Linked bibliography for the SEP article "Quantum Theory and Mathematical Rigor" by Fred Kronz and Tracy Lupher

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Alvarez, J., 2020, “A Mathematical Presentation of Laurent Schwartz’s Distributions,” Surveys in Mathematics and its Applications 15:1–137. (Scholar)
Antoniou, I. and Prigogine, I., 1993, “Intrinsic Irreversibility and Integrability of Dynamics”, Physica A, 192: 443–464. (Scholar)
Baker, D., 2016, “Philosophy of Quantum Field Theory”, Oxford Handbooks Online, doi: 10.1093/oxfordhb/9780199935314.013.33. (Scholar)
Birkhoff, G., and von Neumann, J., 1936, “The Logic of Quantum Mechanics”, Annals of Mathematics, 37: 823–843. (Scholar)
Berezanskii, J. M., 1968, Expansions in Eigenfunctions of Selfadjoint Operators, Providence, RI: American Mathematical Society, Translations of Mathematical Monographs, 17. [First published in Russian in 1965.] (Scholar)
Bogoliubov, N. N., Logunov, A. A., and Todorov, I. T., 1975, Introduction to Axiomatic Quantum Field Theory, Reading, Massachusetts: The Benjamin/Cummings Publishing Company, Inc. [First published in Russian in 1969.] (Scholar)
Böhm, A., 1966, “Rigged Hilbert Space and Mathematical Description of Physical Systems”, Physica A, 236: 485–549. (Scholar)
Böhm, A. and Gadella, M., 1989, Dirac Kets, Gamow Vectors and Gel’fand Triplets, New York: Springer-Verlag. (Scholar)
Böhm, A., Maxson, S., Loewe, M. and Gadella, M., 1997, “Quantum Mechanical Irreversibility”, in Lectures in Theoretical Physics, 9A: Mathematical Methods of Theoretical Physics, New York: Wiley. (Scholar)
Bratteli, O. and Robinson, D.W., 1979–1981, Operator Algebras and Quantum Statistical Mechanics, Volumes 1–2, New York: Springer-Verlag. (Scholar)
Brunetti, R., Dütsch, M., Fredenhagen, K., 2009, “Perturbative Algebraic Quantum Field Theory and the Renormalization Groups”, Advances in Theoretical and Mathematical Physics, 13 (5): 1541–1599. (Scholar)
Butterfield, J., Bouatta, N., 2015, “Renormalization for philosophers”, In: Bigaj, T., Wüthrich, C. (eds.) Metaphysics in Contemporary Physics, 104: 437–485. (Scholar)
Castagnino, M. and Gadella, M., 2003, “The role of self-induced decoherence in the problem of the classical limit of quantum mechanics,” Foundations of Physics, 36(6): 920–952. (Scholar)
Colombeau, J., 1992, Multiplication of Distributions, Berlin: Springer-Verlag. (Scholar)
–––, 2007, “Mathematical Problems on Generalized Functions and the Canonical Hamiltonian Formalism”, 15 pp. eprint arXiv:0708.3425. (Scholar)
Colombeau, J., and Gsponer, A., 2008, “The Heisenberg-Pauli Canonical Formalism of Quantum Field Theory in the Rigorous Setting of Nonlinear Generalized Functions (Part I)”, 107 pp. eprint arXiv:0807.0289v2. (Scholar)
Colombeau, J.F., Gsponer, A. and Perrot, B., 2008, “Nonlinear generalized functions and the Heisenberg-Pauli foundations of Quantum Field Theory”, 20 pp. eprint arXiv:0705.2396. (Scholar)
Connes, A., 1994, Noncommutative Geometry, San Diego: Academic Press. (Scholar)
DeWitt-Morette, C. Maheshwari, A. and Nelson, B., 1979, “Path Integration in Non-Relativisitic Quantum Mechanics”, in Physics Reports, 50C: 255–372. (Scholar)
Dirac, P. A. M., 1927, “The Quantum Theory of the Emission and Absorption of Radiation”, Proceedings of the Royal Society of London, Series A, 114: 243–265. [It is reprinted in (Schwinger 1958).] (Scholar)
–––, 1930, The Principles of Quantum Mechanics, Oxford: Clarendon Press. (Scholar)
–––, 1933, “The Lagrangian in Quantum Mechanics”, Physikalische Zeitschrift der Sowietunion, 3: 64–72. (Scholar)
–––, 1939, “A New Notation for Quantum Mechanics”, Proceedings of the Cambridge Philosophical Society, 35: 416–418. (Scholar)
