Related papers: Topos Analogues of the KMS State
It is known that fuzzy set theory can be viewed as taking place within a topos. There are several equivalent ways to construct this topos, one is as the topos of \'{e}tal\'{e} spaces over the topological space $Y=[0,1)$ with lower topology.…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
Matrix product states (MPS) provide a powerful framework for characterizing one-dimensional symmetry-protected topological (SPT) phases of matter and for formulating Lieb-Schultz-Mattis (LSM)-type constraints. Here we generalize the MPS…
We describe correlations functions of topological quantum mechanics (TQM) in terms of Morse theory. We review the basics of topological field theories and discuss geometric and algebraic interpretations of TQM. We prove that correlators in…
This paper is the third in a series whose goal is to develop a fundamentally new way of viewing theories of physics. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a…
Here we show how the Minimally Entangled States (MES) of a 2d system with topological order can be identified using the geometric measure of entanglement. We show this by minimizing this measure for the doubled semion, doubled Fibonacci and…
We extend the theory of perturbations of KMS states to a class of unbounded perturbations using noncommutative $L_p$-spaces. We also prove certain stability of the domain of the Modular Operator associated with a ||.||p-continuous state.…
We study topological group theoretic properties of algebraic groups over local fields. In particular, we find conditions under which such groups have closed images under arbitrary continuous homomorphisms into arbitrary topological groups.
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
We study the topological structure of the automorphism groups of compact quantum groups showing that, in parallel to a classical result due to Iwasawa, the connected component of identity of the automorphism group and of the "inner"…
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…
Within the framework of relativistic quantum field theory, a novel method is established which allows to distinguish non-equilibrium states admitting locally a thermodynamic interpretation. The basic idea is to compare these states with…
We classify local unitary equivalence classes of symmetric states via a classification of their local unitary stabilizer subgroups. For states whose local unitary stabilizer groups have a positive number of continuous degrees of freedom,…
We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced.…
Quantum theory has the property of "local tomography": the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We…
We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are…
This paper provides a new categorical definition of a normalization operator motivated by topos theory and its applications to algebraic language theory. We first define a normalization operator $\Xi \to \Xi$ in any category that admits a…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
We construct a space of quantum states and an algebra of quantum observables, over the set of all metrics of arbitrary but fixed signature, defined on a manifold. The construction is diffeomorphism invariant, and unique up to natural…
The state of a knot is defined in the realm of Chern-Simons topological quantum field theory as a holomorphic section on the SU(2) character manifold of the peripheral torus. We compute the asymptotics of the torus knot states in terms of…