Abstract
Assuming locality of the observables and positivity of the energy it is shown that the joint spectrum of the energy-momentum operators has a Lorentz-invariant lower boundary in all superselection sectors. This result is of interest if the Lorentz-symmetry is (spontaneously) broken, such as in the charged sectors of quantum electrodynamics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Wigner, E.P.: On unitary representations of the inhomogeneous Lorentz group. Ann. Math.40, 149 (1939)
Borchers, H.J.: Local rings and the connection of spin with statistics. Commun. Math. Phys.1, 281 (1965)
Fröhlich, J., Morchio, G., Strocchi, F.: Infrared problem and spontaneous breaking of the Lorentz group in QED. Phys. Lett.89 B, 61 (1979)
Strocchi, F., Wightman, A.S.: Proof of the charge superselection rule in local relativistic quantum field theory. J. Math. Phys.15, 2198 (1974)
Haag, R., Kastler, D.: An algebraic approach to quantum field theory. J. Math. Phys.5, 848 (1964)
Borchers, H.J.: Translation group and spectrum condition. Commun. Math. Phys.96, 1–13 (1984)
Fröhlich, J., Morchio, G., Strocchi, F.: Charged sectors and scattering states in quantum electrodynamics. Ann. Phys.119, 241 (1979)
Buchholz, D.: The physical state space of quantum electrodynamics. Commun. Math. Phys.85, 49 (1982)
Buchholz, D., Fredenhagen, K.: Locality and the structure of particle states. Commun. Math. Phys.84, 1 (1982)
Hepp, K., Jost, R.: Über die Matrixelemente des Translationsoperators. Helv. Phys. Acta35, 34 (1962)
Maison, D.: Eine Bemerkung zur Clustereigenschaft. Commun. Math. Phys.10, 48 (1968)
Yosida, K.: Functional analysis. Berlin, Heidelberg, New York: Springer 1966
Pedersen, G.K.:C*-algebras and their automorphism groups. London, New York, San Francisco: Academic Press 1979
Vladimirov, V.S.: Methods of the theory of functions of many complex variables. Cambridge, MA, London: MIT-Press 1966
Bros, J., Messiah, A., Stora, R.: A problem of analytic completion related to the Jost-Lehmann-Dyson formula. J. Math. Phys.2, 639 (1961)
Pflug, P.: Eine Bemerkung über die Konstruktion von Holomorphiehüllen. Zeszyty Nankowe Uniwersytetu Jagiellonskiego, Vol. 23
Borchers, H.J., Stora, R.: Unpublished notes (1963)
Stora, R.: Hyperfunctions and Theoretical Physics, Nice 1973. In: Lecture Notes in Mathematics, Vol. 449. Berlin, Heidelberg, New York: Springer 1975
Doplicher, S.: Fock representation and massless particles. Commun. Math. Phys.3, 228 (1966)
Author information
Authors and Affiliations
Additional information
Communicated by G. Mack
Rights and permissions
About this article
Cite this article
Borchers, HJ., Buchholz, D. The energy-momentum spectrum in local field theories with broken Lorentz-symmetry. Commun.Math. Phys. 97, 169–185 (1985). https://doi.org/10.1007/BF01206185
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01206185