Abstract.
After revisiting some high points of particle physics and QFT of the two decades from 1960 to 1980, I comment on the work by Jorge André Swieca. I explain how it fits into the quantum field theory during these two decades and draw attention to its relevance to the ongoing particle physics research. A particular aim of this article is to direct the readers mindfulness to the relevance of what at the time of Swieca was called “the Schwinger Higgs screening mechanism” which, together with recent ideas which generalize the concept of gauge theories, has all the ingredients to revolutionize the issue of gauge theories and the standard model.
Similar content being viewed by others
References
R.J. Jost, TCP-Invarianz der Streumatrix und interpolierende Felder, Helv. Phys. Acta 36, 77 (1963)
G.F. Chew, S-Matrix Theory of Strong Interactions(W.A. Benjamin Inc., New York, 1961)
R. Haag, Local Quantum Physics (Springer, 1996)
B. Schroer, A critical look at 50 years particle theory from the perspective of the crossing property, e-print arXiv:0905.4006
B. Schroer, Localization and the interface between quantum mechanics, quantum field theory and quantum gravity I (The two antagonistic localizations and their asymptotic compatibility), e-print arXiv:0912.2874
B. Schroer, Localization and the interface between quantum mechanics, quantum field theory and quantum gravity II (The search of the interface between QFT and QG), e-printarXiv:0912.2886
W. Heisenberg, Der mathematische Rahmen der quantentheorie der Wellenfelder, Z. Naturforsch. 1, 608 (1946), and references to prior work therein
W.H. Furry, J.R. Oppenheimer, On the theory of the electron and positive, Phys. Rev. 45, 245 (1934)
P. Di Vecchia, The birth of string theory, Lect. Notes Phys. 737, 59 (2008)
D. Kastler, D.W. Robinson, J.A. Swieca, Conserved Currents and Associated Symmetries; Goldstone’s Theorem, Commun. Math. Phys. 2, 108 (1966)
B. Schroer, BMS symmetry, holography on null-surfaces and area proportionality of “light-slice” entropy, e-print arXiv:0905.4435
R.F. Streater, A.S. Wightman, PCT, Spin and Statistics and all that(Benjamin Inc., New York, 1964)
J. Mund, in preparation
R. Haag, J.A. Swieca, When does a quantum field theory describe particles? Commun. Math. Phys. 1, 308 (1965)
H. Epstein, V. Glaser, Role of locality in perturbation theory, Ann. Inst. Henri Poincaré A XIX, 211 (1973)
J. Mund, B. Schroer, J. Yngvason, String-localized quantum fields and modular localization, Commun. Math. Phys. 268, 621 (2006)
D. Buchholz, E.H. Wichmann, Causal Independence and the energy-level density of states in local quantum field theory, Commun. Math. Phys. 106, 321 (1986)
D. Buchholz, P. Junglas, On the existence of equilibrium states in local quantum field theory, Commun. Math. Phys. 121, 255 (1989)
W. Dybalski, A sharpened nuclearity condition and the uniqueness of the vacuum in QFT, e-print arXiv:0706.4049
G. Lechner, Construction of quantum field theories with factorizing S-matrices, Commun. Math. Phys. 277, 821 (2008)
J. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2, 231 (1997)
K.-H. Rehren, Local quantum observables in the AdS-CFT correspondence, Phys. Lett. B 493, 383 (2000)
M. Dütsch, K.-H. Rehren, Generalized free fields and the AdS-CFT correspondence, Annales Henri Poincaré 4, 613 (2003), and references to previous work
