78,045 research outputs found
State-based and process-based value passing
State-based and process-based formalisms each come with their own distinct set of assumptions and properties. To combine them in a useful way it is important to be sure of these assumptions in order that the formalisms are combined in ways which have, or which allow, the intended combined properties. Consequently we cannot necessarily expect to take on state-based formalism and one process-based formalism and combine them and get something sensible, especially since the act of combining can have subtle consequences.
Here we concentrate on value-passing, how it is treated in each formalism, and how the formalisms can be combined so as to preserve certain properties. Specifically, the aim is to take from the many process-based formalisms definitions that will best fit with our chosen stat-based formalism, namely Z, so that the fit is simple, has no unintended consequences and is as elegant as possible
Realizations of Conformal and Heisenberg Algebras in PP-wave-CFT Correspondence
We elaborate on the symmetry breaking pattern involved in the Penrose limit
of spacetimes and the corresponding limit of the CFT
dual. For d=2 we examine in detail how the symmetries contract to products of
rotation and Heisenberg algebras, both from the bulk and CFT points of view.
Using a free field realization of these algebras acting on products of
elementary fields of the CFT with SO(2) R charge +1, we show that this process
of contraction restricts all the fields to a few low angular momentum modes and
ensures that the field with R charge -1 does not appear. This provides an
understanding of several important aspects of the proposal of Berenstein,
Maldacena and Nastase. We also indicate how the contraction can be performed on
correlation functions.Comment: 24 pages, LaTe
Quantum Mechanics: Harbinger of a Non-Commutative Probability Theory?
In this paper we discuss the relevance of the algebraic approach to quantum
phenomena first introduced by von Neumann before he confessed to Birkoff that
he no longer believed in Hilbert space. This approach is more general and
allows us to see the structure of quantum processes in terms of non-commutative
probability theory, a non-Boolean structure of the implicate order which
contains Boolean sub-structures which accommodates the explicate classical
world. We move away from mechanical `waves' and `particles' and take as basic
what Bohm called a {\em structure process}. This enables us to learn new
lessons that can have a wider application in the way we think of structures in
language and thought itself.Comment: 20 pages, one figure. Invited pape
An alternative Gospel of structure: order, composition, processes
We survey some basic mathematical structures, which arguably are more
primitive than the structures taught at school. These structures are orders,
with or without composition, and (symmetric) monoidal categories. We list
several `real life' incarnations of each of these. This paper also serves as an
introduction to these structures and their current and potentially future uses
in linguistics, physics and knowledge representation.Comment: Introductory chapter to C. Heunen, M. Sadrzadeh, and E. Grefenstette.
Quantum Physics and Linguistics: A Compositional, Diagrammatic Discourse.
Oxford University Press, 201
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