The Spectral Action Principle
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We propose a new action principle to be associated with a noncommutative space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(\psi ,D\psi) + \Trace (\chi (D /$ $\Lb))$ where $\psi$ is a spinor on the Hilbert space, $\Lb$ is a scale and $\chi$ a positive function. When this principle is applied to the noncommutative space defined by the spectrum of the standard model one obtains the standard model action coupled to Einstein plus Weyl gravity. There are relations between the gauge coupling constants identical to those of $SU(5)$ as well as the Higgs self-coupling, to be taken at a fixed high energy scale.
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Cited by 3 Pith papers
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Canonical quantization of all minisuperspaces with consistent symmetry reductions
Canonical quantization of all consistent symmetry reductions of the Einstein-Hilbert Lagrangian, with solutions to the Wheeler-DeWitt equation both with and without imposed conformal symmetries.
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Canonical quantization of all minisuperspaces with consistent symmetry reductions
All minisuperspaces from symmetry reductions of the Einstein-Hilbert Lagrangian that obey the principle of symmetric criticality are canonically quantized and their Wheeler-DeWitt equations are solved.
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Noncommutative Gauge Theories and Gravity
The paper reviews gauge-theoretic formulations of gravity in ordinary and noncommutative spaces based on the authors' earlier works.
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