# Unsharp Values, Domains and Topoi

@article{Doering2012UnsharpVD, title={Unsharp Values, Domains and Topoi}, author={A. Doering and Rui Soares Barbosa}, journal={arXiv: Quantum Physics}, year={2012}, pages={65-96} }

The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics. There is a state object \(\underline\sum\), analogous to the state space of a classical system, and a quantity-value object \(\underline{\mathbb{R}^{\leftrightarrow}}\), generalising the real numbers. Physical quantities are maps from the state object to the quantity-value object – hence the ‘values’ of physical quantities… Expand

#### 17 Citations

Sheaf-theoretic methods in quantum mechanics and quantum information theory

- Mathematics, Physics
- 2015

In this thesis we use the language of sheaf theory in an attempt to develop a deeper understanding of some of the fundamental differences - such as entanglement, contextuality and non-locality -… Expand

The regular histories formulation of quantum theory

- Mathematics, Computer Science
- 2012

It can be argued that RH compares favourably with other proposed interpretations of quantum mechanics in that it resolves the measurement problem while retaining an essentially classical worldview without parallel universes, a framework-dependent reality or action-at-a-distance. Expand

Fibred contextual quantum physics

- Computer Science, Mathematics
- 2014

A contextual quantum mechanics via the geometric mathematics to propose a quantum contextuality adaptable in every topos, corresponding to the belief that the quantum world must only be seen from the classical viewpoints a la Bohr. Expand

Group action in topos quantum physics

- Mathematics, Physics
- 2011

Topos theory has been suggested first by Isham and Butterfield, and then by Isham and Doring, as an alternative mathematical structure within which to formulate physical theories. In particular, it… Expand

The Logos Categorical Approach to Quantum Mechanics: I. Kochen-Specker Contextuality and Global Intensive Valuations

- Computer Science, Physics
- 2018

The logos categorical approach to QM attempts to consider the main features of the quantum formalism as the standpoint to develop a conceptual representation that explains what the theory is really talking about —rather than as problems that need to be bypassed to allow a restoration of a classical “common sense” understanding of what there is. Expand

A Second Course in Topos Quantum Theory

- Mathematics
- 2018

Logic of Propositions in Topos Quantum Theory -- Developments on Self Adjoint Operators in Topos Quantum Theory -- Physical quantities interpreted as modal operators -- Group action in Topos Quantum… Expand

Topos Analogues of the KMS State

- Mathematics, Physics
- 2012

We identify the analogues of KMS state in topos theory. Topos KMS states can be viewed as classes of truth objects associated with a measure \mu^\rho (in one-to-one correspondence with an original… Expand

Some Remarks on the Logic of Quantum Gravity

- Physics, Mathematics
- 2013

We discuss some conceptual issues that any approach to quantum gravity has to confront. In particular, it is argued that one has to find a theory that can be interpreted in a realist manner, because… Expand

Flows on Generalised Gelfand Spectra of Nonabelian Unital C*-Algebras and Time Evolution of Quantum Systems

- Mathematics, Physics
- 2012

In arXiv:1212.2613, we associated a presheaf \Sigma^A with each unital C*-algebra A. The spectral presheaf \Sigma^A generalises the Gelfand spectrum of an abelian unital C*-algebra. In the present… Expand

Spectral presheaves as quantum state spaces

- Physics, Medicine
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2015

It is explained how the structure of the spectral presheaf geometrically mirrors the double role played by self-adjoint operators in quantum theory, as quantum random variables and as generators of time evolution. Expand

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