ALGEBRAIC QUANTUM THEORY

(UNDER CONSTRUCTION !)



Introduction

  • (TO BE WRITTEN , but see below for suggestions about papers to read which are already available and are written in an accessible manner.)



    • Texts on Algebraic Quantum Theory

  • H. Araki, Mathematical Theory of Quantum Fields, (Oxford University Press, Oxford), 1999.

  • J.C. Baez, I.E. Segal and Z. Zhou, Introduction to Algebraic and Constructive Quantum Field Theory , (Princeton University Press, Princeton), 1992.

  • H. Baumgärtel and M. Wollenberg, Causal Nets of Operator Algebras - Mathematical Aspects of Algebraic Quantum Field Theory, (Akademie Verlag, Berlin), 1992.

  • H. Baumgärtel, Operatoralgebraic Methods in Quantum Field Theory, (Akademie Verlag, Berlin), 1995.

  • N.N. Bogolubov, A.A. Logunov and I.T. Todorov, Introduction to Axiomatic Quantum Field Theory, (W.A. Benjamin, Reading, Mass.) 1975 (translation of Russian original, published in 1969).

  • N.N. Bogolubov, A.A. Logunov, A.I. Oksak and I.T. Todorov, General Principles of Quantum Field Theory, (Kluwer Academic Publishers, Dordrecht) 1990 (translation of Russian original, published in 1987).

  • H.-J. Borchers, Translation Group and Particle Representations in Quantum Field Theory, Lecture Notes in Physics (Springer Verlag, Berlin), 1996.

  • O. Bratteli and D. W. Robinson, Operator Algebras and Quantum Statistical Mechanics, two volumes, (Springer Verlag, New York) 1979 and 1981.

  • E.B. Davies, Quantum Theory of Open Systems, (Academic Press, London) 1976.

  • S. Doplicher, R. Longo, J.E. Roberts, and L. Zsido, editors, Operator Algebras and Quantum Field Theory, (International Press, distributed by AMS) 1997.

  • G.G. Emch, Algebraic Methods in Statistical Mechanics and Quantum Field Theory, (John Wiley & Sons, New York), 1972.

  • D.E. Evans and Y. Kawahigashi, Quantum Symmetries on Operator Algebras, (Oxford University Press, Oxford), 1998.

  • R. Haag, Local Quantum Physics, (Springer Verlag, Berlin) 1992. (A second edition was released in 1996.)

  • J. Hamhalter, Quantum Measure Theory , (Kluwer Academic, Dordrecht, Boston and London) 2003.

  • A. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, (North-Holland, Amsterdam) 1982.

  • A. Holevo, Statistical Structure of Quantum Theory, ( Springer Verlag, Berlin) 2001.

  • S.S. Horuzhy, Introduction to Algebraic Quantum Field Theory, (Kluwer Academic Publishers, Dordrecht) 1990 (translation of Russian edition (1986)).

  • R. Jost, General Theory of Quantized Fields, (American Mathematical Society, Providence, RI), 1965.

  • D. Kastler, editor, The Algebraic Theory of Superselection Sectors, (World Scientific, Singapore), 1990. (A collection of articles which intends to serve as an introduction to aspects of AQFT.)

  • K. Kraus, States, Effects, and Operations, Lecture Notes in Physics, (Springer Verlag, Berlin) 1983.

  • N.P. Landsman, Mathematical Topics Between Classical and Quantum Mechanics, (Springer Verlag, New York), 1998.

  • J. von Neumann, Mathematical Foundations of Quantum Mechanics , (Princeton University Press, Princeton) 1955 (amended version of original German edition Mathematische Grundlagen der Quantenmechanik, (Springer Verlag, Berlin) 1932).

  • M. Ohya and D. Petz, Quantum Entropy and Its Use, (Springer Verlag, Berlin) 1993.

  • D. Petz, An Invitation to the Algebra of Canonical Commutation Relations, (Leuven University Press, Leuven), 1990.

  • H. Primas, Chemistry, Quantum Mechanics and Reductionism (Springer Verlag, Berlin) 1983.

  • M. Rédei, Quantum Logic in Algebraic Approach, (Kluwer Academic Publishers, Dordrecht) 1998.

  • M. Rédei and M. Stölzner, editors, John von Neumann and the Foundations of Quantum Physics, (Vienna Circle Yearbook series, Kluwer Academic Press) 2001.

  • G.L. Sewell, Quantum Theory of Collective Phenomena, (Oxford University Press, Oxford) 1986.

  • G.L. Sewell, Quantum Mechanics and Its Emergent Macrophysics, (Princeton University Press, Oxford) 2002.

  • O. Steinmann, Perturbative QED and Axiomatic Field Theory, (Springer Verlag, Berlin) 2000.

  • R.F. Streater and A.S. Wightman, PCT, Spin and Statistics, and All That, (W.A. Benjamin, Reading, Mass.), 1964 (particularly the new edition with an appendix on AQFT).

