Some Mathematical Problems in the Renormalization of Quantum Field Theories
Marcel Guenin (1969)
Recherche Coopérative sur Programme n°25
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Marcel Guenin (1969)
Recherche Coopérative sur Programme n°25
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Marcel Guenin (1973)
Recherche Coopérative sur Programme n°25
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Janys̆ka, Joseph, Modugno, Marco (1997)
General Mathematics
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Kundu, Anjan (2010)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
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Bishop, R.C., Bohm, A., Gadella, M. (2004)
Discrete Dynamics in Nature and Society
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Atmanspacher, Harald (2004)
Discrete Dynamics in Nature and Society
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Diego de Falco, Dario Tamascelli (2011)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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Quantum annealing, or quantum stochastic optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by quantum...
Diego de Falco, Dario Tamascelli (2011)
RAIRO - Theoretical Informatics and Applications
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Quantum annealing, or quantum stochastic optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an example of proficuous cross contamination between classical and quantum computer science. In this survey paper we illustrate how hard combinatorial problems are tackled by quantum computation and present some examples of the heuristics provided by quantum...
James Glimm (1973-1974)
Séminaire Jean Leray
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Piotr Mikołaj Sołtan (2010)
Banach Center Publications
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We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of C*-algebras) do not admit any quantum group structure. We also provide a number of examples which include some very well known quantum spaces. Our tools include several purely quantum group theoretical results as well as study of existence of characters and traces on C*-algebras describing the considered quantum spaces as well as...
Jan Dereziński, Christian Gérard (2010)
Banach Center Publications
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The abstract mathematical structure behind the positive energy quantization of linear classical systems is described. It is separated into three stages: the description of a classical system, the algebraic quantization and the Hilbert space quantization. Four kinds of systems are distinguished: neutral bosonic, neutral bosonic, charged bosonic and charged fermionic. The formalism that is described follows closely the usual constructions employed in quantum physics to introduce noninteracting...
Bernard Kay (2000)
Journées équations aux dérivées partielles
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Several situations of physical importance may be modelled by linear quantum fields propagating in fixed spacetime-dependent classical background fields. For example, the quantum Dirac field in a strong and/or time-dependent external electromagnetic field accounts for the creation of electron-positron pairs out of the vacuum. Also, the theory of linear quantum fields propagating on a given background curved spacetime is the appropriate framework for the derivation of black-hole evaporation...
Robert, Didier (2008)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 81Q60, 35Q40. A standard supersymmetric quantum system is defined by a Hamiltonian [^H] = ½([^Q]*[^Q] +[^Q][^Q]*), where the super-charge [^Q] satisfies [^Q]2 = 0, [^Q] commutes with [^H]. So we have [^H] ≥ 0 and the quantum spectrum of [^H] is non negative. On the other hand Pais-Ulhenbeck proposed in 1950 a model in quantum-field theory where the d'Alembert operator [¯] = [(∂2)/( ∂t2)] − Δx is replaced by fourth order operator [¯]([¯]...