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Hilbert space sectors for solutions of non-linear relativistic field equations

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Abstract

In the set of Cauchy data corresponding to the solutions of non-linear classical relativistic field equations having locally finite kinetic energy a structure of Hilbert space sectors is introduced. Each sector is invariant under time evolution and a total energy and linear momentum functionals can be defined as global quantities. Within this framework the existence of conserved dynamical charges is proved and the mechanism by which a symmetry can be spontaneously broken is explained.

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References

  1. Lee, T. D., Wick, G. C.: Phys. Rev. D9, 2291 (1974)

    Google Scholar 

  2. Ferretti, B.: Atti Acc. Scienze Bologna, Serie XII, Tomo I, 45 (1974)

    Google Scholar 

  3. 't Hooft, G.: Nucl. Phys. B79, 276 (1974)

    Google Scholar 

  4. Ferretti, B., Velo, G.: Nuovo Cimento Letters10, 451 (1974)

    Google Scholar 

  5. Dashen, R., Hasslacher, B., Neveu, A.: Phys. Rev. D10, 4114, 4130, 4138 (1974)

    Google Scholar 

  6. Goldstone, J., Jackiw, R.: Phys. Rev. D11, 1486 (1975)

    Google Scholar 

  7. Coleman, S.: Phys. Rev. D11, 2088 (1975)

    Google Scholar 

  8. Fröhlich, J.: Phys. Rev. Letters34, 833 (1975)

    Google Scholar 

  9. Gervais, J. L., Sakita, R.: Phys. Rev. D11, 2943 (1975)

    Google Scholar 

  10. Mandelstam, S.: Phys. Rev. D11, 3026 (1975)

    Google Scholar 

  11. Fadeev, L. D.: IAS lectures and references therein, April 1975

  12. Christ, N., Lee, T. D.: Phys. Rev. D12, 1606 (1975)

    Google Scholar 

  13. Goldstone, J.: Nuovo Cimento19, 154 (1961)

    Google Scholar 

  14. Whitham, G. B.: Linear and nonlinear waves. New York: Wiley 1974

    Google Scholar 

  15. Finkelstein, D., Misner, C. W.: Ann. Phys.6, 230 (1959)

    Google Scholar 

  16. Finkelstein, D.: J. Math. Phys.7, 1218 (1966)

    Google Scholar 

  17. Hepp, K.: Commun. math. Phys.35, 265 (1974)

    Google Scholar 

  18. Parenti, C., Strocchi, F., Velo, G.: preprint S.N.S. 22/1975, to appear in Ann. Scuola Norm. Sup. (Pisa). A brief account has been given in Phys. Lett.59B, 157 (1975)

  19. Segal, I.: Ann. Math.78, 339 (1963)

    Google Scholar 

  20. Volevic, L. R., Paneyakh, B. P.: Russian Math. Surveys20, 1 (1965)

    Google Scholar 

  21. Gel'fand, I. M., Shilov, G. E.: Generalized Functions, Vol. 2. New York, London: Academic Press 1968

    Google Scholar 

  22. Halmos, P. R.: Measure Theory. New York: Van Nostrand 1950

    Google Scholar 

  23. Yoshida, K.: Functional Analysis. Berlin-Heidelberg-New York: Springer 1966

    Google Scholar 

Download references

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Authors and Affiliations

  1. Instituto Matematico “S. Pincherle”, University of Bologna, Bologna, Italy

    C. Parenti

  2. Scuola Normale Superiore and I.N.F.N., Sez. di Pisa, Pisa, Italy

    F. Strocchi

  3. Istituto di Fisica “A. Righi”, University of Bologna and I.N.F.N., Sez. di Bologna, Bologna, Italy

    G. Velo

Authors
  1. C. Parenti
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  2. F. Strocchi
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  3. G. Velo
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Additional information

Communicated by J. Glimm

Partially supported by C.N.R. (gruppo G.N.A.F.A.)

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Parenti, C., Strocchi, F. & Velo, G. Hilbert space sectors for solutions of non-linear relativistic field equations. Commun.Math. Phys. 53, 65–96 (1977). https://doi.org/10.1007/BF01609167

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  • DOI: https://doi.org/10.1007/BF01609167

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