Henry Li, Department of Pure Mathematics, University of Waterloo
“BRST Quantization”
With the tools of conformal field theory, we can now construct the state space of a bosonic string in a fairly rigorous manner. However, not all the states will be physical states, which must be annihilated by the Virasoro algebra. Fortunately, there is a simple criterion for a state to be physical: we shall construct an operator, called the BRST charge, such that its cohomology is precisely the physical state space. This operator lives within a larger framework, called BRST quantization, for systematically constructing the physical state spaces of a large class of gauge theories with constraints. We briefly discuss the relationship between BRST and symplectic reduction, and then apply it to the bosonic string. After all that work, we shall see the no-ghost theorem, which allows us to avoid using the heavy machinery of BRST in practice.
MC 5479
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