2,845 research outputs found

    Comparison between the two definitions of AI

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    Two different definitions of the Artificial Intelligence concept have been proposed in papers [1] and [2]. The first definition is informal. It says that any program that is cleverer than a human being, is acknowledged as Artificial Intelligence. The second definition is formal because it avoids reference to the concept of human being. The readers of papers [1] and [2] might be left with the impression that both definitions are equivalent and the definition in [2] is simply a formal version of that in [1]. This paper will compare both definitions of Artificial Intelligence and, hopefully, will bring a better understanding of the concept.Comment: added four new section

    Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case

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    In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the fact that they belong to a narrow class of algebras, which we call 'conformal Lie algebras', which have very similar properties to the conformal algebras of Minkowski space-time. We give the main multiplets and the main reduced multiplets of indecomposable elementary representations for n=6, including the necessary data for all relevant invariant differential operators. In fact, this gives by reduction also the cases for n<6, since the main multiplet for fixed n coincides with one reduced case for n+1.Comment: Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text overlap with arXiv:0812.2690, arXiv:0812.265

    Intertwining Operator Realization of the AdS/CFT Correspondence

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    We give a group-theoretic interpretation of the AdS/CFT correspondence as relation of representation equivalence between representations of the conformal group describing the bulk AdS fields ϕ\phi and the coupled boundary fields ϕ0\phi_0 and O{\cal O}. We use two kinds of equivalences. The first kind is equivalence between bulk fields and boundary fields and is established here. The second kind is the equivalence between coupled boundary fields. Operators realizing the first kind of equivalence for special cases were given by Witten and others - here they are constructed in a more general setting from the requirement that they are intertwining operators. The intertwining operators realizing the second kind of equivalence are provided by the standard conformal two-point functions. Using both equivalences we find that the bulk field has in fact two boundary fields, namely, the coupled boundary fields. Thus, from the viewpoint of the bulk-boundary correspondence the coupled fields are on an equal footing. Our setting is more general since our bulk fields are described by representations of the Euclidean conformal group G=SO(d+1,1)G=SO(d+1,1), induced from representations τ\tau of the maximal compact subgroup SO(d+1)SO(d+1) of GG. From these large reducible representations we can single out representations which are equivalent to conformal boundary representations labelled by the conformal weight and by arbitrary representations μ\mu of the Euclidean Lorentz group M=SO(d)M=SO(d), such that μ\mu is contained in the restriction of τ\tau to MM. Thus, our boundary-to-bulk operators can be compared with those in the literature only when for a fixed μ\mu we consider a 'minimal' representation τ=τ(μ)\tau=\tau(\mu) containing μ\mu.Comment: 25 pages, TEX file using harvmac.tex; v2: misprints corrected; to appear in Nuclear Physics