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Discrete Quantum Causal Dynamics
 International Journal of Theoretical Physics
, 2003
"... We give a mathematical framework to describe the evolution of an open quantum systems subjected to nitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently but may also interact. This evolut ..."
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We give a mathematical framework to describe the evolution of an open quantum systems subjected to nitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems which evolve independently but may also interact. This evolution, driven both by unitary operators and measurements, is coded in a precise mathematical structure in such a way that the crucial properties of causality, covariance and entanglement are faithfully represented. We show how our framework may be expressed using the language of (poly)categories and functors. Remarkably, important physical consequences  such as covariance  follow directly from the functoriality of our axioms. We establish strong links between the physical picture we propose and linear logic. Specifically we show that the rened logical connectives of linear logic can be used to describe the entanglements of subsystems in a precise way. Furthermore, we show that there is a precise correspondence between the evolution of a given system and deductions in a certain formal logical system based on the rules of linear logic. This framework generalizes and enriches both causal posets and the histories approach to quantum mechanics. 1
Decoherent histories on graphs
, 2002
"... The consistent histories approach to quantum mechanics is traditionally based on linearly ordered sequences of events. We extend the histories formalism to sets of events whose causal ordering is described by directed acyclic graphs. The need for a global time is eliminated and our construction re ..."
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The consistent histories approach to quantum mechanics is traditionally based on linearly ordered sequences of events. We extend the histories formalism to sets of events whose causal ordering is described by directed acyclic graphs. The need for a global time is eliminated and our construction reflects the causal structure faithfully.
Sheafifying Consistent Histories
, 2001
"... Isham’s topostheoretic perspective on the logic of the consistenthistories theory [34] is extended in two ways. First, the presheaves of consistent sets of history propositions in their corresponding topos originally proposed in [34] are endowed with a Vietoristype of topology and subsequently the ..."
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Isham’s topostheoretic perspective on the logic of the consistenthistories theory [34] is extended in two ways. First, the presheaves of consistent sets of history propositions in their corresponding topos originally proposed in [34] are endowed with a Vietoristype of topology and subsequently they are sheafified with respect to it. The category resulting from this sheafification procedure is the topos of sheaves of sets varying continuously over the Vietoristopologized base poset category of Boolean subalgebras of the universal orthoalgebra UP of quantum history propositions. The second extension of the topos in [34] consists in endowing the stalks of the aforementioned sheaves, which were originally inhabited by structureless sets, with further algebraic structure
Journal of Space Mixing 1 ( 2003) 117. Founding Principles of Space Mixing Theory
, 2003
"... Abstract: This article develops from first principles some of the key ingredients necessary to successfully construct a Theory of Everything (TOE). The heart of a successful TOE must contain an accurate model of space. The basic principles governing existence have been used to show that space is a n ..."
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Abstract: This article develops from first principles some of the key ingredients necessary to successfully construct a Theory of Everything (TOE). The heart of a successful TOE must contain an accurate model of space. The basic principles governing existence have been used to show that space is a network of linked perceptions. The exchange of perceptions, or information, in space is called space mixing. By implicitly representing all the properties of space, this network of linked perceptions has been shown to be a selfscalar field called the Latent Scalar, L. It is shown that all physical properties of the multiverse are embedded in this selfscalar field, a principle called the space mixing theorem. It is also shown that distances between points in a selfscalar field are characterized by an invariant distance parameter and an associated metric tensor, a principle called the space metric theorem. Space Mixing Theory is based on a combination of mathematical and logical inferences.