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Full-Text Articles in Physics
Introduction To Classical Field Theory, Charles G. Torre
Introduction To Classical Field Theory, Charles G. Torre
All Complete Monographs
This is an introduction to classical field theory. Topics treated include: Klein-Gordon field, electromagnetic field, scalar electrodynamics, Dirac field, Yang-Mills field, gravitational field, Noether theorems relating symmetries and conservation laws, spontaneous symmetry breaking, Lagrangian and Hamiltonian formalisms.
Understanding Noether’S Theorem By Visualizing The Lagrangian, Seth Moser
Understanding Noether’S Theorem By Visualizing The Lagrangian, Seth Moser
Physics Capstone Projects
By approaching Lagrangian mechanics from a graphical perspective the implications of Noether’s Theorem can be made easier to understand. Plotting the Lagrangian for classical single particle systems for one coordinate onto a position-velocity phase space along with the corresponding equations of motion can demonstrate how a system is invariant under continuous transforms in that coordinate. This invariance can be shown to be associated with a quantity in the system that’s conserved via Noether’s Theorem. The relationship between the symmetry of the system and conserved quantities can then be extended to fields. Invariance in this case is extended to include invariance …
Symmetric Criticality In Classical Field Theory, Charles G. Torre, Ian M. Anderson
Symmetric Criticality In Classical Field Theory, Charles G. Torre, Ian M. Anderson
All Physics Faculty Publications
This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais’ Principle of Symmetric Criticality. After providing a little history, I describe necessary and sufficient conditions on a group action such that reduction of a group-invariant Lagrangian by the symmetry group yields the correct symmetry-reduced Euler-Lagrange equations.