Abstract
The physical content of a para-Fermi field theory is analysed from the point of view of its local observables. The parafield theory leads to parastatistics only for special choices of the observable algebra, and only then does it give a complete description of the relevant physical states. On the other hand there is always a physically equivalent description in terms of a certain number of ordinary Fermi fields from which the observables are selected by a gauge group (in general non-Abelian). Thus one can always achieve a reduction to Fermi statistics by considering a system with different particle types which are distinguished by hidden (unobservable) quantum numbers.
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References
Green, H. S.: A generalized method of field quantization. Phys. Rev.90, 270 (1953).
Volkov, D.:S-matrix in the generalized quantization method. Soviet Phys. JETP11, 375 (1960).
Greenberg, O. W., Messiah, A. M. L.: Selection rules for parafields and the absence of para particles in nature. Phys. Rev. B138, 1155 (1965).
—— Parafield theory. In: Proceedings of Conference on the Mathematical Theory of Elementary Particles. Edited by R. Goodman and I. Segal. London-New York: MIT-Press 1966.
Landshoff, P. V., Stapp, Henry P.: Parastatistics and a unified theory of identical particles. Ann. Phys.45, 72 (1967).
Doplicher, S., Haag, R., Roberts, J. E.: Fields, observables and gauge transformations I. Commun. Math. Phys.13, 1 (1969).
Segal, I. E.: Tensor algebras over Hilbert spaces II. Ann. Math.63, 160 (1956).
Guichardet, A.: Produits tensoriels infinis et répresentations des relations d'anticommutation. Ann. Sci. Ecole Norm. Super.83, 1 (1966).
Doplicher, S., Kastler, D., Robinson, D. W.: Covariance algebras in field theories and statistical mechanics. Commun. Math. Phys.3, 1 (1966).
Borchers, H. J.: Local rings and the connection of spin and statistics. Commun. Math. Phys.1, 291 (1965).
Doplicher, S., Haag, R., Roberts, J. E.: Fields, observables and gauge transformation II. Commun. Math. Phys.15, 173 (1969).
Yang, C. N.: Concept of off-diagonal long-range order and the quantum phases of liquid He and of superconductors. Rev. Mod. Phys.34, 694 (1962).
Ohnuki, Y., Kamefuchi, S.: Some general properties of para-Fermi field theory. Phys. Rev.170, 1279 (1968).
—— —— Wavefunctions of identical particles. Ann. Phys.51, 337 (1969).
Weyl, H.: The classical groups. Princeton University Press, Princeton 1946.
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Drühl, K., Haag, R. & Roberts, J.E. On parastatistics. Commun.Math. Phys. 18, 204–226 (1970). https://doi.org/10.1007/BF01649433
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DOI: https://doi.org/10.1007/BF01649433