of Symmetry by Sidney Coleman (Cambridge 1985), Introduction to Quantum Field Theory by Michael E. Peskin and Daniel V. Schroeder (Westview 1995), Field Theory: A Modern Primer by Pierre Ramond (Addison-Wesley 1990), Fields by Warren Siegel (arXiv.org 2005), The Quantum Theory of Fields, Volumes I, II, and III, by Steven Weinberg (Cambridge 1995), and Quantum Field Theory in a Nutshell by my colleague Tony Zee (Princeton 2003), to name just a few of the more recent texts. Nevertheless, despite the excellence of these and other books, I have never followed any of them very closely in my twenty years of on-and-off teaching of a year-long course in relativistic quantum field theory.

As discussed in the Preface for Students, this book is based on the notion that quantum field theory is most readily learned by starting with the simplest examples and working through their details in a logical fashion. To this end, I have tried to set things up at the very beginning to anticipate the eventual need for renormalization, and not be cavalier about how the fields are normalized and the parameters defined.