Gauged Gravity via Spectral Asymptotics of non-Laplace type Operators

Abstract

We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms and the gauge transformations and can be used to induce a new theory of gravitation. It can be viewed as a matrix generalization of Einstein general relativity that reproduces the standard Einstein theory in the weak deformation limit. Relations with various mathematical constructions such as Finsler geometry and Hodge-de Rham theory are discussed.

arXiv commentVersion accepted by J. High Energy Phys. Introduction and Discussion significantly expanded. References added and updated. (41 pages, LaTeX: JHEP3 class, no figures)

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• Determination of isometric real-analytic metric and spectral invariants for elastic Dirichlet-to-Neumann map on Riemannian manifolds
• Heat coefficient $a_4$ for nonminimal Laplace type operators
• Kinematics in Matrix Gravity
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• Dirac Operator in Matrix Geometry
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• Non-commutative Corrections in Spectral Matrix Gravity
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• MOND via Matrix Gravity
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• Consistent Massive Colored Gravitons
• Operator-Valued Tensors on Manifolds: A Framework for Field Quantization
• Non-Perturbative Aspects of Quantum Electrodynamics on Curved Space and Investigations in Matrix Gravity