Abstract
We take advantage of the symmetry present in quadratic boson and fermion hamiltonians to give a short and simple derivation of their diagonalizations. This is of particular relevance to bosons. Both procedures are critically evaluated and a striking resemblance is pointed out.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Van Kramendonk, J., Van Vleck, J.H.: Rev. Mod. Phys.30, 1 (1958)
Dicke, R.H.: Phys. Rev.93, 99 (1954)
Tikochinsky, Y.: J. Math. Phys.20, 406 (1979)
Avery, J.: Creation and Annihilation Operators. App. A New York: McGraw-Hill 1976
Chi, B.E.: Nucl. Phys. A146, 449 (1970)
Thouless, D.J.: Nucl. Phys.22, 78 (1961)
Tsallis, C.: J. Math. Phys.19, 277 (1978)
Colpa, J.H.P.: Physica93A, 327 (1978)
Tyablikov, S.V.: Methods in the Quantum Theory of Magnetism. Chap. IV, Sect. 13. New York: Plenum 1967
Berezin, F.A.: The Method of Second Quantization. New York: Academic Press 1966
Lieb, E., Schultz, T., Mattis, D.: Ann. Phys. (N.Y.)16, 407 (1961)
Van Hemmen, J.L., Vertogen, G.: Physica81A, 391 (1975); Sect. 4.
Van Hemmen, J.L.: Fortschr. Physik26, 397 (1978); Chap. II.
Ref. 12, App. A.
Gantmacher, F.R.: The Theory of Matrices, Vol. I. pp. 297 and 334. New York: Chelsea 1959
Flanders, H.: Differential Forms: With Applications to the Physical Sciences. Sect. 2.5. New York: Academic Press 1963
Ref. 6, p. 88.
Tikochinsky, Y.: J. Math. Phys.19, 270 (1979); Sect. 4.
Van Hemmen, J.L.: Z. Physik B38, 279 (1980)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
van Hemmen, J.L. A note on the diagonalization of quadratic boson and fermion hamiltonians. Z. Physik B - Condensed Matter 38, 271–277 (1980). https://doi.org/10.1007/BF01315667
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01315667