We extend the quadratic form of the Gaussian functional of the free quantum scalar field theory to the set of functions decreasing in the infinity as \( {\left|\overrightarrow{x}\right|}^{-1} \). We use the momentum-space representation (after the Fourier transform) and the scalar product is generated by the quadratic form of the Laplace operator (potential term of the quantum Hamiltonian).
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 494, 2020, pp. 64–74.
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Bolokhov, T.A. Infrared Extensions of the Quadratic form of the Ground State of Scalar Field Theory. J Math Sci 264, 244–251 (2022). https://doi.org/10.1007/s10958-022-05995-6
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DOI: https://doi.org/10.1007/s10958-022-05995-6