Localization and Entanglement in Relativistic Quantum Physics

The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum Field Theory but less well known outside this community. The paper is intended as a concise survey of some selected aspects of relativistic quantum physics, in particular regarding localization and entanglement.

[1]  M. Planck,et al.  Vorträge und Erinnerungen , 1970 .

[2]  Representations of uniformly hyperfinite algebras and their associated von Neumannn rings , 1967 .

[3]  Classification of Two-Dimensional Local Conformal Nets with c < 1 and 2-Cohomology Vanishing for Tensor Categories , 2003, math-ph/0304022.

[4]  J. Fröhlich,et al.  Infrared problem and spontaneous breaking of the Lorentz group in QED , 1979 .

[5]  Rudolf Haag,et al.  Fields, observables and gauge transformations I , 1969 .

[6]  M. Takesaki,et al.  Analyticity and the Unruh effect: a study of local modular flow , 2024, Journal of High Energy Physics.

[7]  Roberto Longo,et al.  On Noether's Theorem in Quantum Field Theory , 1986 .

[8]  P. Porcelli,et al.  On rings of operators , 1967 .

[9]  Hans Halvorson,et al.  Entanglement and Open Systems in Algebraic Quantum Field Theory , 2001 .

[10]  K. Fredenhagen.  A remark on the cluster theorem , 1985 .

[11]  Reinhard F. Werner,et al.  On Bell's inequalities and algebraic invariants , 1995 .

[12]  Deformations of Fermionic Quantum Field Theories and Integrable Models , 2012, 1203.2058.

[13]  J. Yngvason.  Zero-mass infinite spin representations of the Poincaré group and quantum field theory , 1970 .

[14]  J. Perez,et al.  Localization and causality in relativistic quantum mechanics , 1977 .

[15]  String-localized quantum fields from Wigner representations , 2004, math-ph/0402043.

[16]  J. von Neumann,et al.  On rings of operators. II , 1937 .

[17]  Kristian Kirsch,et al.  Methods Of Modern Mathematical Physics , 2016 .

[18]  John E. Roberts,et al.  Local observables and particle statistics I , 1971 .

[19]  R. Shaw,et al.  Unitary representations of the inhomogeneous Lorentz group , 1964 .

[20]  J. Schwartz.  Free Quantized Lorentzian Fields , 1961 .

[21]  H. Grosse,et al.  Wedge-Local Quantum Fields and Noncommutative Minkowski Space , 2007, 0706.3992.

[22]  B. Schubnel,et al.  Quantum Probability Theory and the Foundations of Quantum Mechanics , 2013, 1310.1484.

[23]  Romeo Brunetti,et al.  Perturbative Algebraic Quantum Field Theory and the Renormalization Groups , 2009, 0901.2038.

[24]  M. Rieffel,et al.  A BOUNDED OPERATOR APPROACH TO TOMITA-TAKESAKI THEORY , 1977 .

[25]  The quest for understanding in relativistic quantum physics , 1999, hep-th/9910243.

[26]  G. C. Hegerfeldt,et al.  Causality problems for Fermi's two-atom system. , 1994, Physical review letters.

[27]  P. Blanchard,et al.  DECOHERENCE INDUCED TRANSITION FROM QUANTUM TO CLASSICAL DYNAMICS , 2003 .

[28]  J. Yngvason,et al.  Massless, string localized quantum fields for any helicity , 2011, 1111.5164.

[29]  J. Mund.  String-Localized Quantum Fields, Modular Localization, and Gauge Theories , 2009 .

[30]  D. Buchholz,et al.  New Light on Infrared Problems: Sectors, Statistics, Symmetries and Spectrum , 2013, 1304.2794.

[31]  Romeo Brunetti,et al.  Algebraic approach to Quantum Field Theory , 2004 .

[32]  Detlev Buchholz,et al.  Locality and the structure of particle states , 1982 .

[33]  A. Wightman,et al.  PCT, spin and statistics, and all that , 1964 .

[34]  D. Buchholz,et al.  Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories , 2010, 1005.2656.

[35]  J. Neumann,et al.  On Rings of Operators. III , 1940 .

[36]  H. Borchers.  Half-Sided Translations and tye Type of von Neumann Algebras , 1998 .

[37]  Modular localization and wigner particles , 2002, math-ph/0203021.

[38]  J. Glimm,et al.  Quantum Physics: A Functional Integral Point of View , 1981 .

[39]  Roberto Longo,et al.  Nuclear maps and modular structures II: Applications to quantum field theory , 1990 .

[40]  H. Reeh,et al.  Bemerkungen zur unitäräquivalenz von lorentzinvarianten feldern , 1961 .

[41]  Daniel R. Terno,et al.  Quantum Information and Relativity Theory , 2002, quant-ph/0212023.

[42]  H. Biritz,et al.  On localized states for elementary systems , 1971 .

[43]  Detlev Buchholz,et al.  Scaling algebras and renormalization group in algebraic quantum field theory , 1995 .

[44]  J. Barata,et al.  The ${\mathscr P}(\varphi)_2$ Model on the de Sitter Space , 2013, 1311.2905.

[45]  R. Werner.  Local preparability of states and the split property in quantum field theory , 1987 .

