Nicola Pinamonti's Books

Hadamard States from Light-like Hypersurfaces

By: Claudio Dappiaggi,Valter Moretti,Nicola Pinamonti

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Hadamard States from Light-like Hypersurfaces

By: Claudio Dappiaggi,Valter Moretti,Nicola Pinamonti

This book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal) light-like boundary. The first two sections focus on explaining a few introductory aspects of this topic and on providing the relevant geometric background material. The notions of asymptotically flat spacetimes and of expanding universes with a cosmological horizon are analysed in detail, devoting special attention to the characterization of asymptotic symmetries. In the central part of the book, the quantization of a real scalar field theory on such class of backgrounds is discussed within the framework of algebraic quantum field theory. Subsequently it is explained how it is possible to encode the information of the observables of the theory in a second, ancillary counterpart, which is built directly on the conformal (null) boundary. This procedure, dubbed bulk-to-boundary correspondence, has the net advantage of allowing the identification of a distinguished state for the theory on the boundary, which admits a counterpart in the bulk spacetime which is automatically of Hadamard form. In the last part of the book, some applications of these states are discussed, in particular the construction of the algebra of Wick polynomials. This book is aimed mainly, but not exclusively, at a readership with interest in the mathematical formulation of quantum field theory on curved backgrounds.

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113

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Springer

Published Date

ISBN 10

3319643436

ISBN 13

9783319643434

Wave Packet Analysis of Feynman Path Integrals

By: Fabio Nicola,S. Ivan Trapasso

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Wave Packet Analysis of Feynman Path Integrals

By: Fabio Nicola,S. Ivan Trapasso

The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.

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Page Count

220

Publisher

Springer Nature

Published Date

ISBN 10

3031061861

ISBN 13

9783031061868

Hadamard States from Light-like Hypersurfaces

By: Claudio Dappiaggi,Valter Moretti,Nicola Pinamonti

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Hadamard States from Light-like Hypersurfaces

By: Claudio Dappiaggi,Valter Moretti,Nicola Pinamonti

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N/A

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Solve jigsaw puzzle

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Page Count

113

Publisher

Springer

Published Date

ISBN 10

3319643436

ISBN 13

9783319643434

Book's by Nicola Pinamonti

Hadamard States from Light-like Hypersurfaces

Hadamard States from Light-like Hypersurfaces

Wave Packet Analysis of Feynman Path Integrals

Wave Packet Analysis of Feynman Path Integrals

Hadamard States from Light-like Hypersurfaces

Hadamard States from Light-like Hypersurfaces

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