Pubblicazioni


  • Renormalization and Resolution of Singularities 9999

    C. Bergbauer; R. Brunetti; D. Kreimer, "Renormalization and Resolution of Singularities" in COMMUNICATIONS IN MATHEMATICAL PHYSICS, v. 2012, (In press)

    9999 articolo su rivista

  • Quantum gravity from the point of view of locally covariant quantum field theory 2016

    Brunetti, Romeo; Fredenhagen, Klaus; Rejzner, Katarzyna, "Quantum gravity from the point of view of locally covariant quantum field theory" in COMMUNICATIONS IN MATHEMATICAL PHYSICS, v. 2016, n. 345 (2016), p. 741-779. - DOI: 10.1007/s00220-016-2676-x

    We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales.

    2016 articolo su rivista

  • Cosmological perturbation theory and quantum gravity 2016

    Brunetti, Romeo; Fredenhagen, Klaus; Hack, Thomas-Paul; Pinamonti, Nicola; Rejzner, Katarzyna, "Cosmological perturbation theory and quantum gravity" in JOURNAL OF HIGH ENERGY PHYSICS, v. 2016, n. 8 (2016). - URL: http://link.springer.com/journal/13130 . - DOI: 10.1007/JHEP08(2016)032

    2016 articolo su rivista

  • Advances in Algebraic Quantum Field Theory 2015

    Brunetti, R.; Dappiaggi, ; C, .; Fredenhagen, ; K, .; Yngvason, (edited by), "Advances in Algebraic Quantum Field Theory", by Fredenhagen, Klaus: Rejzner, Katarzyna, Dappiaggi, Claudio, Benini, Marco, Moretti, Valter, Khavkine, Igor, Fewster, J. Christopher, Verch, Rainer, Lechner, Gandalf, Naaijkens, Peter, Hack, Paul-thomas, Rehren, Karl-henning, Bahns, Dorothea, Piacitelli, Gherardo, Morsella, Gerardo, Doplicher, Sergio, Germania: Springer, 2015. - ISBN: 978-3-319-21353-8. - URL: http://www.springer.com/it/book/9783319213521 . - DOI: 10.1007/978-3-319-21353-8

    Relativistic quantum field theory was conceived in the late 1920s as a framework unifying the two fundamental theories that revolutionized physics in the twentieth century: Quantum Mechanics and the Special Theory of Relativity. Algebraic Quantum Field Theory (AQFT) is relativistic quantum field theory regarded from a certain perspective, emphasizing localization of observables in space and time. It has its roots in the pioneering work of Rudolf Haag and Arthur Wightman from the 1950s and is a well-established branch of mathematical physics, distinguished by clear conceptual foundations and mathematically sound arguments.AQFT is also called Local Quantum Physics which is the title of a monograph by Rudolf Haag1 that summarizes the results and insights achieved by many researchers up to the mid-1990s. Since then a number of new developments have taken place. In May 19–23, 2014 a workshop with the title “Algebraic quantum field theory: Its status and its future” was held at the Erwin Schrödinger Institute for Mathematical Physics (ESI) in Vienna. The present volume reflects many of the themes discussed at this workshop but all contributions were written specially for this volume. The first contribution, by Klaus Fredenhagen, is a general introduction to the fundamentals of AQFT while other chapters focus on more specialized topics. The chapter by Fredenhagen and Katarzyna Rejzner in particular, shows how perturbative constructions of models with interactions fit elegantly into the formalism of AQFT.One of the strengths of the algebraic approach is that it can be naturally applied when the underlying space-time manifold is curved, thus allowing to take important aspects of General Relativity into account. A large number of results on the characterization of physically important states, general covariance, perturbation theory, and renormalization, both on flat and curved space-times, have been obtained in the past 20 years and several of the contributions deal with these topics.The introductory chapter by Klaus Fredenhagen has a section on AQFT on curved space times, the chapter by Marco Benini and Claudio Dappiaggi treatsmodels of free quantum fields on such space-times, and that of Igor Khavkine and Valter Moretti is concerned with quasi-free Hadamard states. The contribution of Christopher Fewster and Rainer Verch deals with locally covariant AQFT on curved space-times employing the language of category theory, besides discussing selection criteria for physical states in terms of various stability conditions. The chapter by Thomas-Paul Hack and Nicola Pinamonti is concerned with applications of AQFT to cosmology. Here also, semiclassical back reaction of quantum fields on the metric of space-time is taken into account. The contribution by Dorothea Banhs, Sergio Doplicher, Gerardeo Morsella, and Gherardo Piacitelli goes further into the direction of quantum gravity by replacing classical space-time by a quantum space-time where the coordinates form a noncommutative algebra.Conformal quantum field theory, that has several important applications in condensed matter physics, is a model example where algebraic structures and inequivalent Hilbert space representations that go far beyond standard Lagrangian field theory arise naturally. The chapter by Karl-Henning Rehren reviews this topic from a modern perspective. Pieter Naaijkens treats in his contribution Kitaev’s quantum double model from a local quantum physics point of view. This is a further example where the algebraic and local way of thinking leads to important insights in a situation that is not directly connected with relativistic quantum theory but rather with condensed matter physics and quantum information theory.The last chapter, by Gandalf Lechner, is concerned with new methods for constructing models of relativistic quantum fields. Here, a basic tool is the Tomita-Takesaki modular theory of von Neumann Al

