Related papers: Narratability and Cluster Decomposition
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
Unlike mathematics, in which the notion of truth might be abstract, in physics, the emphasis must be placed on algorithmic procedures for obtaining numerical results subject to the experimental verifiability. For, a physical science is…
We investigate whether commutativity is necessary to represent relativistic locality for localization observables of relativistic quantum systems in Minkowski spacetime. A well known no-go theorem by Halvorson and Clifton shows that…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
Arbitrary quantum states cannot be copied. In fact, to make a copy we must provide complete information about the system. However, can a quantum system self-replicate? This is not answered by the no-cloning theorem. In the classical…
A theory $T$ is said to be relatively decidable if for every model of $T$, one can compute the elementary diagram of that model from its atomic diagram together with $T$. We verify a conjecture of Chubb, Miller, and Solomon by showing that…
The Kochen--Specker (KS) theorem reveals the nonclassicality of single quantum systems. In contrast, Bell's theorem and entanglement concern the nonclassicality of composite quantum systems. Accordingly, unlike incompatibility, entanglement…
We analyze the unitarity of a non-relativistic non-commutative scalar field theory. We show that electric backgrounds spoil unitarity while magnetic ones do not. Furthermore, unlike its relativistic counterparts, unitarity can not be…
This paper examines whether unitary evolution alone is sufficient to explain emergence of the classical world from the perspective of computability theory. Specifically, it looks at the problem of how the choice related to the measurement…
There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decomposition. We use this decomposition to construct unitary irreducible representations. All multiple meson states can be retrieved this way.…
The problem of obtaining a realistic, relativistic description of a quantum system is discussed in the context of a simple (light-cone) lattice field theory. A natural stochastic model is proposed which, although non-local, is relativistic…
Exact solutions of two-particle relativistic equations of quantum field theory describing the scattering $s$-states and the bound $s$-states are found in the cases of delta-shell potential and superposition of delta-shell potentials. Some…
The constraints implied by analyticity in two-dimensional factorised S-matrix theories are reviewed. Whenever the theory is not time-reversal invariant, it is argued that the familiar condition of `Real analyticity' for the S-matrix…
In this paper, we introduce and study the quantum deformations of the cluster superalgebra. Then we prove the quantum version of the Laurent phenomenon for the super-case.
Quantum cluster theories are a set of approaches for the theory of correlated and disordered lattice systems, which treat correlations within the cluster explicitly, and correlations at longer length scales either perturbatively or within a…
I make the case that the Universe according to unitary (no-collapse) quantum theory has a branching structure, and so can literally be regarded as a "many-worlds" theory. These worlds are not part of the fundamental ontology of quantum…
Many physicists limit oneself to an instrumentalist description of quantum phenomena and ignore the problems of foundation and interpretation of quantum mechanics. This instrumentalist approach results to "specialization barbarism" and mass…
A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large…
We argue that a non-perturbative description of quantum gravity should involve two (non-interacting) copies of a dual field theory on the boundary, and describe the states of the spacetimes accordingly. So, for instance, a complete…
I introduce a framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others. From two simple assumptions, a tensor product rule for combining separate systems can be…