Lectures in this Course
The laws of physics are the same in any inertial reference frame.
The Lorentz transformation is the transformation between two inertial frames.
Galilean transformation is appropriate for small velocities.
Proper time is the time an observer measures... [more]
Review Lagrangian techniques in Classical Mechanics.
Coordinates describe the state of a system, position, momentum.
Fields exist throughout space-time.
Example: point masses connected by springs.
The Action integral and the... [more]
Laws take the same form in every reference frame.
Define the infinitesimal distance between two points.
Contravariant, covariant vectors, invariant inner product.
Examples of fields in Nature.
The four-dimensional... [more]
Define the Action integral in four dimensional space-time.
Kinetic and potential energy appear in the Lagrangian.
Symmetries and Conservation Laws
Time invariance implies energy conservation.
Define the canonical momentum.
Invariance under a space... [more]
Two ideas of momentum: Mechanical and canonical.
Conservation of momentum and energy in field theory.
Interaction of fields and particles, mechanical momentum vs. canonical momentum.
Invariance under a phase transformation implies conserved... [more]
The conservation of charge relates to the mathematical statement of a vanishing divergence of the charge current. Study an example: the conservation of charge for a complex wave function. Conservation of charge can be derived using the... [more]
Phase transformation of a complex wave function.
The electromagnetic vector potential appears in the covariant derivative.
The Action for the relativistic wave equation is invariant under a phase (gauge) transformation.
A global gauge transformation has the same phase shift everywhere whereas a local gauge transformation has a phase shift as a function of location.
Benjamin Franklin fixed the convention for positive and negative charge and the direction of current... [more]