  • W. Thirring, Quantenmechanik grosser Systeme, (Springer Verlag, Vienna) 1980; English translation: A Course in Mathematical Physics, 4: Quantum Mechanics of Large Systems , (Springer Verlag, New York).

  • R.M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics , (University of Chicago Press) 1994.



    • Links to Interesting Papers Suggesting the Power of the Algebraic Approach

  • A nicely written, minimally technical SURVEY of the (then) current status of axiomatic quantum field theory, entitled "Current Trends in Axiomatic Quantum Field Theory", by Detlev Buchholz.
  • Another nicely written SURVEY of the (then) current status of axiomatic quantum field theory, entitled "Algebraic Quantum Field Theory: A Status Report", Detlev Buchholz' plenary address at the London IAMP Congress.
  • A somewhat more detailed OVERVIEW of the (then) current status of axiomatic quantum field theory, by Detlev Buchholz and Rudolph Haag.
  • An idiosyncratic (also in its English) but interesting OVERVIEW of the past thirty years of quantum field theory (up to 1994) by Bert Schroer.
  • A plaidoyer for the physical relevance of algebraic quantum field theory in the PAPER entitled "Motivations and Physical Aims of Algebraic QFT", by Bert Schroer.
  • A minimally technical PAPER by Robert M. Wald, which suggests why the algebraic approach is absolutely necessary, if one wishes to treat quantum fields on curved space-times conceptually and mathematically rigorously.
  • A lovely, minimally technical PAPER by Karl-Henning Rehren, which clearly shows the conceptual advantages which accrue when one takes the more intrinsic point of view of algebraic quantum field theory, this time in application to the currently fashionable topic of Anti-deSitter/Conformal "holography".
  • A visionary PAPER on scattering theory and the concept of "particle" by Detlev Buchholz.
  • A visionary PAPER on high-energy structure and confinement by Detlev Buchholz.
  • The technical PAPER by Detlev Buchholz and Rainer Verch, which provides the mathematical and conceptual foundations for the previous two papers.
  • An intoductory overview of what algebraic quantum field theory can say about the relativistic vacuum on Minkowski space is HERE. I wrote this for the proceedings of an interdisciplinary conference held at Princeton.
  • A nontechnical (no formulae) overview of recent advances in the construction of quantum field models in AQFT is HERE . I originally wrote this for John Baez, but I am keeping it up to date with current developments.




    • An Abridged Bibliography of Research Papers in Algebraic Quantum Field Theory


  • DVI-File HERE (Under Occasional Revision - Last updated on October 26, 2008)


    • Note: To keep the work involved in maintaining this list within reasonable limits, and to maximize its usefulness to the LQP community, I shall introduce the following policy. Since there is now a central preprint archive for LQP papers at the LQP Crossroads in Göttingen, papers will be added to this list if they appear in refereed journals or proceedings and if they are of direct relevance to algebraic quantum field theory. This is admittedly a matter of personal judgement. Most papers on algebraic quantum theory, algebraic quantum statistical mechanics or operator algebra theory, though relevant (and of great interest to me personally), will generally not be listed. Papers on the CCR and CAR are also basically not included (though this, too, is a topic I write on). I encourage enterprising persons to post lists for these topics. Preprints already on this list which do not appear in print within two years will be removed.



    REQUEST:

    Please keep me abreast of your publications.


    Martin Florig's Ph.D. Dissertation

    Since some portions of my former Ph.D. student's, Martin Florig, Dissertation will not be published and since some of those results are of interest to practitioners in the field, I have, with Martin's permission, chosen to make available the DVI-File HERE . Unfortunately, due to technical reasons beyond my control, this is not the final, polished version of Martin's thesis. If you want that, you must write to me so that I may have a copy made of my hardcopy of the final version. Many, but not all, of the results of this thesis will appear in the near future in a series of papers with Martin, Detlev Buchholz and myself. Portions have already appeared in

  • M. Florig, On Borchers Theorem, Letters in Mathematical Physics, 46, 289-293 (1998),
  • D. Buchholz, O. Dreyer, M. Florig and S.J. Summers, Geometric Modular Action and Spacetime Symmetry Groups, Reviews of Mathematical Physics, 12, 475-560 (2000),
  • D. Buchholz, M. Florig and S.J. Summers, An Algebraic Characterization of Vacuum States in Minkowski Space, II: Continuity Aspects, Letters in Mathematical Physics, 49, 337-350 (1999).

    This Dissertation has been accepted and hence published by the University of Florida. Use of these results must be accompanied by appropriate citation of this thesis or, preferably, of one of the papers in the mentioned series.



    • Links to other Groups in Algebraic Quantum Theory (NOT exhaustive)


  • Home Page for the Local Quantum Physics Crossroads in Göttingen
  • Algebraic Quantum Field Theory at DESY
  • Schroedinger Institute for Mathematical Physics in Vienna
  • Mathematical Physics in Adelaide
  • Mathematical Physics in Leuven
  • Mathematical Physics in Berlin
  • More Mathematical Physics in Berlin
  • Even More Mathematical Physics in Berlin
  • Mathematical Physics in Braunschweig






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    Last updated on October 26, 2008