Modular localization and the holistic structure of causal quantum theory, a historical perspective

Bert Schroer

Resumo


dx.doi.org/10.7437/NF2318-4957/2014.01.002

Abstract

Recent insights into the conceptual structure of localization in QFT ("modular localization") led to clarications of old unsolved problems.The oldest one is the Einstein-Jordan conundrum which led Jordan in1925 to the discovery of quantum eld theory. This comparison of fluctuations in subsystems of heat bath systems (Einstein) with those resulting from the restriction of the QFT vacuum state to an open subvolume (Jordan) leads to a perfect analogy; the globally pure vacuum state becomes upon local restriction a strongly impure KMS state. This phenomenon of localization-caused thermal behavior as well as the vacuum-polarization clouds at the causal boundary of the localization region places localization n QFT into a sharp contrast with quantum mechanics and justies the attribute "holstic". In fact it positions the E-J Gedankenexperiment into the same conceptual category as the cosmological constant problem and the Unruh Gedankenexperiment. The holistic structure of QFT resulting from "modular localization" also leads to a revision of the conceptual origin of the crucial crossing property which entered particle theory at the time of the bootstrap S-matrix approach but suered from incorrect use in the S-matrix settings of the dual model and string theory. The new holistic point of view, which strengthens the autonomous aspect of QFT, also comes with new messages for gauge theory by exposing the clash between Hilbert space structure and localization and presenting alternative solutions based on the use of stringlocal elds in Hilbert space. Among other things this leads to a radical reformulation of the Englert- Higgs symmetry breaking mechanism.


Palavras-chave


modular localization, stringlocal vectormeson fields in Hilbert space instead of the BRST gauge formulation in indefinite metric space

Texto completo:

PDF

Referências


P. Jordan, Zur Theorie der Quantenstrahlung, Zeitschrift fur Physik 30 (1924) 297

M. Born, W. Heisenberg and P. Jordan, Zur Quantenmechanik II, Zeitschr. fur Physik 35, (1926) 557

A. Duncan and M. Janssen, Pascual Jordan's resolution of the conundrum of the wave-particle duality of light, arXiv:0709.3812

J. Ehlers, D. Ho_mann, J. Renn (es.) "Pascual Jordan (1902-1980), Mainzer Symposium zum 100. Geburtag", MPIWG preprint 329, (2007)

J. Stachel, Einstein and the Quantum: Fifty Years of Struggle, in: From Quarks to Quasars, Philosophical Problems of Modern Physics, edited by Robert G. Colodny, Pittsburgh Studies in the Philosophy of Science, 1986

B. Schroer, Modular localization and the d=1+1 formfactor program, Annals of Physics 295, (1999) 190

R. Haag, Local Quantum Physics, Springer 1996

B. Schroer, The Einstein-Jordan conundrum and its relation to ongoing foundational research in local quantum physics, arXiv:1101.0569

B. Schroer, Pascual Jordan's legacy and the ongoing research in quantum eld theory,Eur.Phys.J.H 35, (2011) 377-434, arXiv:1010.4431

B. Schroer, Causality and dispersion relations and the role of the S-matrix in the ongoing research, arXiv:1102.0168

B. Schroer, The ongoing impact of modular localization on particle theory, to appear

A. Einstein, Physikalische Zeitschrift 18, (1917), 121

P. Jordan, Zeitschrift fur Physik 30 (1924) 297

A. Einstein, Bemerkungen zu P. Jordans: Zur Theorie der Quantenstrahlung, Zeitschrift fur Physik 30, (1925) 784

R. Haag, Eur. Phys. J. H 35, (2010)

R. F. Streater and A. S. Wightman, PCT, Spin And Statistics, And All That, W. A. Benjamin, Inc. New York 1964

B. Schroer, Localization and the interface between quantum mechanics, quantum _eld theory and quantum gravity I, Stud. Hist. Phil. Mod. Phys. 41,(2010) 104

S. J. Summers, Tomita-Takesaki Modular Theory, arXiv:math-ph/0511034

J. J. Bisognano and E. H. Wichmann, On the duality condition for quantum elds, Journal of Mathematical Physics 17, (1976) 303-321