[46]  米谷 民明,et al.  J. Glimm and A. Jaffe: Quantum Physics; A Functional Integral Point of View, Springer-Verlag, New York and Heidelberg, 1981, xx+418ページ, 24.5×16.5cm, DM62. , 1983 .

[47]  A. Wightman,et al.  FIELDS AS OPERATOR-VALUED DISTRIBUTIONS IN RELATIVISTIC QUANTUM THEORY , 1965 .

[48]  E. Wichmann,et al.  On the connection between quantum fields and von Neumann algebras of local operators , 1986 .

[49]  U. Haagerup.  Conne’s bicentralizer problem and uniqueness of the injective factor of type III1 , 1987 .

[50]  竹崎 正道.  Tomita's theory of modular Hilbert algebras and its applications , 1970 .

[51]  Thomas de Quincey.  [C] , 2000, The Works of Thomas De Quincey, Vol. 1: Writings, 1799–1820.

[52]  F. Murray.  On Rings of Operators , 1936 .

[53]  E. Wichmann,et al.  ON THE DUALITY CONDITION FOR QUANTUM FIELDS , 1976 .

[54]  K. Fredenhagen.  On the modular structure of local algebras of observables , 1985 .

[55]  Eyvind H. Wichmann,et al.  On the duality condition for a Hermitian scalar field , 1975 .

[56]  D. Malament.  In Defense of Dogma: Why There Cannot be a Relativistic Quantum Mechanics of (Localizable) Particles , 1996 .

[57]  John E. Roberts,et al.  Fields, observables and gauge transformations II , 1969 .

[58]  QUANTUM FIELD THEORIES , 2004, hep-th/0412158.

[59]  Mark S. C. Reed,et al.  Method of Modern Mathematical Physics , 1972 .

[60]  Roberto Longo,et al.  Standard and split inclusions of von Neumann algebras , 1984 .

[61]  Barry Simon,et al.  Methods of modern mathematical physics. III. Scattering theory , 1979 .

[62]  Rudolf Haag,et al.  On the equilibrium states in quantum statistical mechanics , 1967 .

[63]  Stephen J. Summers.  Tomita-Takesaki Modular Theory , 2005 .

[64]  H. Borchers.  Local rings and the connection of spin with statistics , 1965 .

[65]  S. J. Summers.  On the Independence of Local Algebras in Quantum Field Theory , 1990 .

[66]  G. Lechner.  Deformations of Quantum Field Theories and Integrable Models , 2011, 1104.1948.

[67]  E. J. Woods,et al.  REPRESENTATIONS OF THE CANONICAL COMMUTATION RELATIONS DESCRIBING A NONRELATIVISTIC INFINITE FREE BOSE GAS , 1963 .

[68]  R. Jost.  General Theory of Quantized Fields , 1965 .

[69]  Eyvind H. Wichmann,et al.  Causal independence and the energy-level density of states in local quantum field theory , 1986 .

[70]  H. Araki.  Von Neumann Algebras of Local Observables for Free Scalar Field , 1964 .

[71]  John E. Roberts,et al.  Why there is a field algebra with a compact gauge group describing the superselection structure in particle physics , 1990 .

[72]  D. Buchholz.  Gauss' law and the infraparticle problem , 1986 .

[73]  R. Haag,et al.  Local quantum physics , 1992 .

[74]  H. Araki.  A Lattice of Von Neumann Algebras Associated with the Quantum Theory of a Free Bose Field , 1963 .

[75]  A. Connes.  Une classification des facteurs de type ${\rm III}$ , 1973 .

[76]  Č. Brukner,et al.  Entanglement between smeared field operators in the Klein-Gordon vacuum , 2010, 1003.3354.

[77]  E. J. Woods,et al.  A Classification of Factors , 1968 .

[78]  R. Longo.  Notes on algebraic invariants for non-commutative dynamical systems , 1979 .

[79]  A. Einstein.  On the Quantum Theory of Radiation , 1983 .

[80]  R. Haag.  Quantum field theories with composite particles and asymptotic conditions , 1958 .

[81]  D. Buchholz.  Product states for local algebras , 1974 .

[82]  H. Araki.  Type of von Neumann Algebra Associated with Free Field , 1964 .

[83]  H. Narnhofer.  The role of transposition and CPT operation for entanglement , 2003 .

[84]  J. Yngvason,et al.  Generalized nuclearity conditions and the split property in quantum field theory , 1991 .

[85]  String-Localized Quantum Fields and Modular Localization , 2005, math-ph/0511042.

[86]  D. Buchholz,et al.  The universal structure of local algebras , 1987 .

[87]  O. Bratteli.  Operator Algebras And Quantum Statistical Mechanics , 1979 .

[88]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[89]  Erwin Schrödinger International,et al.  On revolutionizing quantum field theory with Tomita’s modular theory , 2000 .

[90]  A. Connes.  Une classi cation des facteurs de type III , 1973 .

[91]  Huzihiro Araki,et al.  Mathematical theory of quantum fields , 1999 .

[92]  Rudolf Haag,et al.  Local observables and particle statistics II , 1971 .

[93]  Anatolii A. Logunov,et al.  General Principles of Quantum Field Theory , 1990 .

[94]  R. Powers.  Representations of Uniformly Hyperfinite Algebras and Their Associated von Neumann Rings , 1967 .