On space-time, reference frames and the structure of relativity groups

Vittorio Berzi; Vittorio Gorini

Annales de l'I.H.P. Physique théorique (1972)

  • Volume: 16, Issue: 1, page 1-22
  • ISSN: 0246-0211

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Berzi, Vittorio, and Gorini, Vittorio. "On space-time, reference frames and the structure of relativity groups." Annales de l'I.H.P. Physique théorique 16.1 (1972): 1-22. <http://eudml.org/doc/75722>.

@article{Berzi1972,
author = {Berzi, Vittorio, Gorini, Vittorio},
journal = {Annales de l'I.H.P. Physique théorique},
language = {eng},
number = {1},
pages = {1-22},
publisher = {Gauthier-Villars},
title = {On space-time, reference frames and the structure of relativity groups},
url = {http://eudml.org/doc/75722},
volume = {16},
year = {1972},
}

TY - JOUR
AU - Berzi, Vittorio
AU - Gorini, Vittorio
TI - On space-time, reference frames and the structure of relativity groups
JO - Annales de l'I.H.P. Physique théorique
PY - 1972
PB - Gauthier-Villars
VL - 16
IS - 1
SP - 1
EP - 22
LA - eng
UR - http://eudml.org/doc/75722
ER -

References

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  1. [1] (a) G. Birkhoff and J. Von Neumann, Ann. Math., vol. 37, 1936, p. 823, (b) G.W. Mackey, Mathematical Foundations of Quantum Mechanics, Benjamin, New York, 1963. (c) C. Piron, (1) Helv. Phys. Acta, vol. 37, 1964, p. 439; (2) Observables in General Quantum Theory, lectures delivered at the International School of Physics « Enrico Fermi », Foundations of Quantum Mechanics, Varenna, Italy, 29 June-11 July, 1970, to appear in the proceedings; (3) Survey of General Quantum Physics, Seminars delivered at the University of Denver, Colorado, Autumn 1970. (d) R. Haag and D. Kastler, J. Math. Phys., vol. 5, 1964, p. 848. (e) R.M.F. Houtappel, H. Van Dam and E.P. Wigner, Rev. Mod. Phys., vol. 37, 1965, p. 595. (f) V.S. Varadarajan, Geometry of Quantum Theory, vol. I, Van Nostrand, Princeton, New Jersey, 1968. (g) J.M. Jauch, Foundations of Quantum Mechanics, Addison Wesley, Reading, Mass., 1968. (h) G. Ludwig, Lecture Notes in Physics, 4, Berlin1970. (i) R. Giles, J. Math. Phys., vol. 11, 1970, p. 2139. MR1503312
  2. [2] N. Bourbaki, Variétés Différentielles et Analytiques, Résultats, Hermann, Paris, 1967, Section 5.1. Zbl0171.22004MR219078
  3. [3] J.L. Synge, Relativity, the Special Theory, North Holland Publishing Company, Amsterdam, 1956, chap. 1, sections 2, 3 and 4. Zbl0071.21804MR77267
  4. [4] N. Bourbaki, Topologie générale, Hermann, Paris, chap. II (fourth edition, 1965), section 4, No. 1, corollary 2 to theorem 1. MR244924
  5. [5] (a) A. Lichnerowicz, Théories Relativistes de la Gravitation et de l'Électromagnétisme, Masson, Paris, 1955 ; (b) J.L. Anderson, Principles of Relativity Physics, Academic Press, New York, 1967. Zbl0065.20704
  6. [6] B. Mielnik, Commun. Math. Phys., vol. 15, 1969, p. 1. Zbl0182.59601MR258357
  7. [7] J.-P. Antoine and A. Gleit, Int. J. Theor. Phys., vol. 4, 1971, p. 197. 
  8. [8] N. Bourbaki, Topologie générale, Hermann, Paris, chap. X (second edition, 1967), section 1, No. 2, proposition 1. 
  9. [9] N. Bourbaki, Ibid., chap. X (second edition, 1967), section 1, No. 2, remarks 1 and 2 and chap II (fourth edition, 1965), section 2, No. 2, corollary to proposition 3. 
  10. [10] N. Bourbaki, Variétés Différentielles et Analytiques. Résultats, Hermann, Paris, 1967, section 5.1, No. 6. Zbl0171.22004MR219078
  11. [11] N. Bourbaki, Topologie générale, Hermann, Paris, chap. X (second edition, 1967), section 3, n° 5 and exercise No. 17. 
  12. [12] N. Bourbaki, Ibid., chap X (second edition, 1967), section 3, No. 5. 
  13. [13] N. Bourbaki, Ibid., chap. X (second edition, 1967), section 3, No. 4, corollary 1 to theorem 3. 
  14. [14] N. Bourbaki, Ibid., chap. X (second édition, 1967), section 1, No. 2, Remark 1 and chap. II (fourth edition, 1965), section 1, No. 2, proposition 1. 
  15. [15] N. Bourbaki, Ibid., chap. X (second edition, 1967), section 3, No. 4, theorem 2. 
  16. [16] N. Bourbaki, Ibid., chap. X (second edition, 1967), section 3, No. 2, remark 1. 
  17. [17] S. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, New York, 1962, chap. II, theorem 3.2. Zbl0111.18101MR145455
  18. [18] N. Bourbaki, Topologie générale, Hermann, Paris, chap. VII (third edition, 1963), section 1, No. 2. 
  19. [19] V. Gorini, Commun. Math. Phys., vol. 21, 1971, p. 150. Zbl0224.22019MR292402
  20. [20] V. Berzi and V. Gorini, Space-Time, Reference Frames, Relativistic Invariance : a Topological Approach., Milan University report IFUM 108/FT-1970, unpublished. Zbl0231.58005

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