Analytical Mechanics and Field Theory (FYS500)

The course gives an introduction to classical mechanics and field theory, Lagrange and Hamilton formalism.

Introduction to variational calculus. Hamilton’s variational principle and the Lagrange formulation of mechanics. Symmetries and conservation laws. Applications, including motion in central fields, dynamics of rigid bodies, oscillations, and the Lagrangian formulation of special relativity. Hamilton’s formulation of mechanics.

Continuous systems and fields, the Lagrange and Hamilton formulations of mechanics of continuous systems. Conservation laws for fields, the energy-momentum tensor. Overview of important classical field theories, Maxwell’s electrodynamics as a relativistic field theory.

After completing the course, the student should:

K1: Have knowledge of the Lagrangian and Hamiltonian formulations of classical mechanics, and core applications of these formalisms.

K2: Have knowledge of classical field theory, including specific field theories that are important for our understanding of nature.

F1: Be able to apply the Lagrangian and Hamiltonian formalism to advanced mechanical systems, derive the equations of motion and solve them.

F2: Be able to apply the Lagrangian and Hamiltonian formalism to simple field theory models.

G1: Have an understanding of how the topics of the course fit into and connect different areas of physics, including Newtonian mechanics, electromagnetism, quantum mechanics and field theory applications.