Symmetry, Conservation and Noether's Theorem
Abstract
Of utmost importance in studying a physical system is
knowing which physical quantities are conserved, that
is, remain constant over time. These quantities might
be energy, linear or angular momentum, charge, or other,
sometimes less usual, observables, and knowing that such
a quantity is conserved can give a wealth of knowledge
about the system under consideration. A main result of
theoretical physics that makes considerable headway in
solving this problem is Noether's Theorem, which states
that if a system has a particular symmetry, there is a
quantity associated with that symmetry that is conserved.
In both classical and quantum physics, Noether's Theorem
proves to be very powerful because the symmetries of a
system are relatively easy to find given the system's
Lagrangian. It is also an elegant and beautiful result,
an example of the effectiveness of using mathematics to
solve physical problems.
Table of Contents
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