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  • 1
    Electronic Resource
    Electronic Resource
    On A. Connes' noncommutative integration theory (1982)
    Springer
    Communications in mathematical physics 85 (1982), S. 99-120 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper is a comment (written in a self-contained way) upon A. Connes' noncommutative integration theory. A simple observation (Lemma 9) allows the direct definition of transverse measures as functionals on the general positive random functions. Connes' first definition is then recovered by considering the transverse functions as a separating subset of the positive random functions (to which they are related by explicit natural transformations).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02029136
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  • 2
    Electronic Resource
    Electronic Resource
    Group duality and the Kubo-Martin Schwinger condition. II (1982)
    Springer
    Communications in mathematical physics 85 (1982), S. 155-176 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Let ω be an invariant state of theC*-system { $$\mathfrak{A}$$ ,G, α} on a locally compact noncommutative groupG. Assume further that ω is extremal τ-invariant for an action τ of an amenable groupH which is ω-asymptotically abelian and commutes with α. Denoting byF AB,G AB the corresponding two point functions, we give criteria for the fulfillment of the KMS condition with respect to some one parameter subgroup of the center ofG based on the existence of a closable mapT such thatTF AB=G AB for allA,B∈ $$\mathfrak{A}$$ . Closability is either inL ∞(G),B(G) orC ∞(G), according to clustering properties for τ. The basic mathematical technique is the duality theory for noncompact, noncommutative locally compact groups.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02029140
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  • 3
    Electronic Resource
    Electronic Resource
    On the universal Chamseddine–Connes action. I. Details of the action computation (1997)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4929-4950 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We give a detailed computation of the bosonic action of the Chamseddine–Connes model which we performed using different techniques. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531927
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  • 4
    Electronic Resource
    Electronic Resource
    Fuzzy mass relations for the Higgs (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 6232-6254 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The noncommutative approach of the standard model produces a relation between the top and the Higgs masses. We show that, for a given top mass, the Higgs mass is constrained to lie in an interval. The length of this interval is of the order of m2τ/mt. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531242
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  • 5
    Electronic Resource
    Electronic Resource
    Noncommutative geometry and fundamental physical interactions: The Lagrangian level—Historical sketch and description of the present situation (2000)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 41 (2000), S. 3867-3891 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: These notes comprise (i) a descriptive account of the history of the subject showing how physics and mathematics interwove to develop a mathematical concept of quantum manifold relevant to elementary particle theory; (ii) a detailed technical description, from scratch, of the spectral action formalism and computation. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.533330
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  • 6
    Electronic Resource
    Electronic Resource
    A second look at Uq(Sl2) at third root of unity (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 2770-2790 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We revisit the 27-dimensional quotient of Uq(Sl2) at third roots of unity within a presentation adapted to a Hopf bar-operation. We describe in detail the regular representation and display the Hopf automorphisms and the Hopf bar-operations. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1463710
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  • 7
    Electronic Resource
    Electronic Resource
    Cyclic cocycles from graded KMS functionals (1989)
    Springer
    Communications in mathematical physics 121 (1989), S. 345-350 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Each “graded KMS functional” of aZ/2-gradedC*-algebra with respect to a “supersymmetric” one-parameter automorphism group gives rise to a cyclic cocycle.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01217811
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  • 8
    Electronic Resource
    Electronic Resource
    Quantum forms of tensor products (1993)
    Springer
    Communications in mathematical physics 155 (1993), S. 135-142 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We describe the skew tensor-product structure inherent to Yang-Mills procedures pertaining to non-commutative spaces obtained by (skew) tensorization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02100054
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  • 9
    Electronic Resource
    Electronic Resource
    The dirac operator and gravitation (1995)
    Springer
    Communications in mathematical physics 166 (1995), S. 633-643 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give a brute-force proof of the fact, announced by Alain Connes, that the Wodzicki residue of the inverse square of the Dirac operator is proportional to the Einstein-Hilbert action of general relativity. We show that this also holds for twisted (e. g. by electrodynamics) Dirac operators, and more generally, for Dirac operators pertaining to Clifford connections of general Clifford bundles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099890
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  • 10
    Electronic Resource
    Electronic Resource
    Conserved currents and associated symmetries; Goldstone's theorem (1966)
    Springer
    Communications in mathematical physics 2 (1966), S. 108-120 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We consider, in the framework of local field theory with translation symmetry, automorphisms connected with locally conserved currents. We show that such automorphisms lead to symmetries, i.e. are implementable by unitary operators, whenever the smallest mass in the theory is non-zero. Therefore we conclude that a “spontaneously broken symmetry” is possible only in the event that the smallest mass is zero. This establishes the theorem first conjectured byGoldstone.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01773346
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