G. Sewell, Ann. Phys. 141, (1982) 201

W. G. Unruh, Phys. Rev. D14, (1976) 870

H. Epstein, V. Glaser, A.Martin, Commun. Math.Phys. 13, (1969) 257

J. Bros, H. Epstein and V. Glaser, Com. Math. Phys. 1, (1965) 240

B. Schroer and H-J Wiesbrock, Rev. Math. Phys. 12 (2000) 461

S. Hollands and R. M. Wald, General Relativity and Gravitation 36, (2004) 2595-2603

B. Schroer, The foundational origin of integrability in quantum _eld theory,

arXiv:1109.1212

R. Kaehler and H.-P. Wiesbrock, Modular theory and the reconstruction of fourdimensional quantum _eld theories, Journal of Mathematical Physics 42, (2001) 74-86

H. Epstein and V. Glaser, Ann. Inst. Henri Poincar_e A XIX, (1973) 211

S. Mandelstam, Phys. Rev. 175, (1968) 1518

W. Heisenberg, Verhandlungen der Sachsischen Akademie der Wissenschaften zu Leipzig, 86, (1934) 317-322

M. Requardt, Commun. Math. Phzs. 50, (1976) 259

G. 't Hooft, Int. J. Mod. Phys. A11, (1996) 4623

J. Glimm and A. Ja_e, Boson quantum _eld theory models, in mathematics of contemporary physics, edited by R. F. Streater (Academic press, London) 1972

J. Mund and J. Bros, Commun. Math. Phys. 315 (2012) 465

B. Schroer and J. A. Swieca, Spin and Statistics of Quantum Kinks, Nucl.

Phys.B121, (1977) 505

R. Haag and B. Schroer, Postulates of Quantum Field Theory, J. Math. Phys. 3, (1962) 248-256

B. Schroer, An alternative to the gauge theory setting, Foun. of Phys. 41, (2011)1543, arXiv:1012.0013

G. Lechner, An Existence Proof for Interacting Quantum Field Theories with a Factorizing S-Matrix, Commun. Mat. Phys. 227, (2008) 821, arXiv.org/abs/mathph/ 0601022

H-J. Borchers, On revolutionizing quantum _eld theory with Tomita's modular theory, J. Math. Phys. 41, (2000) 8604

J. Mund, Annales Henri Poincar_e 2, (2001) 907, arXiv:hep-th/0101227

S. Doplicher and R. Longo, Standard and split inclusions of von Neumann algebras, Invent. Math. 75, (1984) 49

R. Jost: TCP-Invarianz der Streumatrix und interpolierende Felder, Helvetica Phys. Acta 36, (1963) 77

J. Mund, B. Schroer and J. Yngvason, String-localized quantum _elds and modular localization, CMP 268 (2006) 621, math-ph/0511042

R. Brunetti, D. Guido and R. Longo, Modular localization and Wigner particles, Rev. Math. Phys. 14, (2002) 759

S. Weinberg, The Quantum Theory of Fields I, Cambridge University Press

J. Yngvason, Zero-mass in_nite spin representations of the Poincar_e group and quantum eld theory, Commun. Math. Phys. 18 (1970), 195

B. Schroer, Bondi-Metzner-Sachs symmetry, holography on null-surfaces and area proportionality of light-slice" entropy, Foundations of Physics 41, 2 (2011), 204, arXiv:0905.4435

D. Buchholz and C. Solveen, Unruh E_ect and the Concept of Temperature, Class. Quantum Grav. 30, (2013) 085011, arXiv:1212.2409

C. Solveen, Local Thermal Equilibrium and KMS states in Curved Spacetime, Class. Quantum Grav. 29, (2012) 245015

K. Papadodimas and S. Raju, State-Dependent Bulk-Boundary Maps and Black Hole Complementarity, arXiv:1310.6335

H-J. Borchers and J. Yngvason, J. Math. Phys. 40 (1999) 601

R. Haag, N. M. Hugenholtz and M. Winnink, Commun. Math. Phys. 5, (1967) 215

H. J. Borchers, D. Buchholz and B. Schroer, Commun.Math.Phys. 219 (2001) 125

B. Schroer, A critical look at 50 years particle theory from the perspective of the crossing property, Found.Phys. 40, (2010) 1800-1857, arXiv:0906.2874

