Summers, Stephen J.

• 2752524
  Summers, Stephen J.(1-FL)
  Yet more ado about nothing: the remarkable relativistic vacuum state. Deep beauty, 317–341, Cambridge Univ. Press, Cambridge, 2011.
  81R15 (46L60 81T05)
  
• 2793931
  Buchholz, Detlev(D-GTN-P); Lechner, Gandalf(A-WIENP); Summers, Stephen J.(1-FL)
  Warped convolutions, Rieffel deformations and the construction of quantum field theories. (English summary)
  Comm. Math. Phys. 304 (2011), no. 1, 95–123.
  81Txx (46Lxx 81Rxx)
  
• 2738085
  Rédei, Miklós(4-LSE-DQL); Summers, Stephen J.(1-FL)
  When are quantum systems operationally independent? (English summary)
  Internat. J. Theoret. Phys. 49 (2010), no. 12, 3250–3261.
  81Pxx
  
• 2533174
  Summers, Stephen J.(1-FL)
  Subsystems and independence in relativistic microscopic physics. (English summary)
  Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Modern Phys. 40 (2009), no. 2, 133--141.
  81P05 (81P15 83A05)
  
• 2588578
  Buchholz, Detlev(D-GTN-P); Summers, Stephen J.(1-FL)
  Warped convolutions: a novel tool in the construction of quantum field theories. (English summary) Quantum field theory and beyond, 107--121, World Sci. Publ., Hackensack, NJ, 2008.
  81T08 (81-02)
  
• 2359584
  Rédei, Miklós(H-EOTVO-HQS); Summers, Stephen J.(1-FL)
  Remarks on causality in relativistic quantum field theory. (English summary)
  Corrected republication of Internat. J. Theoret. Phys. 44 (2005), no. 7, 1029--1039 [ MR2199518].
  Internat. J. Theoret. Phys. 46 (2007), no. 8, 2053--2062.
  81R15 (81T05)
  
• 2344471
  Rédei, Miklós(4-LSE-DQL); Summers, Stephen Jeffrey(1-FL)
  Quantum probability theory. (English summary)
  Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Modern Phys. 38 (2007), no. 2, 390--417.
  81S25 (46L53 46L60 46N50 60A05 81P05 81R15)
  
• 2316323
  Buchholz, Detlev(D-GTN-P); Summers, Stephen J.(1-FL)
  String- and brane-localized causal fields in a strongly nonlocal model. (English summary)
  J. Phys. A 40 (2007), no. 9, 2147--2163.
  81T30 (81T05 81T40)
  
