Underground seminar on open problems in quantum foundations

(Underground Quantum Fight Club)

Mondays 5-7pm, Gravity Room, Perimeter Institute for Theoretical Physics, 31 Caroline St N, Waterloo ON

(previously: Mondays, 6:15-8:30 p.m., Sky room, Perimeter Institute for Theoretical Physics, 31 Caroline St N, Waterloo ON)
(previously: Mondays, 9:15-11:15 a.m., Department of Physics, University of Warsaw, Warszawa, Hoża 69, room N21)

organised & supervised by Ryszard Kostecki



Season 4: Fall 2014/Spring 2015: Into the landscape of foundational quandaries

Participants: Ben Burdick, John DeBrota, Dylan Butson, Illan Halpern, Morten Munk-Nielsen, Thomas O'Brien, Daniel Ranard
  1. (10.11.2014). Meeting #0
  2. (20.11.2014). Into the landscape, part I
    stuff to read in advance: Edwin Jaynes - Information theory and statistical mechanics (1957).
  3. (24.11.2014). Into the landscape, part II
    stuff to read in advance: Bogdan Mielnik - Convex geometry: a travel to the limits of our knowledge (2012).
  4. (08.12.2014). Into the landscape, part III
    stuff to read in advance: Chris Fuchs - QBism, the perimeter of quantum bayesianism (2010).
  5. (12.01.2015). Into the landscape, part IV
    stuff to read in advance: Lluís Masanes, Markus Müller - Three-dimensionality of space and the quantum bit: an information-theoretic approach (2013).
  6. (26.01.2015). Symmetric monoidal categories approach to quantum foundations, part I - Illan Halpern & Daniel Ranard.
  7. (02.02.2015). Symmetric monoidal categories approach to quantum foundations, part II - Illan Halpern & Daniel Ranard.
  8. (09.02.2015). Symmetric monoidal categories approach to quantum foundations, part III - Illan Halpern & Daniel Ranard.
  9. (17.02.2015). C*-algebraic approach to quantum foundations, part I - Dylan Butson & Tom O'Brien.
  10. (24.02.2015). C*-algebraic approach to quantum foundations, part II - Dylan Butson & Tom O'Brien.
  11. (03.03.2015). C*-algebraic approach to quantum foundations, part III - Dylan Butson & Tom O'Brien.
  12. (24.03.2015). Convex set/operational approach to quantum foundations, part I - Ben Burdick & Morten Munk-Nielsen.
  13. (31.03.2015). Convex set/operational approach to quantum foundations, part II - Ben Burdick & Morten Munk-Nielsen.
  14. (??.04.2015). Convex set/operational approach to quantum foundations, part III - Ben Burdick & Morten Munk-Nielsen.
  15. (??.04.2015). Quantum information geometric approach to quantum foundations, part I: Classical information geometry - John DeBrota.
  16. (14.04.2015). Quantum information geometric approach to quantum foundations, part II: Kaehler geometry and Poisson flows of density matrices - Dylan Butson.
  17. (21.04.2015). Quantum information geometric approach to quantum foundations, part III: Nonlinear information kinematics and dynamics - Ryszard Kostecki.
  18. (12.06.2015). Into the landscape, part V (coda)
    stuff to read in advance: Ted Jacobson - Thermodynamics of spacetime: the Einstein equation of state (1995).




Season 3: Spring 2014: Beyond von Neumann's foundations of quantum mechanics

Participants: Aysha Abdel-Aziz, Emily Adlam, Dylan Butson, Jeffrey Epstein, Max Klambauer, Nicco Pomata, Jason Wien
  1. (03.02.2014). Differential and symplectic geometry of pure quantum states I - Nicco Pomata
  2. (10.02.2014). Differential and symplectic geometry of pure quantum states II - Nicco Pomata

    Topics: Symplectic and riemannian geometry of projective quantum space, plus geometric phases as holonomies. How the specific conceptual and structural components of the Hilbert space based formalism for QM are reformulated in this setting? Linearity vs nonlinearity. Infinite dimensions? Kaehler manifolds beyond CPn?
     
