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Borel Summability of the Ground-State Energy in Spatially Cutoff<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msup><mml:mrow><mml:mi>ϕ</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>
We show that the ground-state energy for a Hamiltonian ${H}_{0}+\ensuremath{\int}g(x):{\ensuremath{\phi}}^{4}(x):dx$ ($g\ensuremath{\in}{L}^{1}\ensuremath{\cap}{L}^{2}$; $g>~0$; ${H}_{0}=\mathrm{free}$ Hamiltonian for Bose particle of mass $m$ in space-time of two dimensions) may be determined from the Feynman perturbation series by the method of Borel summability. This demonstrates that summability methods can be applicable to divergent series …