Quadratic expressions in a free boson field

Klein, Abel

doi:10.1090/S0002-9947-1973-0406213-5

Quadratic expressions in a free boson field
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by Abel Klein

Trans. Amer. Math. Soc. 181 (1973), 439-456

DOI: https://doi.org/10.1090/S0002-9947-1973-0406213-5

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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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