  3. (17.02.2014). Symplectic geometry of density matrices and nonlinear observables I - Dylan Butson
  4. (24.02.2014). Symplectic geometry of density matrices and nonlinear observables II - Dylan Butson

    Topics: Adjoint actions. Poisson manifolds of quantum states. Nonlinear generalisations of unitary evolution as hamiltonian flows. Nonlinear observables and their properties. Examples.
     
  5. (24.02.2014). Entropy and riemannian geometry of probability densities I - Jeffrey Epstein
  6. (03.03.2014). Entropy and riemannian geometry of probability densities II - Jeffrey Epstein

    Topics: Probabilistic models and manifolds. Examples. Relative entropy functionals. Probabilistic riemannian metrics and affine connections. Norden--Sen and Chencov--Amari geometries. Markovian monotonicity. Chencov theorem. Eguchi equations. Dually flat probabilistic manifolds. Geometry of normal, exponential, and transformation models. Geometrisation of classical statistical mechanics.
     
  7. (24/31.03.2014). Unitarily inequivalent representations, C*-algebraic approach, and noncommutative integration I - Max Klambauer
  8. (31/07.04.2014). Unitarily inequivalent representations, C*-algebraic approach, and noncommutative integration II - Max Klambauer

    Topics: The problem of unitary inequivalence on examples. Haag's theorem and its implication for description of interaction in QFT, and for particle interpretation. Borchers' class of quantum fields. Basic mathematical structure of C*- and W*-algebras. Noncommutative integration theory. Gel'fand--Naimark--Segal construction. KMS states and postulates of AQFT. How much (and why?) these approaches were (un)able to achieve when it comes to the description of predictive quantum dynamics.
     
  9. (14.04.2014). Logico-algebraic approaches to quantum foundations and quantum measure theory I - Jason Wien
  10. (21.04.2014). Logico-algebraic approaches to quantum foundations and quantum measure theory II - Jason Wien

    Topics: Syntactic approaches: Birkhoff--von Neumann approach, framework based on posets (Mackey) vs lattices (Piron); semantic approach: partial boolean algebras (Kochen--Specker). Gleason theorem. Quantum measure theory. Quarrels with reconstruction theorems. Problems with tensor products, sequential measurements, and with interpretation.
     
    the following seminars were scheduled, but have been cancelled due to intense involvement of most of PSI students in their graduation projects:
     
  11. (28.04.2014). Nonequilibrium statistical mechanics as an information theory I - Nafiz Ishtiaque
  12. (05.05.2014). Nonequilibrium statistical mechanics as an information theory II - Nafiz Ishtiaque

    Topics: Jaynes' derivation of equilibrium statistical mechanics from information theory. Information theory vs Clausius entropy. Information theoretic derivation of second law of thermodynamics. Nonequilibrium statistical mechanics from entropy maximisation: Jaynes--Scalapino, Mitchell, Zubarev--Kalashnikov, Grandy.
     
  13. (12.05.2014). Entropy and riemannian geometry of density matrices I - Ryszard Kostecki
  14. (19.05.2014). Entropy and riemannian geometry of density matrices II - Ryszard Kostecki

    Topics: Quantum models and manifolds. Examples. Quantum relative entropies, quantum riemannian metrics and affine connections. Petz, Lesniewski--Ruskai, and Jencova theorems. Geometries of some quantum models. Relationship with information geometries of pure quantum states and of probability densities.
     
  15. (26.05.2014). From POVMs to non-markovian quantum evolutions - Wojciech Kamiński

    Topics: Motivations, structure, and limitations of the framework of POV measures and TPCP instruments. Stinepring, Holevo, and Ozawa theorems. Conclusions from the Pechukas--Alicki discussion. Review of the reasons for and the approaches to non-markovian quantum evolutions.
     
  16. (02.06.2014). Towards new, "general", quantum theory? - Ryszard Kostecki

    Topics: An overview of mathematical and conceptual insights covered in all previous talks. Discussion of their mutual relationships. Big picture questions re-loaded. Which paradigms are reactionary, which may be revolutionary? If von Neumann's quantum mechanics is an analogue of the special relativity, then what may correspond to the general relativity? If quantum field theory is an analogue of the Ptolomean epicycles theory, then what may correspond to the Keplerian theory? Where do we stand? Where do we go from here?
     
