Primer of Field Theory
The purpose of this chapter is to present a very concise introduction to the basic concepts and terminology of field theory which will be encountered in the rest of the book. We shall begin in §1.1 with a discussion of classical mechanics in view of a variational formulation and then consider the Schrödinger equation in quantum mechanics. In §1.2 we present special relativity and relativistic wave equations. In particular, we derive the Maxwell equations for electromagnetism. In §1.3 we study the role of continuous symmetry in field theory and prove Noether’s theorem. In particular, we consolidate the notion of energy and momenta and introduce the concept of conserved charges and currents. In §1.4 we present the Abelian gauge field theory and related concepts such as symmetry-breaking and the Higgs mechanism. In §1.5 we discuss in general the non-Abelian gauge field theory. In §1.6 we establish Einstein’s equations of gravitation and discuss some simplest consequences in cosmology.
KeywordsMaxwell Equation Gauge Field Lagrangian Density Gauge Field Theory Goldstone Particle
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