Microlocal Analysis of Quantum Fields on Curved Spacetimes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Microlocal Analysis of Quantum Fields on Curved Spacetimes write by Christian Gérard. This book was released on 2019. Microlocal Analysis of Quantum Fields on Curved Spacetimes available in PDF, EPUB and Kindle.
Quantum Field Theory on Curved Spacetimes
Quantum Field Theory on Curved Spacetimes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Field Theory on Curved Spacetimes write by Christian Bär. This book was released on 2009-09-18. Quantum Field Theory on Curved Spacetimes available in PDF, EPUB and Kindle. After some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes. Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure, and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as well as more recently the insights from suitable concepts such as microlocal analysis. This primer is an outgrowth of a compact course given by the editors and contributing authors to an audience of advanced graduate students and young researchers in the field, and assumes working knowledge of differential geometry and functional analysis on the part of the reader.
Microlocal Analysis of Quantum Fields on Curved Spacetimes
Microlocal Analysis of Quantum Fields on Curved Spacetimes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Microlocal Analysis of Quantum Fields on Curved Spacetimes write by Christian Gérard. This book was released on 2019. Microlocal Analysis of Quantum Fields on Curved Spacetimes available in PDF, EPUB and Kindle. We focus on free fields and the corresponding quasi-free states and more precisely on Klein-Gordon fields and Dirac fields. The first chapters are devoted to preliminary material on CCR*-algebras, quasi-free states, wave equations on Lorentzian manifolds, microlocal analysis and to the important Hadamard condition, characterizing physically acceptable quantum states on curved spacetimes. In the later chapters more advanced tools of microlocal analysis, like the global pseudo-differential calculus on non-compact manifolds, are used to construct and study Hadamard states for Klein-Gordon fields by various methods, in particular by scattering theory and by Wick rotation arguments. In the last chapter the fermionic theory of free Dirac quantum fields on Lorentzian manifolds is described in some detail.This monograph is addressed to both mathematicians and mathematical physicists. The first will be able to use it as a rigorous exposition of free quantum fields on curved spacetimes and as an introduction to some interesting and physically important problems arising in this domain. The second may find this text a useful introduction and motivation to the use of more advanced tools of microlocal analysis in this area of research.
Perturbative Algebraic Quantum Field Theory
Perturbative Algebraic Quantum Field Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Perturbative Algebraic Quantum Field Theory write by Kasia Rejzner. This book was released on 2016-03-16. Perturbative Algebraic Quantum Field Theory available in PDF, EPUB and Kindle. Perturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn’t require the use of divergent quantities and works on a large class of Lorenzian manifolds. We discuss in detail the examples of scalar fields, gauge theories and the effective quantum gravity. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all, of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses effective quantum gravity. The book aims to be accessible to researchers and graduate students, who are interested in the mathematical foundations of pQFT.
Aspects of Quantum Field Theory in Curved Spacetime
Aspects of Quantum Field Theory in Curved Spacetime - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Aspects of Quantum Field Theory in Curved Spacetime write by Stephen A. Fulling. This book was released on 1989-08-24. Aspects of Quantum Field Theory in Curved Spacetime available in PDF, EPUB and Kindle. The theory of quantum fields on curved spacetimes has attracted great attention since the discovery, by Stephen Hawking, of black-hole evaporation. It remains an important subject for the understanding of such contemporary topics as inflationary cosmology, quantum gravity and superstring theory. This book provides, for mathematicians, an introduction to this field of physics in a language and from a viewpoint which such a reader should find congenial. Physicists should also gain from reading this book a sound grasp of various aspects of the theory, some of which have not been particularly emphasised in the existing review literature. The topics covered include normal-mode expansions for a general elliptic operator, Fock space, the Casimir effect, the 'Klein' paradox, particle definition and particle creation in expanding universes, asymptotic expansion of Green's functions and heat kernels, and renormalisation of the stress tensor. The style is pedagogic rather than formal; some knowledge of general relativity and differential geometry is assumed, but the author does supply background material on functional analysis and quantum field theory as required. The book arose from a course taught to graduate students and could be used for self-study or for advanced courses in relativity and quantum field theory.