Season 2: Spring 2012: Non-orthodox approaches to quantum field theory

Participants: Paweł Duch, Mateusz Iskrzyński, Marcin Kotowski, Michał Kotowski, Jan Liszka-Dalecki
  1. (20.02.2012). Three different approaches to QFT: a background of Schwinger's approach - Paweł Duch
  2. (27.02.2012). Schwinger's source theory - part I - Paweł Duch
  3. (05.03.2012). Schwinger's source theory - part II - Paweł Duch
  4. (12.03.2012). Schwinger's action principle - Mateusz Iskrzyński
  5. (26.03.2012). Dittrich's analysis of Schwinger's approach - Paweł Duch
  6. (07.05.2012). Brunetti--Fredenhagen--Verch approach - part I - Jan Liszka-Dalecki
  7. (14.05.2012). Brunetti--Fredenhagen--Verch approach - part II - Jan Liszka-Dalecki
  8. (21.05.2012). Brunetti--Fredenhagen--Verch approach - part III - Jan Liszka-Dalecki
     
Edition 1: Spring 2011: Foundational issues in quantum theory

Participants: Paweł Duch, Bogusia Gorczyca, Mateusz Iskrzyński, Marcin Kotowski, Michał Kotowski, Jędrek Świeżewski
  1. (17.02.2011). Sketch of the programme - Ryszard Kostecki
    main text:  
  2. (24.02.2011). Elements of mathematical formalism of Hilbert space quantum mechanics & Algebraic approach to quantum theory I - Ryszard Kostecki
    main texts:
    • Miklos Redei, Stephen Summers, 2007, Quantum probability theory
    • Klaas Landsman, 2009, Algebraic quantum mechanics
    additional texts:
    (take a look on introductions, and your favorite topics of interest)
    • Rudolf Haag, 1996, Local quantum physics (see especially II.3, II.4 and III.1 for fundamental motivation of an algebraic approach exposed in mathematical detail but with particle theory oriented "physical" flavour; alternatively see V.1.1-V.1.3 for motivation comming from quantum equilibrium statistical mechanics)
    • Bert Schroer, 1998, A course on modular localization and nonperturbative local quantum physics (here these topics are treated more extensively and with more applications)
    • Gerard Emch, 1972, Algebraic methods in statistical mechanics and quantum field theory (first and still very good book about algebraic approach)
    • Hans Halvorson, 2006, Algebraic quantum field theory (a detailed review of the mathematics of algebraic approach with the extensive discussion of the algebraic analysis of superselection)
    • Miklos Redei, 1998, Quantum logic in algebraic approach (algebraic perspective on quantum logic issues; also very good book)
     
  3. (03.03.2011). Haag's theorem and the failure of particle and field interpretations - Mateusz Iskrzyński
    main texts:
    • John Earman, Doreen Fraser, 2006, Haag's theorem and its implications for the foundations of QFT
    • Doreen Fraser, 2008, The fate of ‘particles’ in quantum field theories with interactions
    • Stephen Summers, 1998, On the Stone-von Neumann uniqueness theorem and its ramifications
    • Frederick Kronz, Tracy Lupher, 2005, Unitarily inequivalent representations in algebraic quantum theory
    additional texts:
    • David Baker, 2008, Against field interpretations of quantum field theory
    • Rob Clifton, Hans Halvorson, 2000, Are Rindler quanta real? Inequivalent particle concepts in quantum field theory
    • Jonathan Bain, 2000, Who is afraid of Haag's theorem?
    • Doreen Fraser, 2009, Quantum field theory - underdetermination, inconsistency, and idealization
    • Tracy Lupher, 2005, Who proved Haag’s theorem?
    • Gerard Emch, 1972, Algebraic methods in statistical mechanics and quantum field theory, pp.247-253
    • Rudolf Haag, 1955, On quantum field theories
     
