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Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds

2008 Mathematics
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Release : 2008
Genre : Mathematics
Kind : eBook
Book Rating : 483/5 ( reviews)

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Book Synopsis Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds by : Raphael Ponge

Download or read book Heisenberg Calculus and Spectral Theory of Hypoelliptic Operators on Heisenberg Manifolds written by Raphael Ponge. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: This memoir deals with the hypoelliptic calculus on Heisenberg manifolds, including CR and contact manifolds. In this context the main differential operators at stake include the Hormander's sum of squares, the Kohn Laplacian, the horizontal sublaplacian, the CR conformal operators of Gover-Graham and the contact Laplacian. These operators cannot be elliptic and the relevant pseudodifferential calculus to study them is provided by the Heisenberg calculus of Beals-Greiner andTaylor.

Principal Symbol Calculus on Contact Manifolds

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Book Rating : 262/5 ( reviews)

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Book Synopsis Principal Symbol Calculus on Contact Manifolds by : Yuri Kordyukov

Download or read book Principal Symbol Calculus on Contact Manifolds written by Yuri Kordyukov. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

Motives, Quantum Field Theory, and Pseudodifferential Operators

2010 Mathematics
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Release : 2010
Genre : Mathematics
Kind : eBook
Book Rating : 993/5 ( reviews)

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Book Synopsis Motives, Quantum Field Theory, and Pseudodifferential Operators by : Alan L. Carey

Download or read book Motives, Quantum Field Theory, and Pseudodifferential Operators written by Alan L. Carey. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles related to the conference ``Motives, Quantum Field Theory, and Pseudodifferntial Operators'' held at Boston University in June 2008, with partial support from the Clay Mathematics Institute, Boston University, and the National Science Foundation. There are deep but only partially understood connections between the three conference fields, so this book is intended both to explain the known connections and to offer directions for further research. In keeping with the organization of the conference, this book contains introductory lectures on each of the conference themes and research articles on current topics in these fields. The introductory lectures are suitable for graduate students and new Ph.D.'s in both mathematics and theoretical physics, as well as for senior researchers, since few mathematicians are expert in any two of the conference areas. Among the topics discussed in the introductory lectures are the appearance of multiple zeta values both as periods of motives and in Feynman integral calculations in perturbative QFT, the use of Hopf algebra techniques for renormalization in QFT, and regularized traces of pseudodifferential operators. The motivic interpretation of multiple zeta values points to a fundamental link between motives and QFT, and there are strong parallels between regularized traces and Feynman integral techniques. The research articles cover a range of topics in areas related to the conference themes, including geometric, Hopf algebraic, analytic, motivic and computational aspects of quantum field theory and mirror symmetry. There is no unifying theory of the conference areas at present, so the research articles present the current state of the art pointing towards such a unification.

Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules

2009-06-05 Mathematics
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Release : 2009-06-05
Genre : Mathematics
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Book Rating : 96X/5 ( reviews)

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Book Synopsis Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules by : AndrŽ Martinez

Download or read book Twisted Pseudodifferential Calculus and Application to the Quantum Evolution of Molecules written by AndrŽ Martinez. This book was released on 2009-06-05. Available in PDF, EPUB and Kindle. Book excerpt: The authors construct an abstract pseudodifferential calculus with operator-valued symbol, suitable for the treatment of Coulomb-type interactions, and they apply it to the study of the quantum evolution of molecules in the Born-Oppenheimer approximation, in the case of the electronic Hamiltonian admitting a local gap in its spectrum. In particular, they show that the molecular evolution can be reduced to the one of a system of smooth semiclassical operators, the symbol of which can be computed explicitely. In addition, they study the propagation of certain wave packets up to long time values of Ehrenfest order.

The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations

2008 Mathematics
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Release : 2008
Genre : Mathematics
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Book Rating : 501/5 ( reviews)

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Book Synopsis The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations by : Salah-Eldin Mohammed

Download or read book The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations written by Salah-Eldin Mohammed. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this paper is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations and stochastic partial differential equations near stationary solutions.

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