–––, 1943, “Quantum Electrodynamics”, Communications of the Dublin Institute for Advanced Studies, A1: 1–36. (Scholar)
Dixmier, J., 1981, Von Neumann Algebras, Amsterdam: North-Holland Publishing Company. [First published in French in 1957: Les Algèbres d’Opérateurs dans l’Espace Hilbertien, Paris: Gauthier-Villars.] (Scholar)
Dyson, F., 1952, “Divergence of perturbation theory in quantum electrodynamics”, Physical Review, 85: 631–632. (Scholar)
Egg, M., Lam, V., Oldofredi, A., 2017, “Particles, cutoffs, and inequivalent representations”, Foundations of Physics, 47 (3): 453–466. (Scholar)
Fell, J. M. G., 1960, “The Dual Spaces of \(C^*\)-Algebras”, Transactions of the American Mathematical Society, 94: 365–403. (Scholar)
Feynman, R. P., 1948, “Space-Time Approach to Non-Relativistic Quantum Mechanics”, Reviews of Modern Physics, 20: 367–387. [It is reprinted in (Schwinger 1958).] (Scholar)
Fleming, G., 2002, “Comments on Paul Teller’s Book ”An Interpretive Introduction to Quantum Field Theory“”, in M. Kuhlmann, H. Lyre and A. Wayne (eds.), Ontological Aspects of Quantum Field Theory, River Edge, NJ: World Scientific: 135–144. (Scholar)
Franssens, G., 2013, “On the impossibility of the convolution of distributions”, CUBO A Mathematical Journal 14(2): 71–77. (Scholar)
Fraser, D., 2009, “Quantum Field Theory: Undetermination, Inconsistency, and Idealization”, Philosophy of Science, 76: 536–567. (Scholar)
–––, 2011, “How to Take Particle Physics Seriously: A Further Defence of Axiomatic Quantum Field Theory”, Studies in History and Philosophy of Modern Physics, 42: 126–135. (Scholar)
Fraser, J., 2016, What is Quantum Field Theory?, Ph.D. Dissertation, University of Leeds. (Scholar)
Fuss, I. G. and Filinkov, A., 2014, “An Introduction to Generalised Functions in Periodic Quantum Theory, 21 pp., eprint arXiv:1406.3436. (Scholar)
Gelfand, I. and Neumark, M., 1943, “On the Imbedding of Normed Rings into the Ring of Operators in Hilbert Space”, Recueil Mathématique [Matematicheskii Sbornik] Nouvelle Série, 12 [54]: 197–213. [Reprinted in \(C^*\)-algebras: 1943–1993, in the series Contemporary Mathematics, 167, Providence, R.I. : American Mathematical Society, 1994.] (Scholar)
Gelfand, I. and Shilov, G. E., 1977, Generalized Functions, Volume 2, New York: Academic Press. [First published in Russian in 1958.] (Scholar)
–––, 1977, Generalized Functions, Volume 3, New York: Academic Press. [First published in Russian in 1958.] (Scholar)
Gelfand, I. and Vilenkin, N. Ya., 1964, Generalized Functions, Volume 4, New York: Academic Press. [First published in Russian in 1961.] (Scholar)
Grosser, M., Kunzinger, M., Oberguggenberger, M., 2001, Geometric Theory of Generalized Functions with Applications to General Relativity, Kluwer Academic Publishers. (Scholar)
Grothendieck, A., 1955, “Produits Tensoriels Topologiques et Espaces Nucléaires”, Memoirs of the American Mathematical Society, 16: 1–140. (Scholar)
Haag, R. and Kastler, D. 1964, “An Algebraic Approach to Quantum Field Theory”, Journal of Mathematical Physics, 5: 848–861. (Scholar)
Haag, R. 1955, “On Quantum Field Theories”, Danske Videnskabernes Selskab Matematisk-Fysiske Meddelelser, 29 (12): 1–37. (Scholar)
–––, 1996, Local Quantum Physics, second revised edition, Berlin: Springer-Verlag. (Scholar)
Halvorson, H., 2007, “Algebraic Quantum Field Theory”, in J. Butterfield and J. Earman (eds.), Philosophy of Physics, Amsterdam: Elsevier: 731–922. (Scholar)
Hancox-Li, L., 2015a, Moving Beyond “Theory T”: The Case of Quantum Field Theory, Ph.D. Dissertation, University of Pittsburgh. (Scholar)
–––, 2015b, “Coarse-Graining as a Route to Microscopic Physics: The Renormalization Group in Quantum Field Theory”, Philosophy of Science, 82 (5): 1211–1223. (Scholar)
