New representations of the Poincaré group describing two interacting bosons

E. Frochaux

Annales de l'I.H.P. Physique théorique (1999)

  • Volume: 71, Issue: 2, page 217-239
  • ISSN: 0246-0211

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Frochaux, E.. "New representations of the Poincaré group describing two interacting bosons." Annales de l'I.H.P. Physique théorique 71.2 (1999): 217-239. <http://eudml.org/doc/76835>.

@article{Frochaux1999,
author = {Frochaux, E.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Schrödinger picture in momentum space; Lorentz invariant measure; Hamiltonian; free Lorentz generators; Poincaré algebra commutation rules; relativistic Schrödinger equation; bound state; scattering matrix},
language = {eng},
number = {2},
pages = {217-239},
publisher = {Gauthier-Villars},
title = {New representations of the Poincaré group describing two interacting bosons},
url = {http://eudml.org/doc/76835},
volume = {71},
year = {1999},
}

TY - JOUR
AU - Frochaux, E.
TI - New representations of the Poincaré group describing two interacting bosons
JO - Annales de l'I.H.P. Physique théorique
PY - 1999
PB - Gauthier-Villars
VL - 71
IS - 2
SP - 217
EP - 239
LA - eng
KW - Schrödinger picture in momentum space; Lorentz invariant measure; Hamiltonian; free Lorentz generators; Poincaré algebra commutation rules; relativistic Schrödinger equation; bound state; scattering matrix
UR - http://eudml.org/doc/76835
ER -

References

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  1. [1] P.A.M. Dirac, Forms of relativistic dynamics, Rev. Mod. Phys.21 (1949) 392- 399. Zbl0035.26803MR33248
  2. [2] D.G. Currie, Interaction contra classical relativistic Hamiltonian particle mechanics, J. Math. Phys.4 (1963); See also E.C.G. Sudarshan and N. Mukunda, Classical Dynamics: A Modern Perspective, Wiley, New York, 1974. Zbl0125.19505MR158737
  3. [3] E. Frochaux, Non-trivial representations of the special relativity group, Forum Math.9 (1997) 75-102. Zbl0863.22005MR1426455
  4. [4] E. Frochaux, Two relativistic boson models in the Schrödinger picture in three space-time dimensions, J. Math. Phys.37 (1996) 2979-3000. Zbl0861.22015MR1390248
  5. [5] E. Frochaux, A relativistic quantum equation for N ≽ 2 bosons in two space-time dimensions, Helv. Phys. Acta68 (1995) 47-63. Zbl0840.35114MR1335349
  6. [6] E. Frochaux and A. Roessl, A relativistic generalization of Quantum Mechanics in two space-time dimensions, in preparation. 
  7. [7] E. Nelson, Analytic vectors, Ann. Math.70 (1959) 572-615. Zbl0091.10704MR107176
  8. [8] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. II, Fourier Analysis and Self-Adjointness, Academic Press, New York, 1975. Zbl0308.47002
  9. [9] J. Sucher, Relativistic invariance and the square-root Klein-Gordon equation, J Math. Phys.4 (1963) 17-23. Zbl0115.44403MR144638
  10. [10] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. III, Scattering Theory, Academic Press, Boston, 1979. Zbl0405.47007MR529429
  11. [11] D.R. Yafaev, Mathematical Scattering Theory, General Theory, Translations of Mathematical Monographs, Amer. Math. Soc., Providence, RI, 1992. Zbl0761.47001MR1180965
  12. [12] N. Dunford and J.T. Schwartz, Linear Operators: Part II: Spectral Theory, Wiley Classical Library, Interscience, 1988. Zbl0635.47002MR1009163
  13. [13] E.P. Wigner, Unitary representations of the inhomogeneous Lorentz group, Ann. Math.40 (1939) 149-204. Zbl0020.29601MR1503456JFM65.1129.01

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