Abstract
The term “General Theory of Quantized Fields”, replacing the synonymous but somewhat misleading term “Axiomatic Field Theory”, is to my knowledge due to Res Jost. He was one of the great pioneers in our field, and I dedicate this lecture to his memory. What is the aim of the general theory of quantized fields?
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Jost, R.: The General Theory of Quantized Fields. AMS 1965, Providence, Rhode Island
Wick, G.C., Wightman, A.S., Wigner, E.P.: Phys.Rev. 88, 101 (1952)
Haag, R., Kastler, D.: J.Math.Phys. 5, 848(1964)
Borchers, H.-J.: Comm.Math.Phys. 1, 281 (1965)
Doplicher, S., Haag, R., Roberts, J.E.: Comm.Math.Phys. 23, 199 (1971);
Doplicher, S., Haag, R., Roberts, J.E.: Comm.Math.Phys. 35, 49 (1974)
Jones, V.F.: Invent.Math. 72, 1 (1983)
Longo, R.: Comm.Math.Phys. 126, 217(1989);
Longo, R.: Comm.Math.Phys. 130, 285 (1990)
Pimsner, M., Popa, S.: Ann. Sci. École Norm. Sup. 19, 57 (1986)
Fredenhagen, K., Rehren, K.H., Schroer, B.: Comm.Math.Phys. 125, 201 (1989)
Birman, J.: Braids, Links and Mapping Class Groups. Ann. Math.Studies 82, Princeton University Press 1974
Ocneanu, A.: London Math.Soc, Lect. Notes Vol. 136, Evans, Takesaki (eds.), 119–172 (1989)
Wenzl, H.: Invent.Math. 92, 349 (1988)
Freyd, P., Yetter, D., Hoste, J., Lickorish, W., Millet, K., Ocneanu, A.: Bull.AMS 12, 103 (1985)
Longo, R.: Minimal Index and Braided Subfactors (preprint)
Rehren, K.H.: Braid Group Statistics and their Superselection Rules. In: The Algebraic Theory of Superselection Sectors. Introduction and Recent Results. D. Kastler (ed.), World Scientific 1990
Birman, J., Wenzl, H.: Trans. AMS 313, 249 (1989)
Murakami, J.: Osaka J.Math. 24, 745 (1987)
Wenzl, H.: Comm. Math. Phys. 133, 383 (1990)
Kauffman, L.H.: On Knots. Annals of Math. Study 115, Princeton University Press (1987)
Buchholz, D., Fredenhagen, K.: Comm.Math.Phys. 84, 1 (1982)
Fredenhagen, K., Comm. Math. Phys. 79, 141 (1981)
Fröhlich, J., Gabbiani, F.: Rev.Math.Phys. 2, 251 (1990)
Fredenhagen, K.: Structure of Superselection Sectors in Low Dimensional Quantum Field Theory. In: Differential Geometric Methods in Theoretical Physics. L.L. Chau, W. Nahm (eds.), Plenum Press 1990
Fredenhagen, K.: Generalizations of the Theory of Superselection Sectors. See ref.15
Fröhlich, J.: Comm. Math. Phys. 47, 269 (1976)
Moore, G., Seiberg, N.: Phys.Lett. 212 B, 451 (1988)
Doplicher, S., Roberts, J.E.: Ann.Math. 130, 75 (1989)
Doplicher, S., Roberts, J.E.: Comm. Math. Phys. 131, 51 (1990)
J.Fröhlich, Kerler, T. (to be published)
Hadjiivanov, L.K., Paunov, R.R., Todorov, I.T.: Quantum Group Extended Chiral p-Models. INRNE-TH-90–7 (preprint)
G. Mack, V. Schomerus: Quasi Quantum Group Symmetry and Local Braid Relations in the Conformai Ising Model. DESY 91–060 (preprint)
Rehren, K.H.: Field Operators for Anyons and Plektons. DESY 91–043
Haag, R.,: Phys.Rev. 112, 669 (1958)
Ruelle, D.: Helv.Phys.Acta 35, 147 (1962)
Buchholz, D.: Comm. Math. Phys. 52, 147 (1977)
Fröhlich, J., Marchetti, P.: Nucl.Phys. B 356, 533 (1991)
