Synopsis for Astronomy 734 "Field Theory for Astronomers" In this 700 level course I will give an elementary introduction to field theory for astronomers. Spontaneous symmetry breaking with a massive scalar field (the Higgs field) provides the foundation for the modern theories of the electromagnetic and weak interactions. Once released from the bottle, the genie of the scalar field has been widely embraced by cosmologists; the `inflaton' is invoked to drive inflation, candidates for the dark matter include the `axion' and related particles, while the existence for the unexpected acceleration of the Universe at late times has led theorists to proposed yet more fields with fanciful names like `quintessence'. In this course, I will focus mainly on bosonic fields. These include all of the cosmologically relevant fields, and also the electromagnetic field. The approach I will take will be to analyze in some detail a very simple mechanical model composed of beads, rods and springs (the BRS model) that turns out to be mathematically equivalent to the fully relativistic scalar field. The advantage of this approach is that the model can be very simply visualized, and understood (the course will make use of animations to illustrate the physics) and yet all of its properties carry over to the physically more abstract fields invoked my cosmologists. The outline for the course is as follows: 1) Quick review of the most elementary concepts of Lagrangian dynamics. The action and the Lagrangian --- the principle of least action --- energy and momentum conservation. (Ch 2) 1.1) Review of properties of dispersive waves (appendix D) 2) The BRS model --- discrete model --- continuum limit --- covariance of the BRS model. (Ch 15-16) 3) Conservation laws. Conservation of wave-momentum --- energy and momentum in the BRS model --- wave-momentum paradoxes --- conservation of `charge' --- conservation of particle number. (Ch 16) 4) Interacting fields. Simple models for interactions between fields --- resonance conditions. (Ch 16) 5) The ideal fluid limit of classical wave-mechanics --- the stress energy tensor and its evolution --- the limits of classical field theory. (Ch 16) 6) Quantum mechanics of fields. The simple harmonic oscillator --- the Heisenberg, Schroedinger and `interaction' pictures --- the S-matrix --- free fields --- interactions --- scattering --- self interactions --- Feynman rules --- kinematic constraints. (Ch 17) 7) Relativistic field theory. The Klein-Gordon field --- quantum electrodynamics --- connection to kinetic theory and nucleosynthesis. (Ch 18) 8) Scalar fields in cosmology. The scalar field in an expanding universe --- non-relativistic scalar fields --- chaotic inflation --- fluctuations from inflation --- self-ordering fields (monopoles, domain walls, cosmic string, texture). (Ch 18, 29, 32) After taking this course, the student will be able to read intelligently any of the many hundreds of cosmology papers each year that invoke hypothetical fields (the generally accepted rule is that you are only allowed to invoke the `tooth fairy' once --- per paper!) and will be able to hold forth with confidence on cosmology and field theory at cocktail parties ;-) More seriously, the course is also intended to give the student a very basic grounding in the current understanding of `the way the world works', including what aspects of the world are fundamentally classical and which require quantum mechanics? what does momentum conservation mean when applied to waves? and last, but not least, what is a photon anyway? Much of the material for the course can be found in chapters 2, 15, 16, 17, 18 29 and 32 of my ``Elements of Astrophysics''. This is available at http://www.ifa.hawaii.edu/~kaiser/lectures/elements.pdf .