Abstract
Starting from the principle of locality of observables we derive localization properties of massive particle states which hold in all models of relativistic quantum theory, including gauge theories. It turns out that particles may always be regarded as well localized distributions of matter, although their mathematical description might require the introduction of non-local (unobservable) fields, which are assigned to infinite string-like regions. In spite of the non-locality of these fields one can show that such particles obey Bose- or Fermi (para) statistics, that to each particle there exists an antiparticle and that collision states of particles exist. A selfcontained exposition of the underlying physical ideas is given in the Introduction, and some perspectives for the structure of field-theoretic models arising from our analysis are discussed in the Conclusions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Swieca, J. A.: Charge screening and mass spectrum, Phys. Rev.D13, 312 (1976)
Streater, R. F., Wightman, A. S.: PCT, spin and statistics and all that, New York: Benjamin Inc 1964
Doplicher, S., Haag, R., Roberts, J. E.: Local observables and particle statistics I. Commun. Math. Phys.23, 199 (1971)
Doplicher, S., Haag, R., Roberts, J. E.: Local observables and particle statistics II. Commun. Math. Phys.35, 49 (1974)
Strocchi, F., Wightman, A. S.: Proof of the charge superselection rule in local relativistic quantum field theory, J. Math. Phys.15, 2198 (1974)
Buchholz, D., Fredenhagen, K.: Charge screening and mass spectrum in Abelian gauge theories, Nucl. Phys.B154, 226 (1979)
Haag, R., Kastler, D.: An algebraic approach to field theory, J. Math. Phys.5, 848 (1964)
Wilson, K.: Confinement of quarks, Phys. Rev.D10, 2445 (1974)
Sakai, S.: C*-algebras and W*-algebras, Berlin, Heidelberg, New-York: Springer 1971
Borchers, H. J.: On the vacuum state in quantum field theory, Commun. Math. Phys.1, 57 (1965)
Fröhlich, J., Morcchio G., Strocchi, F.: Charged sectors and scattering states in Quantum Electrodynamics, Ann. Phys.119, 241 (1979)
Buchholz, D.: (to be published)
Jost, R.: The general theory of quantized fields. Providence, Rhode Island: Am. Math. Soc., 1965
Hepp, K., Jost, R.: Über die Matrixelemente des Translationsoperators, Helv. Phys. Acta35, 34 (1962)
Borchers, H. J., Buchholz D.: (to be published)
Newton, T. D., Wigner, E. P.: Localized states for elementary systems, Rev. Mod. Phys.21, 400 (1949)
Fredenhagen, K.: On the existence of antiparticles, Commun. Math. Phys.79, 141 (1981)
Bisognano, J. J., Wichmann, E.: On the duality condition for a hermitean scalar field. J. Math. Phys.16, 985–1007 (1975)
Borchers, H. J.: Energy and momentum as observables in quantum field theory, Commun. Math. Phys.2, 49 (1966)
Vladimirov, V. S.: Methods of the theory of functions of many complex variables; Cambridge, Massachusetts and London: MIT Press 1966
Borchers, H. J.: On the converse of the Reeh-Schlieder theorem, Commun. Math. Phys.10, 269 (1968)
Driessler, W.: On the type of local algebras in quantum field theory, Commun. Math. Phys.59, 295 (1977)
Fröhlich, J.: New superselection sectors (“soliton states”) in two dimensional Bose quantum field models, Commun. Math. Phys.47, 269 (1976)
Borchers, H. J.: A remark on a theorem of B. Misra, Commun. Math. Phys.4, 315 (1967)
Kadison, R. V.: The trace in finite operator algebras, Proc. Am. Math. Soc.12, 973 (1961)
Borchers, H. J.: Local rings and the connection of spin with statistics, Commun. Math. Phys.1, 281 (1965)
Araki, H.: On the algebra of all local observables. Prog. Theor. Phys.32, 844 (1964)
Hepp, K.: In: Axiomatic Field Theory. Brandeis University New York, London, Paris: Gordon and Breach 1965
Buchholz, D., Fredenhagen, K.: (to be published)
Balian, R., Drouffe, J. M., Itzykson, C.: Gauge fields on a lattice II. Gauge-invariant Ising model, Phys. Rev.D11, 2098 (1974)
West, G. B.: Confinement in Quantum Chromodynamics, Phys. Rev. Lett.46, 1365 (1981)
Aks, S.: Proof that scattering implies production in quantum field theory, J. Math. Phys.6, 516 (1965)
Morpurgo, G.: In: Quarks and Leptons, Acta Phys. Austr. Suppl.XXI, 5 (1979)
Author information
Authors and Affiliations
Additional information
Communicated by R. Haag
Rights and permissions
About this article
Cite this article
Buchholz, D., Fredenhagen, K. Locality and the structure of particle states. Commun.Math. Phys. 84, 1–54 (1982). https://doi.org/10.1007/BF01208370
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01208370