Original sentence: In mathematical physics, a spectral triple (A, H, D) consists of an algebra A, a Hilbert space H and a Dirac operator D and defines a noncommutative space or geometry.That is, the metric is completely determined by the triple (C∞(M), L2(M, S), D).The central objects here are spectral triples (A, H, D), where A is a not necessarily commutative algebra; H a Hilbert space and D an unbounded selfadjoint operator, the Dirac operator.The choice of the Dirac operator D, however, is restricted by these requirements.The interaction between the algebra and the Dirac type operator reproduces the Poisson bracket of general relativity, formulated in terms of Ashtekar variables, and of Yang-Mills theory which can all be interpreted in terms of a non-perturbative quantum field theory.The triple is required to satisfy some interplay relations between A, H, D mimicking those of (C∞(M), L2(M, S), D)
Edited sentence: In mathematical physics, a spectral triple (A', H, D) consists of an algebra A, a Hilbert space H and a Dirac operator D and defines a noncommutative space or geometry.That is, the metric is completely determined by the triple (C∞(M), L2(M, S), D).The central objects here are spectral triples (A, H, D), where A is a not necessarily commutative algebra; H a Hilbert space and D an unbounded selfadjoint operator, the Dirac operator.The choice of the Dirac operator D'', however, is restricted by these requirements.The interaction between the algebra and the Dirac type operator reproduces the Poisson bracket of general relativity, formulated in terms of Ashtekar variables, and of Yang–Mills theory which can all be interpreted in terms of a non-perturbative quantum field theory.The triple is required to satisfy some interplay relations between A, H, D mimicking those of (C∞(M), L2(M, S), D)