相关论文: Some Possible Roles for Topos Theory in Quantum Th…

Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…

This is an introduction to the group field theory approach to quantum gravity, with emphasis on motivations and basic formalism, more than on recent results; we elaborate on the various ingredients, both conceptual and formal, of the…

It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…

This thesis develops the theory of effectuses as a categorical axiomatic approach to quantum theory. It provides a comprehensive introduction to effectus theory and reveals its connections with various other topics and approaches.

These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…

Since the quantum field theory treats a system of particles, there must be a distribution which is associated with the system of particles. It means that a meaningful quantity is adjoined in the system of particles. It seems that these…

I give a review of the conceptual issues that arise in theories of quantum cosmology. I start by emphasising some features of ordinary quantum theory that also play a crucial role in understanding quantum cosmology. I then give motivations…

The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In…

This thesis discusses the topological aspects of quantum gravity, focusing on the connection between 2D quantum gravity and 2D topological gravity. The mathematical background for the discussion is presented in the first two chapters. The…

Loop quantum gravity is a mature theory. To proceed to explicit calculations in cosmology, it is necessary to make assumptions and simplifications based on the symmetries of the cosmological setting. Symmetry reduction is especially…

I would claim that we do not have a suitably general definition of what a topological phase is, or more importantly, any robust understanding of how to enter one even in the world of mathematical models. The latter is, of course, the more…

We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with…

I briefly summarized some recent work which uses the techniques of effective field theory to make quantum predictions in general relativity. In contrast to conventional expectations, these are in fact well behaved. The leading quantum…

In mathematical applications, category theory remains a contentious issue, with enthusiastic fans and a skeptical majority. In a muted form this split applies to the authors of this note. When we learned that the only mathematically sound…

Topoi are categories which have enough structure to interpret higher order logic. They admit two notions of morphism: logical morphisms which preserve all of the structure and therefore the interpretation of higher order logic, and…

Quantum theory is a probabilistic theory with fixed causal structure. General relativity is a deterministic theory but where the causal structure is dynamic. It is reasonable to expect that quantum gravity will be a probabilistic theory…

We briefly discuss the current state, and future computational implications, of quantum type theory.

This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.

We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…

Although general relativity is a predictively successful theory, it treats matter as classical rather than as quantum. For this reason, it will have to be replaced by a more fundamental quantum theory of gravity. Attempts to formulate a…