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arXiv · 1803.00383

BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space

Hans Christian Öttinger
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Abstract

We develop the basic ideas and equations for the BRST quantization of Yang-Mills theories in an explicit Hamiltonian approach, without any reference to the Lagrangian approach at any stage of the development. We present a new representation of ghost fields that combines desirable self-adjointness properties with canonical anticommutation relations for ghost creation and annihilation operators, thus enabling us to characterize the physical states on a well-defined Fock space. The Hamiltonian is constructed by piecing together simple BRST invariant operators to obtain a minimal invariant extension of the free theory. It is verified that the evolution equations implied by the resulting minimal Hamiltonian provide a quantum version of the classical Yang-Mills equations. The modifications and requirements for the inclusion of matter are discussed in detail.

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Hans Christian Öttinger. 2018-03-01. BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on Fock space. https://doi.org/10.1103/physrevd.97.074006

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