    2015 libro

  • The Locality Axiom in Quantum Field Theory and Tensor Products of $C^*$-algebras 2014

    R. Brunetti; K. Fredenhagen; P. Imani; K. Rejzner, "The Locality Axiom in Quantum Field Theory and Tensor Products of $C^*$-algebras" in REVIEWS IN MATHEMATICAL PHYSICS, v. 2014, (2014). - DOI: 10.1142/S0129055X1450010X

    The prototype of mutually independent systems are systems which are localized in spacelike separated regions. In the framework of locally covariant quantum field theory we show that the commutativity of observables in spacelike separated regions can be encoded in the tensorial structure of the functor which associates unital C^*-algebras (the local observable algebras) to globally hyperbolic spacetimes. This holds under the assumption that the local algebras satisfy the split property and involves the minimal tensor product of C^*-algebras.

    2014 articolo su rivista

  • Time in quantum physics : from an external parameter to an intrinsic observable 2010

    R. Brunetti; K. Fredenhagen; M. Hoge, "Time in quantum physics : from an external parameter to an intrinsic observable" in FOUNDATIONS OF PHYSICS, v. 40, n. 9-10 (2010), p. 1368-1378. - URL: http://www.springerlink.com/content/t368722x46q05105/

    2010 articolo su rivista

  • Quantum charges and spacetime topology: the emergence of new superselection sectors 2009

    R. Brunetti; G. Ruzzi, "Quantum charges and spacetime topology: the emergence of new superselection sectors" in COMMUNICATIONS IN MATHEMATICAL PHYSICS, v. 287, n. 2 (2009), p. 523-563. - URL: http://www.springerlink.com/content/jvu116518w852121/ . - DOI: 0.1007/s00220-008-0671-6

    A new form of superselection sectors of topological origin is developed. By that it is meant a new investigation that includes several extensions of the traditional framework of Doplicher, Haag and Roberts in local quantum theories. At first we generalize the notion of representations of nets of C*-algebras, then we provide a brand new view on selection criteria by adopting one with a strong topological flavour. We prove that it is coherent with the older point of view, hence a clue to a genuine extension. In this light, we extend Roberts' cohomological analysis to the case where 1-cocycles bear non-trivial unitary representations of the fundamental group of the spacetime, equivalently of its Cauchy surface in the case of global hyperbolicity. A crucial tool is a notion of group von Neumann algebras generated by the 1-cocycles evaluated on loops over fixed regions. One proves that these group von Neumann algebras are localized at the bounded region where loops start and end and to be factorial of finite type I. All that amounts to a new invariant, in a topological sense, which can be defined as the dimension of the factor. We prove that any 1-cocycle can be factorized into a part that contains only the charge content and another where only the topological information is stored. This second part much resembles what in literature is known as geometric phases. Indeed, by the very geometrical origin of the 1-cocycles that we discuss in the paper, they are essential tools in the theory of net bundles, and the topological part is related to their holonomy content. At the end we prove the existence of net representations.

    2009 articolo su rivista

  • Topological features of massive bosons on two-dimensional Einstein space-time 2009

    R. Brunetti; L. Franceschini; V. Moretti, "Topological features of massive bosons on two-dimensional Einstein space-time" in ANNALES HENRI POINCARE', v. 10, n. 6 (2009), p. 1027-1073. - DOI: 10.1007/s00023-009-0007-x

    2009 articolo su rivista

  • Perturbative algebraic quantum field theory and the renormalization groups 2009

    R. Brunetti; M. Duetsch; K. Fredenhagen, "Perturbative algebraic quantum field theory and the renormalization groups" in ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS, v. 13, n. 5 (2009), p. 1541-1599. - URL: http://www.intlpress.com/ATMP/ATMP-BrowseJournal.php

