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Primer of Field Theory

  • Yisong Yang
Part of the Springer Monographs in Mathematics book series (SMM)

Abstract

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.

Keywords

Maxwell Equation Gauge Field Lagrangian Density Gauge Field Theory Goldstone Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Yisong Yang
    • 1
  1. 1.Department of Applied Mathematics and PhysicsPolytechnic UniversityBrooklynUSA

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