2018/03/01 by Hans Christian Öttinger
Computer Science · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #BRST quantization #Canonical quantization #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Covariant Hamiltonian field theory #Creation and annihilation operators #Fock space #Gauge theory #Hamiltonian (control theory) #Hamiltonian system #Invariant (physics) #Mathematical physics #Mathematics #Physics #Quantization (signal processing) #Quantum #Quantum Information and Cryptography #Quantum gravity #Quantum mechanics #Second quantization #hep-th
paper · pdf · doi:10.1103/physrevd.97.074006
published as Phys. Rev. D 97, 074006 (2018) · 13 pages, 1 figure
arxiv created 2018/03/01 · openalex created_date 2018/03/29 · openalex publication_date 2018/04/03 · arxiv updated 2018/04/11 · openalex updated_date 2026/08/05
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.