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Renormalization of a quadratic interaction in the Hamiltonian formalism

Abstract

The method of the dressing transformation is used to perform a mass renormalization of a neutral scalar free field in the Hamiltonian formalism, for arbitrary space dimension. The resulting situation is analyzed by means of a Bogoliubov transformation, and seen to yield the expected results.

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References

  1. Glimm, J.: Commun. Math. Phys.5, 343 (1967);6, 61 (1967).

    Google Scholar 

  2. —— Commun. Math. Phys.10, 1 (1968).

    Google Scholar 

  3. Guénin, M., Velo, G.: Helv. Phys. Acta41, 362 (1968).

    Google Scholar 

  4. Hepp, K.: Colloque international du CNRS, Gif sur Yvette (1969).

  5. Friedrichs, K. O.: Perturbation of spectra in Hilbert space. Am. Math. Soc., Providence (1965).

    Google Scholar 

  6. Glimm, J.: Lecture notes in Varenna, 1968.

  7. Ginibre, J.: Seminar notes on Euclidean Quantum Field Theory, IHES (1966).

  8. Glauber, R. J.: Phys. Rev.131, 2766 (1963).

    Google Scholar 

  9. Nelson, E.: Operator differential equations. Princeton University lecture notes, 1965.

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Laboratoire associé au C.N.R.S.

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Ginibre, J., Velo, G. Renormalization of a quadratic interaction in the Hamiltonian formalism. Commun.Math. Phys. 18, 65–81 (1970). https://doi.org/10.1007/BF01649639

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  • DOI: https://doi.org/10.1007/BF01649639

Keywords

  • Neural Network
  • Statistical Physic
  • Complex System
  • Nonlinear Dynamics
  • Quantum Computing