Regularization and Renormalization of Quantum Field Theory in Curved Space-time. [Pauli-Villars Regulator Fields]. PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Regularization and Renormalization of Quantum Field Theory in Curved Space-time. [Pauli-Villars Regulator Fields]. PDF full book. Access full book title Regularization and Renormalization of Quantum Field Theory in Curved Space-time. [Pauli-Villars Regulator Fields]. by . Download full books in PDF and EPUB format.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
It is proposed that field theories quantized in a curved space-time manifold can be conveniently regularized and renormalized with the aid of Pauli-Villars regulator fields. The method avoids the conceptual difficulties of covariant point-separation approaches, by starting always from a manifestly generally covariant action, and the technical limitations of the dimensional reqularization approach, which requires solution of the theory in arbitrary dimension in order to go beyond a weak-field expansion. An action is constructed which renormalizes the weak-field perturbation theory of a massive scalar field in two space-time dimensions--it is shown that the trace anomaly previously found in dimensional regularization and some point-separation calculations also arises in perturbation theory when the theory is Pauli-Villars regulated. One then studies a specific solvable two-dimensional model of a massive scalar field in a Robertson-Walker asymptotically flat universe. It is shown that the action previously considered leads, in this model, to a well defined finite expectation value for the stress-energy tensor. The particle production (less than 0 in/vertical bar/theta/sup mu nu/(x, t)/vertical bar/0 in greater than for t .-->. + infinity) is computed explicitly. Finally, the validity of weak-field perturbation theory (in the appropriate range of parameters) is checked directly in the solvable model, and the trace anomaly computed in the asymptotic regions t.-->. +- infinity independently of any weak field approximation. The extension of the model to higher dimensions and the renormalization of interacting (scalar) field theories are briefly discussed.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
It is proposed that field theories quantized in a curved space-time manifold can be conveniently regularized and renormalized with the aid of Pauli-Villars regulator fields. The method avoids the conceptual difficulties of covariant point-separation approaches, by starting always from a manifestly generally covariant action, and the technical limitations of the dimensional reqularization approach, which requires solution of the theory in arbitrary dimension in order to go beyond a weak-field expansion. An action is constructed which renormalizes the weak-field perturbation theory of a massive scalar field in two space-time dimensions--it is shown that the trace anomaly previously found in dimensional regularization and some point-separation calculations also arises in perturbation theory when the theory is Pauli-Villars regulated. One then studies a specific solvable two-dimensional model of a massive scalar field in a Robertson-Walker asymptotically flat universe. It is shown that the action previously considered leads, in this model, to a well defined finite expectation value for the stress-energy tensor. The particle production (less than 0 in/vertical bar/theta/sup mu nu/(x, t)/vertical bar/0 in greater than for t .-->. + infinity) is computed explicitly. Finally, the validity of weak-field perturbation theory (in the appropriate range of parameters) is checked directly in the solvable model, and the trace anomaly computed in the asymptotic regions t.-->. +- infinity independently of any weak field approximation. The extension of the model to higher dimensions and the renormalization of interacting (scalar) field theories are briefly discussed.
Author: Stephen A. Fulling Publisher: Cambridge University Press ISBN: 9780521377683 Category : Mathematics Languages : en Pages : 332
Book Description
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.
Author: Peter Breitenlohner Publisher: Springer ISBN: Category : Computers Languages : en Pages : 256
Book Description
The characteristic feature of many models for field theories based on concepts of differential geometry is their nonlinearity. In this book a systematic exposition of nonlinear transformations in quantum field theory is given. The book starts with a short account of the renormalization theory with examples which can be handled successfully in four space-time dimensions. The second part is devoted to nonlinear sigma-models and their constructions in two dimensions. In the final section geometrical and cohomological methods and the relations to string theory are treated. This book is an important contribution towards rigorous definitions, and the mastering of nonlinear reparametrizations in agreement with the principles of quantum field theory will help to deal with anomalies, geometry and the like consistently and thus to understand better their implications for physics. The collection of papers addresses researchers and graduate students as well and will stimulate further work on the foundations of quantum field theory.
