Causal sites as quantum geometry

Abstract

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural "tangent 2-bundle," analogous to the tangent bundle of a smooth manifold. Examples with reasonable finiteness conditions have an intrinsic geometry, which can approximate classical solutions to general relativity. We propose an approach to quantization of causal sites as well.

21 pages, 3 eps figures; v2: added references; to appear in JMP

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Cited by in corpus (19)

• Quantum field theory without divergences
• Continuous Wavelet Transform in Quantum Field Theory
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• A New Causal Topology and Why the Universe is Co-compact
• Bibliography of Publications related to Classical Self-dual variables and Loop Quantum Gravity
• Knot theory and a physical state of quantum gravity
• Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity
• `Iconoclastic', Categorical Quantum Gravity
• Wavelet regularization of gauge theories
• An abstract theory of physical measurements
• Multiresolution quantum field theory in light-front coordinates
• Wavelet regularization of Euclidean QED
• Sheaf Logic, Quantum Set Theory and the Interpretation of Quantum Mechanics
• Transition probability spaces in loop quantum gravity
• Non-commutative fermion mass matrix and gravity
• Quantum kinetic equation before and after Big Bang
• Ordered Locales
• The Framework, Causal and Co-compact Structure of Space-time
• The Expressional Limits of Formal Languages in the Notion of Observation