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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Quadratic expressions in a free boson field


Author: Abel Klein
Journal: Trans. Amer. Math. Soc. 181 (1973), 439-456
MSC: Primary 81.47
DOI: https://doi.org/10.1090/S0002-9947-1973-0406213-5
MathSciNet review: 0406213
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Abstract: Quadratic expressions in a massive spinless free Boson field are treated by an appropriate extension of the method of second quantization. A certain class of these second quantized operators is shown to generate semigroups that act on a suitable scale of $ {L_p}$-spaces, obtained through the diagonalization of the field at a fixed time, in a particularly regular fashion. The techniques are developed first in an abstract setting, and then applied to the neutral scalar free field. The locally correct generator of Lorentz transformations for $ P{(\varphi )_2}$ is studied in detail, and essential selfadjointness is shown. These techniques are also used to solve explicitly the $ {({\varphi ^2})_n}$ model.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0406213-5
Keywords: Locally correct generator of Lorentz transformations for $ P{(\varphi )_2}$, free Weyl process, neutral scalar free field, unitarily implementable symplectic transformations
Article copyright: © Copyright 1973 American Mathematical Society