Author: Nguyen Viet Dang Publisher: ISBN: Category : Languages : en Pages : 214
Book Description
The subject of the thesis is the construction of a perturbative quantum theory of interacting fields on a curved space-time, following a point of view pioneered by Stueckelberg and Bogoliubov and developed by Epstein-Glaser on the flat Minkowski space-time. In 2000 a breakthrough was done by Brunetti and Fredenhagen who were able to extend the Epstein-Glaser theory by exploiting the point of view developed by Radzikowski to define quantum states on a curved space-time in terms of wave-front sets. These results were further extended by Fredenhagen, Brunetti, Hollands, Wald, Rejzner, etc. to Yang-Mills fields and the gravitation. However, even for theories without gauge invariance, many mathematical details were left unexplored and unquestioned. The task of Viet was precisely to derive fully rigorously this theory in the case there is no gauge invariance. In my work, I propose a complete review of the result, solving numerous questions, adding many new results around this program and, eventually, giving more precise details on the counterterms and ambiguities in the renormalization process, and a deeper understanding of the geometry of the wave front set of the n-point functions. All this thesis uses various mathematical techniques: differential and pseudo Riemannian geometry, microlocal analysis and the symplectic geometry of wavefront sets, functional analysis, fine results from the theory of distributions, Hopf algebras, etc.
Author: Ilia Binder Publisher: American Mathematical Soc. ISBN: 0821842730 Category : Mathematics Languages : en Pages : 414
Book Description
This book covers a wide range of phenomena in the natural sciences dominated by notions of universality and renormalization. The contributions in this volume are equally broad in their approach to these phenomena, offering the mathematical as well as the perspective of the applied sciences. They explore renormalization theory in quantum field theory and statistical physics, and its connections to modern mathematics as well as physics on scales from the microscopic to the macroscopic. Information for our distributors: Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Author: Laurie M. Brown Publisher: Springer Science & Business Media ISBN: 1461227208 Category : Science Languages : en Pages : 187
Book Description
The purpose of this section is to give you a sketch of how quantum field theory works, where Feynman graphs come from and why they are so useful, where the infinities come from, and how we have learned to deal with them without compromising the physical principles involved. I am purposely treating the problem at the level of the 1940s and 1950s, so as to keep the basic ideas clear and avoid the more difficult problems and more sophisticated methods of recent years. I shall relate my discussion simply to quantum electrodynamics (QED) since that is the most familiar case and the case that was in the forefront from the beginning (though in fact I shall ignore many of the special complications that have to be dealt with when you quantize a gauge field). The methods I shall be describing are applicable to all sorts of quantized fields: the detailed factors are different but the structure of the logical development isjust the same. Not surprisingly, though, the renormalization procedure breaks down if the theory in question is nonrenormalizable. Whether nonrenormalizable theories are theories at all is a matter for debate; in any case, they hold no practical interest for physicists since they are essentially unusable. Quantum electrodynamics was devised in 1927 by Dirac, less than a year after the Schrodinger equation appeared and before the Dirac equa tion for the relativistic electron had been invented.
Author: Timothy J Hollowood Publisher: Springer Science & Business Media ISBN: 3642363121 Category : Science Languages : en Pages : 78
Book Description
This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.
Author: Mario C. Rocca Publisher: Cambridge Scholars Publishing ISBN: 1527565920 Category : Mathematics Languages : en Pages : 248
Book Description
One major problem of contemporary physics is posed by the incompatibility of the two greatest theories of the 20th century: quantum mechanics (QM) and general relativity (GR). Joining them gives rise to a perturbatively non-renormalizable quantum gravity theory. The two theories, on their own, have been amazingly successful, and quantum mechanics, in particular, gave rise to many of the recent technical advances that have revolutionized our lives. Today, however, there is a lack of an over-arching theoretical framework within which both QM and GR successes could be accommodated. This book provides an accessible guideline to a possible over-arching framework, based on well-known mathematical structures.
Author: Gerard't Hooft Publisher: ISBN: 9781502591852 Category : Languages : en Pages : 70
Book Description
Relativistic Quantum Field Theory is a mathematical scheme to describethe sub-atomic particles and forces. The basic starting point is that the axiomsof Special Relativity on the one hand and those of Quantum Mechanics on theother, should be combined into one theory. The fundamental ingredients forthis construction are reviewed. A remarkable feature is that the constructionis not perfect; it will not allow us to compute all amplitudes with unlimitedprecision. Yet in practice this theory is more than accurate enough to coverthe entire domain between the atomic scale and the Planck scale, some 20orders of magnitude
![Regularization and Renormalization of Quantum Field Theory in Curved Space-time. [Pauli-Villars Regulator Fields]. PDF](https://books.google.com/books/content/images/frontcover/tO6QwgEACAAJ?fife=w150-h200)
Author: ![Regularization and Renormalization of Quantum Field Theory in Curved Space-time. [Pauli-Villars Regulator Fields]. PDF](https://books.google.com/books/content/images/frontcover/tO6QwgEACAAJ?fife=w80-h100)
Author: 
Author: Stephen A. Fulling
Author: 
Author: Peter Breitenlohner
Author: Nguyen Viet Dang
Author: Ilia Binder
Author: Laurie M. Brown
Author: Timothy J Hollowood
Author: Mario C. Rocca
Author: Gerard't Hooft