• 2211835
  Buchholz, Detlev(D-GTN-P); Summers, Stephen J.(1-FL)
  Geometric modular action and spontaneous symmetry breaking. (English. English summary)
  Ann. Henri Poincaré 6 (2005), no. 4, 607--624.
  81T05 (81R15 81R40)
• 2199518
  Svozil, Karl(A-TUWN); Rédei, Miklós(H-EOTVO-HQS); Summers, Stephen J.(1-FL)
  Remarks on causality in relativistic quantum field theory. (English. English summary)
  Internat. J. Theoret. Phys. 44 (2005), no. 7, 1029--1039.
  81R15 (81T05)
• 2120161
  Buchholz, Detlev(D-GTN-P); Summers, Stephen J.(1-FL)
  Quantum statistics and locality. (English. English summary)
  Phys. Lett. A 337 (2005), no. 1-2, 17--21.
  81R15 (81Pxx)
• 2105223
  Buchholz, Detlev(D-GTN-P); Summers, Stephen J.(1-FL)
  Stable quantum systems in anti-de Sitter space: causality, independence, and spectral properties. (English. English summary)
  J. Math. Phys. 45 (2004), no. 12, 4810--4831.
  81T20
• 2053946
  Buchholz, Detlev(D-GTN-P); Summers, Stephen J.(1-FL)
  An algebraic characterization of vacuum states in Minkowski space. III. Reflection maps. (English. English summary)
  Comm. Math. Phys. 246 (2004), no. 3, 625--641.
  81T05 (46Lxx)
• 2007180
  Summers, Stephen J.(1-FL); White, Richard K.
  On deriving space-time from quantum observables and states. (English. English summary)
  Dedicated to Rudolf Haag.
  Comm. Math. Phys. 237 (2003), no. 1-2, 203--220.
  81Txx (46Lxx 81Pxx)
• 1956312
  Buchholz, Detlev(D-GTN-P); Mund, Jens(D-GTN-P); Summers, Stephen J.(1-FL)
  Covariant and quasi-covariant quantum dynamics in Robertson-Walker spacetimes. (English. English summary)
  Classical Quantum Gravity 19 (2002), no. 24, 6417--6434.
  81T20 (81T05 83C47)
• 1899281
  Rédei, Miklós(H-EOTVO-HQS); Summers, Stephen J.(1-FL)
  Local primitive causality and the common cause principle in quantum field theory. (English. English summary)
  Found. Phys. 32 (2002), no. 3, 335--355.
  81T05 (81P05 81R15)
• 2042745
  Summers, Stephen J.(1-FL)
  On the Stone-von Neumann uniqueness theorem and its ramifications.
  John von Neumann and the foundations of quantum physics (Budapest, 1999), 135--152,
  Vienna Circ. Inst. Yearb., 8,
  Kluwer Acad. Publ., Dordrecht, 2001.
  81P05 (22D05 47N50 81-03 81S05)
• 1867547
  Buchholz, Detlev(D-GTN-P); Mund, Jens(D-GTN-P); Summers, Stephen J.(1-FL)
  Transplantation of local nets and geometric modular action on Robertson-Walker space-times. (English. English summary)
  Mathematical physics in mathematics and physics (Siena, 2000), 65--81,
  Fields Inst. Commun., 30,
  Amer. Math. Soc., Providence, RI, 2001.
  81T20 (46L60 81T05)
• 1763842
  Buchholz, Detlev(D-GTN-P); Dreyer, Olaf(1-PAS-P); Florig, Martin(1-FL); Summers, Stephen J.(1-FL)
  Geometric modular action and spacetime symmetry groups. (English. English summary)
  Rev. Math. Phys. 12 (2000), no. 4, 475--560.
  81T05 (46L60 46N50 47N50)
• 1739258
  Buchholz, Detlev(D-GTN-P); Florig, Martin(1-FL); Summers, Stephen J.(1-FL)
  The second law of thermodynamics, TCP and Einstein causality in anti-de Sitter spacetime. (English. English summary)
  Classical Quantum Gravity 17 (2000), no. 2, L31--L37.
  83C47 (46L60 81T05 81T20)
• 1734324
  Florig, Martin(1-FL); Summers, Stephen J.(1-FL)
  Further representations of the canonical commutation relations.
  Proc. London Math. Soc. (3) 80 (2000), no. 2, 451--490.
  81S05 (46L60 47N50 81T10)
• 1749576
  Buchholz, Detlev(D-GTN-P); Florig, Martin(1-FL); Summers, Stephen J.(1-FL)
  An algebraic characterization of vacuum states in Minkowski space. II. Continuity aspects. (English. English summary)
  Lett. Math. Phys. 49 (1999), no. 4, 337--350.
  81T05 (46L60)
• 1491147
  Summers, Stephen J.(1-FL)
  Bell's inequalities and algebraic structure.
  Operator algebras and quantum field theory (Rome, 1996), 633--646,
  Internat. Press, Cambridge, MA, 1997.
  46L60 (46L10 81P15)
• 1435671
  Florig, Martin(1-FL); Summers, Stephen J.(1-FL)
  On the statistical independence of algebras of observables. (English. English summary)
  J. Math. Phys. 38 (1997), no. 3, 1318--1328.
  81T05 (46L50 46L60)
• 1407754
  Summers, Stephen J.(1-FL)
  Geometric modular action and transformation groups. (English. English, French summary)
  New problems in the general theory of fields and particles, Part II (Paris, 1994).
  Ann. Inst. H. Poincaré Phys. Théor. 64 (1996), no. 4, 409--432.
  81T05 (46L10 46L60)
• 1391196
  Summers, Stephen J.(1-FL); Verch, Rainer(D-HAMB-2P)
  Modular inclusion, the Hawking temperature, and quantum field theory in curved spacetime. (English. English summary)
  Lett. Math. Phys. 37 (1996), no. 2, 145--158.
  81T05 (46L60 81T20 83C47 83C57)
• 1367671
  Proksch, Martin(D-WRZB-P); Reents, George(D-WRZB-P); Summers, Stephen J.(1-FL)
  Quadratic representations of the canonical commutation relations. (English. English summary)
