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The Quantum Commutator of a Perfect Fluid

General Relativity and Quantum Cosmology 2011-04-04 v1 High Energy Physics - Theory Quantum Algebra Fluid Dynamics

Abstract

A perfect fluid is quantized by the canonical method. The constraints are found and this allows the Dirac brackets to be calculated. Replacing the Dirac brackets with quantum commutators formally quantizes the system. There is a momentum operator in the denominator of some coordinate quantum commutators. It is shown that it is possible to multiply throughout by this momentum operator. Factor ordering differences can result in a viscosity term. The resulting quantum commutator algebra is \vspace{1.0truein} \bcv4(v3v2v2v3)=i,v_{4}(v_{3}v_{2}-v_{2}v_{3})=-i,\ec \bcv4(v1v3v3v1)=iv3,v_{4}(v_{1}v_{3}-v_{3}v_{1})=-iv_{3},\ec \bcv4v1v1v4=i,v_{4}v_{1}-v_{1}v_{4}=-i,\ec \bcv5v2v2v5=iv_{5}v_{2}-v_{2}v_{5}=-i.\ec

Keywords

Cite

@article{arxiv.gr-qc/9810089,
  title  = {The Quantum Commutator of a Perfect Fluid},
  author = {Mark D. Roberts},
  journal= {arXiv preprint arXiv:gr-qc/9810089},
  year   = {2011}
}

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10 pages