Category Archives: Lecture Notes

Today we introduced spinors in various dimensions D=p+q. In particular, starting from the basic Dirac matrix algebra anticommutation relations, we derived the fact that Dirac spinors in D dimensions have dimensionality 2[D/2].

Today we restarted our discussion of the superstring, and built the state space using Ramond and Neveu-Schwarz fermions.

This time we discuss construction of the closed bosonic string state space; supersymmetric string theory.

This lecture covers the physics of how the critical dimension and zero-point mass shift come about.  Here are my notes from today’s lecture.

Ahhhh, open string quantization, at last! In light-front gauge, that is. Next time, we prove closure of the Lorentz algebra if the critical dimension is given by (d-2)=24 and the mass-squared shift is -1 (in appropriate units).

Today’s chapter of Zwiebach, Ch.11, discusses [first] quantization for the relativistic point particle (with geometric action) in light front gauge. LF gauge leads to a number of simplifications. We also construct the Poincare symmetry generators as a prelude to open … Continue reading →

Here are the lecture notes for quantization of fields of spin s=0,1,2 in LF gauge. The relevant chapter of Zwiebach is Chapter 10, which runs through light-front quantization of fields carrying intrinsic spin s=0,1,2.

Focus for today: the light front gauge: light-front (LF) coordinates X^+, X^- ; noncovariant physical gauges, such as LF gauge, for handling string worldsheet reparametrization invariance; consequences for string equations of motion, boundary conditions, conserved momenta, and constraints; open string … Continue reading →

This lecture, on Worldsheet symmetry currents and conserved quantum numbers, is related to Chapter Eight of Zwiebach. Here are my lecture notes