No Approximate Complex Fermion Coherent States |
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Authors: | Tomáš Tyc Brett Hamilton Barry C Sanders William D Oliver |
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Institution: | (1) Institute of Theoretical Physics, Masaryk University, 61137 Brno, Czech Republic;(2) Institute for Quantum Information Science, University of Calgary, Calgary, ABT2N 1N4, Canada;(3) Australian Centre of Excellence for Quantum Computer Technology, Macquarie University, Sydney, NSW 2109, Australia;(4) MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420, USA |
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Abstract: | Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart
for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude
and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately,
by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states.
Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum
state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate
complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of
Grassman algebras as an appropriate alternative.
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Keywords: | coherent state fermion field correlator factorization Grassmann numbers |
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