Asymptotic behaviour of spin-momentum distribution observables for fermion fields with cut-off self-coupling |
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Authors: | E Prugove?ki E B Manoukian |
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Institution: | (1) Department of Mathematics, University of Toronto, Canada;(2) Department of Physics, University of Toronto, Canada;(3) Present address: Theoretical Physics Institute, University of Alberta, Edmonton, Canada |
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Abstract: | In a previous paper asymptotic creation and annhilation operatorsa
±
#
have been constructed by the Kato-Mugibayashi method from the creation and annihilation operatorsa
# for spin 1/2 fields with an interaction Hamiltonian density which is an evendegree polynomial in the field with ultra-violet cut-off and its derivatives. For any eigenvector of the total HamiltonianH=H
0+H
I partial isometries ± have been defined so thata
±
#
equal ±
a
# *± on the ranges ± of ±. Since the existence of a groundstate ofH has been proved, the existence of at least one pair ± follows. The purpose of this paper is to show that for any ± orthogonal to the distribution of spins and momenta of the interacting Schrödinger states exp–itH] ± approaches fort![rarr](/content/t07551412166w4u8/xxlarge8594.gif) ![mnplus](/content/t07551412166w4u8/xxlarge8723.gif) the distributions of spins and momenta of the free state exp–itH
0] if a wave-amplitude renormalization is carried out in ±. This is achieved by studying the expectation values of the operators in themaximally abelian W*-algebra generated by operators of the form ![int](/content/t07551412166w4u8/xxlarge8747.gif) a*a, in terms of whichany information about spins and momenta can be expressed.Supported in part by the National Research Council of Canada. |
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Keywords: | |
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