J. Goldstone, Field theories with superconductor solutions, Nuovo Cim. 19, 154 (1961)
J. Schwinger, Gauge invariance and mass 2, Phys. Rev. 128, 2425 (1962)
The idea of a screened massive phase of QED appeared first, in Theoretical Physics, Trieste Lectures, 1962, edited by J. Schwinger (IAEA, Vienna, 1963), p. 89
N.D. Mermin, H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or 2-Dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17, 1133 (1966)
P.W. Higgs, Broken symmetries, massless particles and Gauge fields, Phys. Lett. 12, 132 (1964)
R. Brout, F. Englert, Broken Symmetry + Mass of Gauge vector Mesons, Phys. Rev. Lett. 13, 321 (1964)
P.W. Anderson, Plasmons, Gauge invariance, and mass, Phys. Rev. 130, 439 (1963)
H. Ezawa, J.A. Swieca, Spontaneous breakdown of symmetries and zero-mass states, Commun. Math. Phys. 5, 330 (1967)
J.A. Swieca, Conserved currents renormalization and zero-mass states, Nuovo Cim. A 52, 242 (1967)
J.A. Swieca, Comoun. Math. Phys. 4, 1 (1967), in Cargèse Lectures in Physics, edited by D. Kastler (Gordon and Breach, New York, 1970)
J.A. Swieca, Charge screening and mass-spectrum, Phys. Rev. D 13, 312 (1976)
T.W. Kibble, International Conference on Elementary Particles, Oxford Conference Report (1965)
D.C. Brydges, P. Federbush, Debye-screening , Commun. Math. Phys. 73, 197 (1980)
B. Schroer, Pascual Jordan’s legacy and the ongoing research in quantum field theory, in preparation
J.E. Lowenstein, J.A. Swieca, Quantum electrodynamics in 2 DIMensions, Ann. Phys. (N.Y.) 68, 172 (1971)
O. Steinmann, A New Look at the Higgs-Kibble Model, e-print arXiv:0804.2989
V. Kurak, B. Schroer, J.A. Swieca, Comments on confinement criteria, Nucl. Phys. B 134, 61 (1978)
L.V. Belvedere, J.A. Swieca, K.D. Rothe, B. Schroer, Generalized 2-dimensional Abelian Gauge-Theories and confinement, Nucl. Phys. B 153, 112 (1979)
D. Buchholz, K. Fredenhagen, Charge screening and mass-spectrum in Abelian Gauge-Theories, Nucl. Phys. B 154, 226 (1979)
D. Buchholz, Gauss law and the infraparticle problem, Phys. Lett. B 174, 331 (1986)
J.H. Lowenstein, B. Schroer, Gauge invariance and ward identities in a massive-vector-Meson model, Phys. Rev. D 6, 1553 (1972)
D. Buchholz, K. Fredenhagen, Locality and the structure of particle states, Comm. Math. Phys. 84, 1 (1982)
B. Schroer, String Theory deconstructed, in preparation
B. Schroer, A note on Infraparticles and Unparticles, e-print arXiv:0804.3563
F. Bloch, A. Nordsiek, Note on the Radiation Field of the Electron, Phys. Rev. 52, (1934) 54
D. Yenni, S. Frautschi, H. Suura, The infrared divergence phenomena and high-energy processes, Ann. Phys. 13, 379 (1961)
J.D. Dollard, Asymptotic convergence and the Coulomb interaction, J. Math. Phys. 5, 729 (1964)
B. Schroer, Modular wedge localization and the d=1+1 formfactor program, Ann. Phys. 275, 190 (1999)
R. Brunetti, D. Guido, R. Longo, Modular localization and Wigner particles, Rev. Math. Phys. 14, 759 (2002)
R.F. Dashen, B. Hasslacher, A. Neveu, Nonperturbative methods and extended-Hadron models in field-theory. 3. 4-Dimensional non-Abelian models, Phys. Rev. D 10, 4138 (1974)
B. Schroer, T.T. Truong, P. Weisz, Towards an explicit construction of Sine-gordon field-theory, Phys. Lett. B 63, 422 (1976)
M. Karowski, H.J. Thun, T.T. Truong, P. Weisz, Uniqueness of a purely elastic S-matrix in (1+1) dimensions, Phys. Lett. B 67, (1977) 321
