String Theory Demystified

CHAPTER 6
BRST Quantization
So far we have seen two methods that can be utilized to quantize the string: the
covariant approach and light-cone quantization. Each offers its advantages.
Covariant quantization makes Lorentz invariance manifest but allows for the
existence of “ghost states” (states with negative norm) in the theory. In contrast,
light-cone quantization is ghost free. However, Lorentz invariance is no longer
obvious. Another trade-off is that the proof of the number of space-time dimensions
(D = 26 for the bosonic theory) is rather diffi cult in covariant quantization, but it’s
rather straightforward in light-cone quantization. Finally identifying the physical
states is easier in the light-cone approach.
Another method of quantization, that in some ways is a more advanced approach,
is called BRST quantization. This approach takes a middle ground between the two
methods outlined above. BRST quantization is manifestly Lorentz invariant, but
includes ghost states in the theory. Despite this, BRST quantization makes it easier
to identify the physical states of the theory and to extract the number of space-time
dimensions relatively easily.
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