Fritjof Persson: BRST quantization and the (re)formulation of the No-ghost theorem

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Fritjof Persson


BRST quantization and the (re)formulation of the No-ghost theorem


Symmetries of a classical physical system should still be present post quantization. BRST quantization does this by extending the original physical system, turning it into a graded differential complex, in which the physical state space is identified with the 0:th order cohomology class. This does however unavoidably require an indefinite inner product, contradicting the probabilistic interpretation of the amplitudes in quantum theory. The No-ghost theorem ensures that the inner product is positive definite on the physical state space, a theorem typically only proved on a case-by-case basis.

We begin by presenting the general idea of the BRST method, why preserves our symmetries. Then we present the generic structure of a BRST complex in which we reformulate the No-ghost theorem into a form suitable for proving it. 


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