Spring, 2008
In 1905, while only twenty-six years old, Albert Einstein published "On the Electrodynamics of Moving Bodies" and effectively extended classical laws of relativity to all laws of physics, even electrodynamics. In this course, we will take a close look at the special theory of relativity and also at classical field theory. Concepts addressed here will include space-time and four-dimensional space-time, electromagnetic fields and and Maxwell’s equations. We will also encounter the work of the German mathematician Hermann Minkowski. (Image credit: KIPAC at Stanford University)
Lectures in this Course
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1
Inertial reference frames
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] -
2
Principle of least action
Review Lagrangian techniques in Classical Mechanics. Coordinates describe the state of a system, position, momentum. Euler's equations. Fields exist throughout space-time. Example: point masses connected by springs. The Action integral and the... [more] -
3
Invariance of the laws of nature
Laws take the same form in every reference frame. Define the infinitesimal distance between two points. Contravariant, covariant vectors, invariant inner product. Summation convention. Examples of fields in Nature. The four-dimensional... [more] -
4
Lagrangian mechanics
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] -
5
Conservation of charge and momentum
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] -
6
Relativistic wave equation and conservation laws
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] -
7
Invariance under gauge transformations
Gauge theory. 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. The... [more] -
8
Gauge theory
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]