  4. (17.03.2011). Haag theorem, etc. II - Mateusz Iskrzyński
     
  5. (24.03.2011). POVM's and the failure of usual notion of observable - Paweł Duch
    main texts:
    • Paul Busch, Pekka Lahti, 2008, Observable
    • D.A. Dubin, M. A. Hennings, P. Lahti, J.-P. Pellonpää, 2002, A dilemma in representing observables in quantum mechanics
    • W. M. de Muynck, W. De Baere, H. Martens, 1994, Interpretations of quantum mechanics, joint measurement of incompatible observables, and counterfactual definiteness
    additional texts:
    • Pekka Lahti, Juha-Pekka Pellonpää, Kari Ylinen, 2005, Two questions on quantum probability
    • E.B. Davies, J.T. Lewis, 1970, An operational approach to quantum probability
    • Teiko Heinosaari, Mario Ziman, 2008, Guide to mathematical concepts of quantum theory
    • Roderich Tumulka, 2007, POVM
    • E.B. Davies, 1976, Quantum theory of open systems
     
  6. (31.03.2011). Algebraic approach to quantum theory II - Ryszard Kostecki
    main texts:
    • Ryszard Kostecki, 2011, An introduction to algebraic approach to quantum theory (draft)
    additional texts:
    • Rudolf Haag, 1996, Local quantum physics (sections II.5.5 and V.1-3)
     
  7. (07.04.2011). Path integrals: review of approaches and problems - Jędrek Świeżewski
    main texts:
    • John Klauder, 2003, The Feynman path integral: an historical slice
    • Pierre Cartier, Cecile DeWitt-Morette, 1995, A new perspective on functional integration
    • Sergio Albeverio, Raphael Høegh-Krohn, Sonia Mazzucchi, 2008, Mathematical theory of Feynman path integrals (chapter 1 and section 10.4)
    additional texts:
    • R.J. Rivers, 1987, Path integral methods in quantum field theory (chapter 6)
    • Hagen Kleinert, 2003, Path integrals in quantum mechanics, statistics, polymer physics, and financial markets
    • M. Chaichian, A. Demichev, 2001, Path integrals in physics
     
  8. (21.04.2011). Renormalisation: review of approaches - Bogusia Gorczyca
    main texts:
    • Tian Yu Cao, Silvan S. Schweber, 1993, The conceptual foundatons and the philosophical aspects of renormalization theory
    • Bertrand Delamotte, 2003, A hint of renormalization
    additional texts:
    • John C. Collins, 1984, Renormalization - An introduction to renormalization, the renormalization group, and the operator-product expansion
    • Giuseppe Benfatto, Giovanni Gallavotti, 1993, Renormalization group
    • Michael Duetsch, 2010, Connection between the renormalization groups of Stückelberg-Petermann and Wilson
    • Michael Duetsch, Klaus Fredenhagen, 2004, Perturbative renormalisation and BRST
     
  9. (05.05.2011). Renormalisation: Epstein--Glaser approach - Paweł Duch
    main texts:
    • Günter Scharf, 1995, Finite quantum electrodynamics - the causal approach
    • Gudrun Pinter, 2000, Epstein-Glaser Renormalization - Finite Renormalizations, the S-Matrix of phi4 Theory and the Action Principle
    additional texts:
    • H. Epstein, V. Glaser, 1973, The role of locality in perturbation theory
    • Romeo Brunetti, Klaus Fredenhagen, 1997, Interacting quantum fields in curved space - renormalizability of phi4
     
  10. (19.05.2011). Renormalisation: Epstein--Glaser approach II - Paweł Duch
  11. (24.06.2011). Quantum theory and space-time from quantum information geometry - Ryszard Kostecki
     
Season 0: Summer 2008: From germs and groupoids to quantum theory

Participants: Jan Gutt, Wojciech Kamiński, Jacek Kopeć
  1. (22.07.2008). Differential geometry and smooth analysis in toposes, part II - Ryszard Kostecki
  2. (22.07.2008). Germs of algebraic states in Haag-Ojima-Bostelmann approach, part III - Jacek Kopeć
  3. (21.07.2008). Germs of algebraic states in Haag-Ojima-Bostelmann approach, part II - Jacek Kopeć
  4. (21.07.2008). Differential geometry and smooth analysis in toposes, part I - Ryszard Kostecki
  5. (21.07.2008). Quantisation of groupoids a la Landsman, part II - Jan Gutt
  6. (21.07.2008). Germs of algebraic states in Haag-Ojima-Bostelmann approach, part I - Jacek Kopeć
  7. (20.07.2008). Quantisation of groupoids a la Landsman, part I - Jan Gutt

 
last update: 12.5.2015, 23:34