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Fermionic Gaussians

Published online by Cambridge University Press:  24 October 2008

P. L. Robinson
P. L. Robinson
Affiliation:
Department of Mathematics, University of Florida, Gainesville, FL32611, U.S.A.
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Extract

The notion of a Gaussian as the exponential of a quadratic is rather familiar. Such functions are of considerable importance in a number of contexts, for example within quantum theory. Thus, in the Schrödinger representation of the canonical commutation relations they alone minimize uncertainty and they appear as ground states for harmonic oscillators. Also in the complex-wave representation of a free boson field they arise as transforms of the Fock vacuum under certain Bogoliubov automorphisms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 3 , November 1995 , pp. 543 - 554
Copyright
Copyright © Cambridge Philosophical Society 1995

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References

REFERENCES

[1]Araki, H.. Bogoliubov automorphisms and Fock representations of canonical anticom-mutation relations; in Operator algebras and mathematical physics, Contemporary Mathematics 62 (Amer. Math. Soe., 1987), 23–141.CrossRefGoogle Scholar
[2]Bourbaki, N.. Topological Vector Spaces (Springer-Verlag, 1987) Chapters 1–5.CrossRefGoogle Scholar
[3]Bratteli, O. and Robinson, D. W.. Operator algebras and quantum statistical mechanics II (Springer- Verlag, 1981).CrossRefGoogle Scholar
[4]Cartier, P.. A course on determinants; in Conformal invariance and string theory (Academic Press, 1989), 443–557.CrossRefGoogle Scholar
[5]Jaffe, A., Lesniewski, A. and Weitsman, J.. Pfaffians on Hilbert space. J. Functional analysis 83 (1989), 348–363.CrossRefGoogle Scholar
[6]Pressley, A. and Segal, G.. Loop groups (Oxford University Press, 1986).Google Scholar
[7]Simon, B.. Trace ideals and their applications. L.M.S. Lecture Notes 35 (Cambridge University Press, 1979).Google Scholar
[8]Seiler, E. and Simon, B.. On finite mass renormalizations in the two-dimensional Yukawa model. J. Math. Phys. 16 (1975), 2289–2293.CrossRefGoogle Scholar
[9]Thaller, B., The Dirac equation (Springer-Verlag, 1992).CrossRefGoogle Scholar