A New Approach to Quantising Systems: II. Quantising on a Category of Sets
نویسندگان
چکیده
منابع مشابه
A New Approach to Quantising Systems: II. Quantising on a Category of Sets
In [1], a new approach was suggested for finding quantum structures that might, in particular, be used in potential approaches to quantum gravity that involve non-manifold models for space and/or space-time (for example, causal sets). This involved developing a procedure for quantising a system whose configuration space—or historytheory analogue—is the set of objects in a (small) category Q. In...
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In [1], a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space—or history-theory analogue—is the set of objects in a (small) category Q. In the present paper, we show how this theory can be applied to the special case when Q is a category of sets. This includes the physically important examples whe...
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A new approach is suggested to the problem of quantising causal sets, or topologies, or other such models for space-time (or space). The starting point is the observation that entities of this type can be regarded as objects in a category whose arrows are structure-preserving maps. This motivates investigating the general problem of quantising a system whose ‘configuration space’ (or history-th...
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In [1], a new approach was suggested for quantising space-time, or space. This involved developing a procedure for quantising a system whose configuration space—or history-theory analogue—is the set of objects, Ob(Q), in a (small) category Q. The quantum states in this approach are cross-sections of a bundle A ; K[A] of Hilbert spaces over Ob(Q). The Hilbert spaces K[A], A ∈ Ob(Q), depend stron...
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Since many real-world problems arising in the fields of compiler optimisation, automatised software engineering, formal proof systems, and so forth are equivalent to the Halting Problem—the most notorious undecidable problem—there is a growing interest, not only academically, in understanding the problem better and in providing alternative solutions. Halting computations can be recognised by si...
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ژورنال
عنوان ژورنال: Advances in Theoretical and Mathematical Physics
سال: 2003
ISSN: 1095-0761,1095-0753
DOI: 10.4310/atmp.2003.v7.n5.a3