–––, 2017, “Solutions in Constructive Field Theory”, Philosophy of Science, 84 (2): 335–358. (Scholar)
Holevo, A. S., 2011, Probabilistic and Statistical Aspects of Quantum Theory, Pisa: Scuola Normale Superiore. (Scholar)
Holland, S. S. Jr., 1970, “The Current Interest in Orthomodular Lattices”, in Trends in Lattice Theory, J. C. Abbott (ed.), New York: Van Nostrand: 41–116. [Reprinted in The Logico-Algebraic Approach to Quantum Mechanics, Vol. 1, C. A. Hooker (ed.), New York: Academic Press, 1972: 437–496] (Scholar)
Horuzhy, S. S., 1990, Introduction to Algebraic Quantum Field Theory, Dordrecht: Kluwer Academic Publishers. (Scholar)
König, H., 1953, “Neue Begründung der Theorie der "Distributionen" von L. Schwartz,” Mathematische Nachrichten 9(3): 129–148. (Scholar)
–––, 1955, “Multiplikation von Distributionen. I,” Mathematische Annalen 128: 420–452. (Scholar)
Kronz, F. M., 1998, “Nonseparability and Quantum Chaos” , Philosophy of Science, 65: 50–75. (Scholar)
–––, 1999, “Bohm’s Ontological Interpretation and Its Relation to Three Formulations of Quantum Mechanics”, Synthese, 117: 31–52. (Scholar)
–––, 2000, “A Model of a Chaotic Open Quantum System”, Proceedings of the 1998 Biennial Meeting of the Philosophy of Science Association: 446–453. (Scholar)
Kronz, F., and Lupher, T., 2005, “Unitarily Inequivalent Representations in Algebraic Quantum Theory”, International Journal of Theoretical Physics, 44 (8): 1239–1258. (Scholar)
Loomis, L., 1955, “The Lattice-Theoretic Background of the Dimension Theory of Operator Algebras”, Memoirs of the American Mathematical Society, 18: 1–36. (Scholar)
Lupher, T., 2018, “The Limits of Physical Equivalence in Algebraic Quantum Field Theory”, British Journal for the Philosophy of Science, 69 (2): 553–576. (Scholar)
Mandl, F., 1959, Introduction to Quantum Field Theory, New York: Wiley. (Scholar)
Nagel, B., 1989, “Introduction to Rigged Hilbert Spaces”, in E. Brändas and N. Elander (eds), Resonances (Springer Lecture Notes in Physics: Volume 325), Berlin: Springer: 1–10. (Scholar)
Nagy, K. L., 1966, State Vector Spaces with Indefinite Metric in Quantum Field Theory, Groningen: P. Noordhoff Ltd. (Scholar)
Nedeljkov, M., Pilipović, S., Scarpalezos, D., 1998, Linear Theory of Colombeau's Generalized Functions, Addison Wesley, Longman. (Scholar)
Oberguggenberger, M., 1992, Multiplication of Distributions and Applications to Partial Differential Equations, Longman Higher Education. (Scholar)
Pavičić, M., 1992, “Bibliography on Quantum Logics and Related Structures”, International Journal of Theoretical Physics, 31: 373–461. (Scholar)
Pauli, W., 1943, “On Dirac’s New Method of Field Quantizations”, Reviews of Modern Physics, 15: 175–207. (Scholar)
Rédei, M., 1998, Quantum Logic in Algebraic Approach, Dordrecht: Kluwer Academic Publishers. (Scholar)
Rédei, M. and Stöltzner, M. (eds), 2001, John von Neumann and the Foundations of Quantum Physics, Vol. 8, Dordrecht: Kluwer Academic Publisers. (Scholar)
Rivers, R. J., 1987, Path Integral Methods in Quantum Field Theory, Cambridge: Cambridge University Press. (Scholar)
Roberts, J. E., 1966, “The Dirac Bra and Ket Formalism”, Journal of Mathematical Physics, 7: 1097–1104. (Scholar)
Ruetsche, L., 2011, Interpreting Quantum Theories, Oxford: Oxford University Press. (Scholar)
–––, 2003, “A Matter of Degree: Putting Unitary Inequivalence to Work”, Philosophy of Science, 70: 1329–1342. (Scholar)
Salmhofer, M., 2007, Renormalization: An Introduction, Berlin: Springer. (Scholar)
Scharf, G., 2014, Finite Quantum Electrodynamics – The Causal Approach (3^rd edition), Dover Publications. (Scholar)
