A heuristic philosophical discourse on various applications of abstract differential geometry in quantum gravity research
DOI10.1007/S10773-024-05798-2MaRDI QIDQ6651667
Publication date: 10 December 2024
Published in: International Journal of Theoretical Physics (Search for Journal in Brave)
category theorysheaf cohomologyabstract differential geometrytopos theorysheaf theorycanonical quantisationbackground spacetime manifold independencegauge theory of the third kindgeometric prequantisationnatural philosophy of quantum gravity and quantum Yang-Mills gauge theoriesquantum gravity as a purely quantum gauge theorysheaf cohomological third quantisation of gravity and gauge theories
Foundations, quantum information and its processing, quantum axioms, and philosophy (81Pxx) Global differential geometry (53Cxx) General relativity (83Cxx)
Cites Work
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- On Utiyama's theme through ``\(\mathcal {A}\)-invariance
- Computing the Lagrangians of the standard model II. The ghost term
- \(u\)-singularity and \(t\)-topos theoretic entropy
- Obstacles on the way towards the quantisation of space, time and matter - and possible resolutions
- Quantising on a category
- A new approach to quantising space-time. I: Quantising on a general category
- Geometry and physics today
- Glafka-2004: categorical quantum gravity
- Quantum observables algebras and abstract differential geometry: the topos-theoretic dynamics of diagrams of commutative algebraic localizations
- Finitary topos for locally finite, causal and quantal vacuum Einstein gravity
- Second quantization, projective modules, and local gauge invariance
- Sheaves in geometry and logic: a first introduction to topos theory
- Abstract differential geometry, differential algebras of generalized functions, and de Rham cohomology
- Topos perspective on the Kochen-Specker theorem. I: Quantum states as generalized valuations
- Topos theory and consistent histories: The internal logic of the set of all consistent sets
- Forks in the road, on the way to quantum gravity
- Finitary, causal, and quantal vacuum Einstein gravity
- Quantization of discretized spacetimes and the correspondence principle
- Algebraic quantization of causal sets.
- Finitary spacetime sheaves
- Topos perspective on the Kochen-Specker theorem. III: Von Neumann algebras as the base category.
- A topos perspective on the Kochen-Specker theorem. II: Conceptual aspects and classical analogues
- Finitary Čech-de Rham cohomology
- On an axiomatic approach to geometric prequantization: a classification scheme à la Kostant-Souriau-Kirillov
- A dodecalogue of basic didactics from applications of abstract differential geometry to quantum gravity
- A new approach to quantising space-time. III: State vectors as functions on arrows
- Finitary-algebraic `resolution' of the inner Schwarzschild singularity
- What is a singularity in general relativity?
- `Third' quantization of vacuum Einstein gravity and free Yang-Mills theories
- Unsolved problems on mathematics for the 21st century. A tribute to Kiyoshi Iséki's 80th birthday
- Algebraic description of spacetime foam
- The tangled origins of the Leibnizian calculus. A case study of a mathematical revolution
- Differential Sheaves and Connections
- Quantised singularities in the electromagnetic field,
- The singularities of gravitational collapse and cosmology
- Emergent geometry, emergent forces
- Gauge fields on the quantum net
- Geometry of Principal Sheaves
- Local Characterization of Singularities in General Relativity
- The Large Scale Structure of Space-Time
- Space-time foam dense singularities and de Rham cohomology
- Finitary spacetime sheaves of quantum causal sets: curving quantum causality
- Electricity and gravitation.
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