G. Lechner, Deformations of quantum _eld theories and integrable models,

arXiv:1104.1948

H. Babujian, A. Fring, M. Karowski and A. Zapletal, Nucl. Phys. B538, (1999) 535

A. B. Zamolodchikov and A. Zamolodchikov, AOP 120, (1979) 253

B. Schroer, The ongoing impact of modular localization on particle theory, to appear

J. A. Swieca, Goldstone's Theorem and Related Topics, Carg_ese Lectures in Physics, Vol. 4, page 215 (1970)

D. Buchholz and K. Fredenhagen, Nucl. Phys. B154, (1979) 226

A. Ja_e, Phys. Rev. 158, (1967) 1454

Interactions with quadratic dependence on string-localized massive vectormesons: massive scalar quantum electrodynamics, arXiv:1307.3469

D. Buchholz and K. Fredenhagen, Commun. Math. Phys. 84, (1982) 1

B. Schroer, Jorge A. Swieca's contributions to quantum _eld theory in the 60s and 70s and their relevance in present research, Eur. Phys. J. H 35, (2010), 53, arXiv:0712.0371

G. Scharf, Quantum Gauge Theory, A True Ghost Story, John Wiley & Sons, Inc. New York 2001

A. Aste, G. Scharf and M. Duetsch, J. Phys. A30, (1997) 5785

M. Duetsch and G. Scharf, Ann. Physik 8, (1999) 359

M. Duetsch, J. M. Gracia-Bondia, F. Scheck, J. C. Varilly, Quantum gauge models without classical Higgs mechanism, arXiv:1001.0932

M. Dutsch and K. Fredenhagen,

J. Mund and B. Schroer, in preparation

H. Ezawa and J. A. Swieca, Commun. Math. Phys. 5, (1967) 330

J. A. Swieca, Phys. Rev. D 12, (1976) 312

D. Buchholz, Commun. Math. Phys. 85, (1982) 40

J. Frohlich, G. Morchio and F. Strocchi, Ann. of Phys. 119, 241 (1979)

K. Bardackci and B. Schroer, Local Approximations in Renormalizable and Nonrenormalizable Theories II, J. Math. Phys 7, (1966) 16

M. Duetsch and B. Schroer, J. Phys. A 33, (2000) 4317

J. Mund, String-localized massive vector Bosons without ghosts: the example of massive QED, to appear

B. Schroer, Quadratic dependence on string-localized massive vectormesons: the example of scalar QED, in preparation

J. H. Lowenstein and B. Schroer, Phys. Rev. D7, (1975) 1929

D. Buchholz, New Light on Infrared Problems: Sectors, Statistics, Spectrum and All That, arXiv:1301.2516

D. Buchholz and J. Roberts, New Light on Infrared Problems: Sectors, Statistics, Symmetries and Spectrum, arXiv:1304.2794

P. Di Vecchia, The birth of string theory, arXiv 0704.0101

N. N. Bogoliubov, A. Logunov, A. I. Oksak and I. T. Todorov, General principles of quantum _eld theory, Dordrecht Kluwer

D. Bahns, K. Rejzner and J. Zahn, The e_ective theory of strings, arXiv:1204.6263

D. Bahns, J. Math. Phys. 45, (2004) 4640

E. Martinec, Class. Quant. Grav. 10, (1993) 1874

D. A. Lowe, Phys. Lett. B 326, (1994) 223

R. Haag and J. A. Swieca, Commun. Math. Phys. 1, (1965) 308

G. Mack, D-dimensional Conformal Field Theories with anomalous dimensions as Dual Resonance Models, arXiv:0909.1024, D-independent representations of conformal eld theories in D dimensions via transformations to auxiliary dual resonance models. The scalar case, arXiv:0907:2407

M. Duetsch, K.-H. Rehren, A comment on the dual _eld in the AdS-CFT correspondence, Lett.Math.Phys. 62 (2002) 171

K-H. Rehren, Algebraic Holography, Annales Henri Poincar_e1, (2000) 607, arXiv:hepth/ 9905179

B. Schroer, Dark matter and Wigner's third positive energy representation class, arXiv:1306.3876


Apontamentos

  • Não há apontamentos.