#anticommutator

PHY2403H Quantum Field Theory. Lecture 20: Dirac Lagrangian, spinor solutions to the KG equation, Dirac matrices, plane wave solution, helicity. Taught by Prof. Erich Poppitz

[Here is another PDF only post, containing my notes for Lecture 20 of the UofT QFT I (quantum field theory) course.]

In this lecture Professor Poppitz derived a rest frame solution of the Dirac equation, then demonstrated that the generalization to non-zero momentum satisfied the equation. We also saw that Dirac spinor solutions of the Dirac equation are KG equation solutions, and touched on the…

The many faces of Maxwell’s equations

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The following is a possible introduction for a report for a UofT ECE2500 project associated with writing a small book: “Geometric Algebra for Electrical Engineers”. Given the space constraints for the report I may have to drop much of this, but some of the history of Maxwell’s equations may be…

A derivation of the quaternion Maxwell’s equations using geometric algebra.

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Motivation.

The quaternion form of Maxwell’s equations as stated in [2] is nearly indecipherable. The modern quaternionic form of these equations can be found in [1]. Looking for this representation was driven by the question of whether or not the compact geometric algebra representations of Maxwell’s equations \( \grad F = J \), was…

Can anticommuting operators have a simulaneous eigenket?

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Question: Can anticommuting operators have a simulaneous eigenket? ([1] pr. 1.16)

Two Hermitian operators anticommute

\begin{equation}\label{eqn:anticommutingOperatorWithSimulaneousEigenket:20} \symmetric{A}{B} = A B + B A = 0. \end{equation}

Is it possible to have a simultaneous eigenket of \( A \) and \( B \)? Prove or illustrate your…