Schrödinger, E., 1926, “On the Relation of the Heisenberg-Born-Jordan Quantum Mechanics and Mine”, Annalen der Physik, 79: 734–756. (Scholar)
–––, 1928, Collected Papers on Wave Mechanics, London: Blackie & Son. (Scholar)
Schwartz, L., 1945, “Généralisation de la Notion de Fonction, de Dérivation, de Transformation de Fourier et Applications Mathématiques et Physiques”, Annales de l’Université de Grenoble, 21: 57–74. (Scholar)
–––, 1951–1952, Théorie des Distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, Volumes 9–10, Paris: Hermann. (Scholar)
–––, 1954, “Sur l’impossibilite de la multiplications des distributions”, Paris: Comptes Rendus de l'Académie des Sciences 239: 847–848 (Scholar)
Schwinger, J. S., 1958, Selected Papers on Quantum Electrodynamics, New York: Dover. (Scholar)
Segal, I. E., 1947a, “Irreducible Representations of Operator Algebras”, Bulletin of the American Mathematical Society, 53: 73–88. (Scholar)
–––, 1947b, “Postulates for General Quantum Mechanics”, Annals of Mathematics, 4: 930–948. (Scholar)
–––, 1959, “Foundations of the Theory of Dynamical Systems of Infinitely Many Degrees of Freedom I”, Danske Videnskabernes Selskab Matematisk-Fysiske Meddelelser, 31 (12): 1–39. (Scholar)
Steinmann, O., 2000, Perturbative Quantum Electrodynamics and Axiomatic Field Theory, Berlin, Heidelberg: Springer. (Scholar)
Sewell, G.L., 1986, Quantum Theory of Collective Phenomena, Oxford: Oxford University Press. (Scholar)
Streater, R. F. and Wightman, A. S., 1964, PCT, Spin and Statistics, and All That, New York: W. A. Benjamin. (Scholar)
Sunder, V. S., 1987, An Invitation to von Neumann Algebras, New York: Springer-Verlag. (Scholar)
Swanson, N., 2014, Modular Theory and Spacetime Structure in QFT, Ph.D. Dissertation, Princeton University. (Scholar)
–––, 2017, “A philosopher’s guide to the foundations of quantum field theory”, Philosophy Compass, 12 (5): e12414.
Treves, F., 1967, Topological Vector Spaces, Distributions and Kernels, Academic Press. (Scholar)
von Mises, R., 1981, Probability, Statistics and Truth, second revised English edition, New York: Dover; first published in German, Wahrscheinlichkeit, Statistik und Wahrheit, Berlin: Springer, 1928. (Scholar)
von Neumann, J., 1937, “Quantum Mechanics of Infinite Systems”, first published in (Rédei and Stöltzner 2001, 249–268). [A mimeographed version of a lecture given at Pauli’s seminar held at the Institute for Advanced Study in 1937, John von Neumann Archive, Library of Congress, Washington, D.C.] (Scholar)
–––, 1938, “On Infinite Direct Products”, Compositio Mathematica, 6: 1–77. [Reprinted in von Neumann 1961–1963, Vol. III).] (Scholar)
–––, 1955, Mathematical Foundations of Quantum Mechanics, Princeton, NJ: Princeton University Press. [First published in German in 1932: Mathematische Grundlagen der Quantenmechank, Berlin: Springer.] (Scholar)
–––, 1961–1963, Collected Works, 6 volumes, A. H. Taub (ed.), New York: Pergamon Press. (Scholar)
–––, 1981, Continuous geometries with a transition probability, Halperin, I. (ed.), Providence: Memoirs of the American Mathematical Society. (Scholar)
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Waerden, B. L. van der, (ed.), 1967, Sources of Quantum Mechanics, Amsterdam: North Holland Publishing Company. (Scholar)
Wallace, D., 2006, “In Defense of Naiveté: The Conceptual Status of Lagrangian Quantum Field Theory”, Synthese, 151: 33–80. (Scholar)
–––, 2011, “Taking Particle Physics Seriously: A Critique of the Algebraic Approach to Quantum Field Theory”, Studies in History and Philosophy of Modern Physics, 42: 116–125. (Scholar)
Weinberg, S., 1995, The Quantum Theory of Fields, New York: Cambridge University Press. (Scholar)
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