M. Karowski, P. Weisz, Exact form-factors in (1+1)-dimensional field theoretic models with soliton behavior, Nucl. Phys. B 139, (1978) 455
M. Karowski, V. Kurak, B. Schroer, Confinement in 2-dimensional models with factorization, Phys. Lett. B 81, 200 (1979)
H. Babujian, M. Karowski, Exact form factors for the scaling Z(N)-Ising and the affine A(N-1)-Toda quantum field theories, Phys. Lett. B 575, 144 (2003)
V. Kurak, J.A. Swieca, Anti-particles as bound-states of particles in the factorized S-matrix framework, Phys. Lett. B 82, 289 (1979)
S. Coleman, There are no Goldstone bosons in 2 dimensions, Commun. Math. Phys. 31, 259 (1973)
R. Koberle, V. Kurak, J.A. Swieca, Scattering theory and 1-n expansion in the chiral Gross-Neveu model, Phys. Rev. D 20, 897 (1979)
E. Witten, Chiral symmetry, 1-N expansion and Su(N) Thirring model, Nucl. Phys. B 145, 110 (1978)
E. Abdalla, B. Berg, P. Weisz, More about the S-matrix of the chiral Su(N) Thirring model, Nucl. Phys. B 157, 387 (1979)
H. Babujian, A. Foerster, M. Karowski, Exact form factors of the SU(N) Gross–Neveu model and 1/N expansion, Nucl. Phys. B 825, 396 (2010)
B. Schroer, J.A. Swieca, Spin and statistics of quantum kinks, Nucl. Phys. B 121, 505 (1977)
J. Mund, Modular localization of massive particles with “any” spin in d=2+1, J. Math. Phys. 44, 2037 (2003)
G.C. Marques, J.A. Swieca, Complex masses and acausal propagation in field-theory, Nucl. Phys. B 43, 205 (1972)
B. Schroer, An anthology of non-local QFT and QFT on non-commutative spacetime, Ann. Phys. 319, 92 (2005)
F. Coester, W.N. Polyzou, Relativistic quantum-mechanics of particles with direct interactions, Phys. Rev. D 26, 1348 (1982), and references therein
M. Hortacsu, B. Schroer, R. Seiler, Conformal symmetry and reverberations, Phys. Rev. D 5, 2519 (1972)
J.A. Swieca, A.H. Volkel, Remarks on conformal invariance, Commun. Math. Phys. 29, 319 (1973)
P.D. Hislop, R. Longo, Modular structure of the local Algebras associated with the free massless scalar field-theory, Commun. Math. Phys. 84, 71 (1982)
B. Schroer, J.A. Swieca, Conformal transformations for quantized fields, Phys. Rev. D 10, 480 (1974)
B. Schroer, J.A. Swieca, A.H. Völkel, Global operator expansions in conformally invariant relativistic quantum field theory, Phys. Rev. D 11, 1509 (1972)
B. Bakalov, N.M. Nikolov, K.-H. Rehren, I. Todorov, Unitary positive-energy representations of scalar bilocal quantum fields, Commun. Math. Phys. 271, 223 (2007)
B. Bakalov, N.M. Nikolov, K.-H. Rehren, I. Todorov, Infinite Dimensional Lie Algebras in 4D Conformal Quantum Field Theory, J. Phys. A: Math. Theor. 41, 194002 (2008)
K.-H. Rehren, B. Schroer, Einstein causality and Artin Braids, Nucl. Phys. B 312, 715 (1989)
H.J. Borchers, D. Buchholz, B. Schroer, Polarization-free generators and the S-matrix, Commun. Math. Phys. 219, 125 (2001)
R. Koberle, J.A. Swieca, Factorizable Z(N) models, Phys. Lett. 86, 209 (1979)
J.A. Swieca, Solitons and confinement, Fortschr. Phys. 25, 303 (1977)
E. Marino, J.A. Swieca, Order, disorder and generalized statistics, Nucl. Phys. B 170, 175 (1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Schroer, B. Jorge A. Swieca’s contributions to quantum field theory in the 60s and 70s and their relevance in present research. EPJ H 35, 53–88 (2010). https://doi.org/10.1140/epjh/e2010-00004-1
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjh/e2010-00004-1