    A new formalism for the perturbative construction of algebraic quantum field theory is developed. The formalism allows the treatment of low-dimensional theories and of non-polynomial interactions. We discuss the connection between the Stuckelberg-Petermann renormalization group which describes the freedom in the perturbative construction with the Wilsonian idea of theories at different scales. In particular, we relate the approach to renormalization in terms of Polchinski's Flow Equation to the Epstein-Glaser method. We also show that the renormalization group in the sense of Gell-Mann-Low (which characterizes the behaviour of the theory under the change of all scales) is a one-parametric subfamily of the Stuckelberg-Petermann group and that this subfamily is in general only a cocycle. Since the algebraic structure of the Stuckelberg-Petermann group does not depend on global quantities, this group can be formulated in the (algebraic) adiabatic limit without meeting any infrared divergencies. In particular we derive an algebraic version of the Callan-Symanzik equation and define the beta-function in a state independent way.

    2009 articolo su rivista

  • Quantum field theory on curved backgrounds 2009

    R. Brunetti; K. Fredenhagen, "Quantum field theory on curved backgrounds" in C. Baer, K. Fredenhagen (edited by), Quantum field theory on curved spacetimes: concepts and mathematical foundations, Berlin; Heidelberg: Springer, 2009, p. 129-155. - (LECTURE NOTES IN PHYSICS). - ISBN: 9783642027796. - DOI: 10.1007/978-3-642-02780-2_5

    Quantum field theory is an extremely successful piece of theoretical physics. Based on few general principles, it describes with an incredibly good precision large parts of particle physics. But also in other fields, in particular in solid state physics, it yields important applications. At present, the only problem which seems to go beyond the general framework of quantum field theory is the incorporation of grav- ity. Quantum field theory on curved backgrounds aims at a step toward solving this problem by neglecting the back reaction of the quantum fields on the spacetime metric.

    2009 capitolo

  • Algebraic Approach to Quantum Field Theories 2007

    R. Brunetti; K. Fredenhagen, Algebraic Approach to Quantum Field Theories in: "Encyclopedia of Mathematical Physics", Amsterdam: Elsevier, 2007. - ISBN: 9780125126601

    2007 voce

  • Superselection sectors and general covariance. I 2007

    R. Brunetti; G. Ruzzi, "Superselection sectors and general covariance. I" in COMMUNICATIONS IN MATHEMATICAL PHYSICS, v. v. 270, n. 1 (2007), p. 69-108. - URL: http://www.springerlink.com/content/36273w70k644t804/

    This paper is devoted to the analysis of charged superselection sectors in the framework of the locally covariant quantum field theories. We shall analyze sharply localizable charges, and use net-cohomology of J.E. Roberts as a main tool. We show that to any 4-dimensional globally hyperbolic spacetime a unique, up to equivalence, symmetric tensor C*-category with conjugates (in case of finite statistics) is attached; to any embedding between different spacetimes, the corresponding categories can be embedded, contravariantly, in such a way that all the charged quantum numbers of sectors are preserved. This entails that to any spacetime is associated a unique gauge group, up to isomorphisms, and that to any embedding between two spacetimes there corresponds a group morphism between the related gauge groups. This form of covariance between sectors also brings to light the issue whether local and global sectors are the same. We conjecture this holds that at least on simply connected spacetimes. It is argued that the possible failure might be related to the presence of topological charges. Our analysis seems to describe theories which have a well defined short-distance asymptotic behaviour.

    2007 articolo su rivista

  • Towards a background independent formulation of perturbative quantum gravity 2007

    R. Brunetti; K. Fredenhagen, "Towards a background independent formulation of perturbative quantum gravity" in B. Fauser, J. Tolksdorf, E. Zeidler (edited by), Quantum gravity : mathematical models and experimental bounds, Basel ; Boston: Birkhäuser, 2007, p. 151-160. - ISBN: 9783764379773

    The recent formulation of locally covariant quantum field theory may open the way towards a background independent perturbative formula- tion of Quantum Gravity.

