347 research outputs found
Modular Theory, Non-Commutative Geometry and Quantum Gravity
This paper contains the first written exposition of some ideas (announced in
a previous survey) on an approach to quantum gravity based on Tomita-Takesaki
modular theory and A. Connes non-commutative geometry aiming at the
reconstruction of spectral geometries from an operational formalism of states
and categories of observables in a covariant theory. Care has been taken to
provide a coverage of the relevant background on modular theory, its
applications in non-commutative geometry and physics and to the detailed
discussion of the main foundational issues raised by the proposal.Comment: Special Issue "Noncommutative Spaces and Fields
A mathematical formalism for the Kondo effect in WZW branes
In this paper, we show how to adapt our rigorous mathematical formalism for
closed/open conformal field theory so that it captures the known physical
theory of branes in the WZW model. This includes a mathematically precise
approach to the Kondo effect, which is an example of evolution of one
conformally invariant boundary condition into another through boundary
conditions which can break conformal invariance, and a proposed mathematical
statement of the Kondo effect conjecture. We also review some of the known
physical results on WZW boundary conditions from a mathematical perspective.Comment: Added explanations of the settings and main result
Adversus singularitates: The ontology of space-time singularities
I argue that there are no physical singularities in space-time. Singular
space-time models do not belong to the ontology of the world, because of a
simple reason: they are concepts, defective solutions of Einstein's field
equations. I discuss the actual implication of the so-called singularity
theorems. In remarking the confusion and fog that emerge from the reification
of singularities I hope to contribute to a better understanding of the
possibilities and limits of the theory of General Relativity.Comment: 13 pages, accepted for publication in Foundations of Scienc
The ontology of General Relativity
I discuss the ontological assumptions and implications of General Relativity. I maintain
that General Relativity is a theory about gravitational fields, not about space-time. The latter is
a more basic ontological category, that emerges from physical relations among all existents. I
also argue that there are no physical singularities in space-time. Singular space-time models do
not belong to the ontology of the world: they are not things but concepts, i.e. defective solutions
of Einstein’s field equations. I briefly discuss the actual implication of the so-called singularity
theorems in General Relativity and some problems related to ontological assumptions of Quantum
Gravity
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