Rüger, S.: Streutheorie für Teilchen mit Zopfgruppenstatistik. Diplomarbeit FU Berlin 1990
Barata, J.C.A., Fredenhagen, K.: Comm. Math. Phys. 138, 507 (1991)
Buchholz, D., Porrmann, M., Stein, U.: Dirac versus Wigner: Towards a Universal Particle Concept in Local Quantum Field Theory. DESY 91–062 (preprint) (to appear in Phys.Lett.B)
Narnhofer, H., Requardt, H., Thirring, W.: Comm. Math. Phys. 92, 247 (1983)
Landsman, N.P.: Nucl.Phys. A 525, 397 (1991)
Haag, R., Swieca, J.A.: Comm. Math. Phys. 1, 308 (1965)
Buchholz, D., Wichmann, E.: Comm. Math. Phys. 106, 106 (1986)
Buchholz, D., Junglas, P.: Lett. Math. Phys. 11, 51 (1986)
Reeh, H., Schlieder, S.: Nuovo Cim. X 22, 1051 (1961)
Bisognano, J.J., Wichmann, E.H.: J.Math.Phys 17, 303 (1975)
Borchers, H.J.: The CPT Theorem in Two-Dimensional Theories of Local Observables (preprint 1991)
Buchholz, D., D’Antoni, C., Longo, R.: J.Funct.Anal. 88, 233 (1990);
Buchholz, D., D’Antoni, C., Longo, R.: Commun. Math. Phys. 129, 115 (1990)
Buchholz, D., Yngvason, J.: Generalized Nuclearity Conditions and the Split Property in Quantum Field Theory (preprint)
Borchers, H.J., Zimmermann, W.: Nuovo Cim. 31, 1047 (1964)
Driessler, W., Fröhlich, J.: Ann.Inst.H. Poincaré 27, 221 (1977)
Driessler, W., Summers, S.J., Wichmann, E.H.: Comm.Math.Phys. 105, 49 (1986)
Buchholz, D.: J.Math.Phys. 31, 1839 (1990)
Borchers, H.J., Yngvason, J.: Comm. Math. Phys. 127, 607 (1990)
Fredenhagen, K., Hertel, J.: Comm. Math. Phys. 80, 555 (1981)
Summers, S.J.: Helv.Phys.Acta 60, 1004 (1987)
Rehberg, H., Wollenberg, M.: Math. Nachr. 125, 1 (1986)
Wollenberg, M.: Rep.Math.Phys. 22, 409 (1985);
Wollenberg, M.: Math.Nachr. 128, 169 (1986)
Jörß, M.: Lokale Netze auf dem eindimensionalen Lichtkegel. Diplomarbeit FU Berlin 1991
Powers, R.T.: Comm.Math.Phys. 21, 85 (1971);
Powers, R.T.: Trans.AMS 187, 261 (1974)
Fulling, S.A.: Phys.Rev. D 7, 2850 (1973)
Haag, R., Narnhofer, H., Stein, U.: Comm. Math. Phys. 94, 219 (1984)
Kay, B.S.: contribution to these proceedings and references therein
Fredenhagen, K., Haag, R.: Comm.Math.Phys. 108, 91 (1987)
Adler, S., Liebermann, J., Ng, Y.J.: Ann.Phys. 106, 279 (1978)
Kay, B.S., Wald, R.M.: Theorems on the Uniqueness and Thermal Properties of Stationary, Nonsingular, Quasi-Free States on Spacetime with a Bifurcate Killing Horizon (preprint)
Bernard, D.: Phys.Rev. D 33, 3581 (1986)
Lüders, C., Roberts, J.E.: Comm. Math. Phys. 134, 29 (1990)
Fredenhagen, K., Haag, R.: Comm. Math. Phys. 127, 273 (1990)
Salehi, H.: Ph.D.Thesis Hamburg 1991
U. Bannier, U.: Ph.D.Thesis Hamburg 1987
Buchholz, D., D’Antoni, C., Fredenhagen, K.: Comm.Math.Phys. 111, 123 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fredenhagen, K. (1992). On the General Theory of Quantized Fields. In: Schmüdgen, K. (eds) Mathematical Physics X. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-77303-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-77303-7_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-77305-1
Online ISBN: 978-3-642-77303-7
eBook Packages: Springer Book Archive