    2007 capitolo

  • Quantum field theories in curved spacetime 2007

    R. Brunetti; V. Moretti, Quantum field theories in curved spacetime in: "Encyclopedia of mathematical physics", Berlin: Springer, 2007, p. 1-6. - URL: http://refworks.springer.com/mrw/index.php?id=423

    2007 voce

  • General Covariance in Algebraic Quantum Field Theory 2006

    R. Brunetti; M. Porrmann; G. Ruzzi, "General Covariance in Algebraic Quantum Field Theory" in E. Barletta (edited by), Variations on a century of relativity: theory and applications, Potenza: Universita' degli studi della Basilicata, 2006, p. 31-71. - (Lecture notes of Seminario Interdisciplinare di Matematica)

    2006 capitolo

  • Locally Covariant Quantum FIeld Theory 2006

    R. Brunetti, "Locally Covariant Quantum FIeld Theory" in Rigorous Quantum Field Theory, A Festschrift for Jacques Bros, Basel: Birkhauser, 2006, p. 39-47. - (Progress in Mathematics; 251). - ISBN: 3764374330. Proceedings of: Rigorous Quantum Field Theory, A Festschrift for Jacques Bros, Paris, June 2005

    2006 articolo in conferenza

  • A remark on alpha vacua for quantum field theories on de Sitter space 2005

    R. Brunetti; K. Fredenhagen; S. Hollands, "A remark on alpha vacua for quantum field theories on de Sitter space" in JOURNAL OF HIGH ENERGY PHYSICS, v. 2005, n. 5 (2005), p. 063

    2005 articolo su rivista

  • The generally covariant locality principle - A new paradigm for local quantum field theory 2003

    R. Brunetti; K. Fredenhagen; R. Verch, "The generally covariant locality principle - A new paradigm for local quantum field theory" in COMMUNICATIONS IN MATHEMATICAL PHYSICS, v. v. 237, n. 1-2 (2003), p. 31-68. - URL: http://www.springerlink.com/content/wc96l46c780yqtny/

    2003 articolo su rivista

  • Time of occurrence observable in quantum mechanics 2002

    R. Brunetti; K. Fredenhagen, "Time of occurrence observable in quantum mechanics" in PHYSICAL REVIEW A, v. v. 66, n. 4 (2002), p. 044101. - URL: http://pra.aps.org/abstract/PRA/v66/i4/e044101

    2002 articolo su rivista

  • Remarks on time-energy uncertainty relations 2002

    R. Brunetti; K. Fredenhagen, "Remarks on time-energy uncertainty relations" in REVIEWS IN MATHEMATICAL PHYSICS, v. v. 14, n. 7-8 (2002), p. 897-903. - URL: http://www.worldscinet.com/rmp/14/1407n08/S0129055X02001417.html . - DOI: 10.1142/S0129055X02001417

    2002 articolo su rivista

  • Modular localization and Wigner particles 2002

    R. Brunetti; D. Guido; R. Longo, "Modular localization and Wigner particles" in REVIEWS IN MATHEMATICAL PHYSICS, v. v. 14, n. 7-8 (2002), p. 759-785. - URL: http://www.worldscinet.com/rmp/14/1407n08/S0129055X02001387.html . - DOI: 10.1142/S0129055X02001387

    2002 articolo su rivista

  • Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds 2000

    R. Brunetti; K. Fredenhagen, "Microlocal analysis and interacting quantum field theories: Renormalization on physical backgrounds" in COMMUNICATIONS IN MATHEMATICAL PHYSICS, v. v. 208, n. 3 (2000), p. 623-661. - URL: http://www.springerlink.com/content/wenup0dhvae80frk/ . - DOI: 10.1007/s002200050004

    2000 articolo su rivista

  • Interacting Quantum Fields On Curved Background 1999

    R. Brunetti; K. Fredenhagen, "Interacting Quantum Fields On Curved Background" in XII International Congress of Mathematical Physics, Somerville: International Press, 1999. - ISBN: 9781571460554. Proceedings of: XII International Congress in Mathematical Physics, Brisbane, 13-19 July 2007

    1999 articolo in conferenza

  • Interacting quantum fields in curved space: Renormalization of φ4 1997

    R. Brunetti; K. Fredenhagen, "Interacting quantum fields in curved space: Renormalization of φ4" in Operator Algebras and Quantum Field Theory, Somerville: International Press, 1997. - ISBN: 9781571460479. Proceedings of: Operator Algebras and Quantum Field Theory, Roma, Luglio 1996

    1997 articolo in conferenza

  • The microlocal spectrum condition and wick polynomials of free fields on curved spacetimes 1996

    R. Brunetti; K. Fredenhagen; M. Kohler, "The microlocal spectrum condition and wick polynomials of free fields on curved spacetimes" in COMMUNICATIONS IN MATHEMATICAL PHYSICS, v. v. 180, n. 3 (1996), p. 633-652. - URL: http://www.springerlink.com/content/v0561k8128863102/ . - DOI: 10.1007/BF02099626

    1996 articolo su rivista