  Publ. Res. Inst. Math. Sci. 31 (1995), no. 5, 755--804.
  81S05 (46L60 46N50 47D45 81T08 81V80)
• 1326345
  Summers, Stephen J.(1-FL); Werner, Reinhard F.(D-OSNB-P)
  On Bell's inequalities and algebraic invariants. (English. English summary)
  Lett. Math. Phys. 33 (1995), no. 4, 321--334.
  81T05 (46L60 47N50)
• 1350574
  Reents, Georg(D-WRZB-P); Summers, Stephen J.(1-FL)
  Beyond coherent states: higher order representations. (English. English summary)
  On Klauder's path: a field trip, 179--188,
  World Sci. Publishing, River Edge, NJ, 1994.
  81S05 (81R30)
• 1231637
  Buchholz, Detlev(D-HAMB-2P); Summers, Stephen J.(1-FL)
  An algebraic characterization of vacuum states in Minkowski space. (English. English summary)
  Comm. Math. Phys. 155 (1993), no. 3, 449--458.
  81T05 (46L60 46N50 81T20)
• 1091323
  Summers, Stephen J.(F-CNRS-T)
  Bell's inequalities and quantum field theory.
  Quantum probability and applications, V (Heidelberg, 1988), 393--413,
  Lecture Notes in Math., 1442,
  Springer, Berlin, 1990.
  81P15 (46L60 81T99)
• 1090281
  Summers, Stephen J.(1-FL)
  On the independence of local algebras in quantum field theory.
  Rev. Math. Phys. 2 (1990), no. 2, 201--247.
  81T05 (46L60)
• 984150
  Summers, Stephen J.(1-RCT); Werner, Reinhard(D-OSNB-P)
  Maximal violation of Bell's inequalities for algebras of observables in tangent spacetime regions. (English. French summary)
  Ann. Inst. H. Poincaré Phys. Théor. 49 (1988), no. 2, 215--243.
  81E05 (46N05 81B05)
• 929934
  Summers, Stephen J.(1-RCT)
  From algebras of local observables to quantum fields: generalized $H$-bounds.
  Helv. Phys. Acta 60 (1987), no. 8, 1004--1023.
  81E05 (46L60 46N05)
• 921310
  Summers, Stephen J.(1-RCT); Wichmann, Eyvind H.(1-CA-P)
  Concerning the condition of additivity in quantum field theory. (English. French summary)
  Ann. Inst. H. Poincaré Phys. Théor. 47 (1987), no. 2, 113--124.
  81E05
• 908016
  Summers, Stephen J.(1-RCT); Werner, Reinhard(D-OSNB-P)
  Bell's inequalities and quantum field theory. II. Bell's inequalities are maximally violated in the vacuum.
  J. Math. Phys. 28 (1987), no. 10, 2448--2456.
  81B05 (81E05)
• 908015
  Summers, Stephen J.(1-RCT); Werner, Reinhard(D-OSNB-P)
  Bell's inequalities and quantum field theory. I. General setting.
  J. Math. Phys. 28 (1987), no. 10, 2440--2447.
  81B05 (81E05)
• 887998
  Summers, Stephen J.(1-RCT); Werner, Reinhard(D-OSNB-P)
  Maximal violation of Bell's inequalities is generic in quantum field theory.
  Comm. Math. Phys. 110 (1987), no. 2, 247--259.
  81E05 (46L60 81B10)
• 847127
  Driessler, Wulf(D-OSNB-P); Summers, Stephen J.(D-OSNB-P); Wichmann, Eyvind H.(1-CA-P)
  On the connection between quantum fields and later von Neumann algebras of local operators.
  Comm. Math. Phys. 105 (1986), no. 1, 49--84.
  46L60 (81E05)
• 845432
  Driessler, Wulf(D-OSNB-P); Summers, Stephen J.(1-RCT)
  On the decomposition of relativistic quantum field theories into pure phases.
  Helv. Phys. Acta 59 (1986), no. 3, 331--348.
  81E05
• 817532
  Driessler, Wulf(D-OSNB-P); Summers, Stephen J.(1-RCT)
  Central decomposition of Poincaré-invariant nets of local field algebras and absence of spontaneous breaking of the Lorentz group. (English. French summary)
  Ann. Inst. H. Poincaré Phys. Théor. 43 (1985), no. 2, 147--166.
  81E05 (46L60)
• 803854
  Summers, Stephen J.(1-RCT); Werner, Reinhard(D-OSNAV)
  The vacuum violates Bell's inequalities.
  Phys. Lett. A 110 (1985), no. 5, 257--259.
  81B05 (81E99)
• 731205
• 727774
  Driessler, Wulf(D-OSNB); Summers, Stephen J.(D-OSNB)
  A dense set of cyclic vectors for quantum field polynomial algebras.
  J. Math. Phys. 24 (1983), no. 12, 2809--2819.
  81E05 (47D45)
• 719464
• 709463
  Driessler, Wulf(D-OSNB); Summers, Stephen J.(D-OSNB)
  Nonexistence of quantum fields associated with two-dimensional spacelike planes.
  Comm. Math. Phys. 89 (1983), no. 2, 221--226.
  81E05 (47D45)
• 678005
  Summers, Stephen J.
  Normal product states for fermions and twisted duality for CCR- and CAR-type algebras with application to the Yukawa$\sb{2}$ quantum field model.
  Comm. Math. Phys. 86 (1982), no. 1, 111--141.
  81E05 (46L60)
• 610865
  Summers, Stephen J.
  On the phase diagram of a $P(\varphi )\sb{2}$ quantum field model. (English. French summary)
  Ann. Inst. H. Poincaré Sect. A (N.S.) 34 (1981), no. 2, 173--229.
  81E10 (82A25)
• 594327
  Summers, Stephen J.
  A new proof of the asymptotic nature of perturbation theory in $P(\varphi )\sb{2}$ models.
  Helv. Phys. Acta 53 (1980), no. 1, 1--30.
  81E10 (81C12)
• 376002
  Osterwalder, Konrad; Schrader, Robert
  Axioms for Euclidean Green's functions. II.
  With an appendix by Stephen Summers.
  Comm. Math. Phys. 42 (1975), 281--305.
  81.46