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Effective Hamiltonian for Scalar Theories in the Gaussian Approximation

H. W. L. Naus·T. Gasenzer·H. --J. Pirner
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Abstract

We use a Gaussian wave functional for the ground state to reorder the Hamiltonian into a free part with a variationally determined mass and the rest. Once spontaneous symmetry breaking is taken into account, the residual Hamiltonian can, in principle, be treated perturbatively. In this scheme we analyze the $O(1)$ and $O(2)$ scalar models. For the $O(2)$--theory we first explicitly calculate the massless Goldstone excitation and then show that the one-loop corrections of the effective Hamiltonian do not generate a mass.

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H. W. L. Naus, T. Gasenzer, H. --J. Pirner. 1995-08-21. Effective Hamiltonian for Scalar Theories in the Gaussian Approximation. https://doi.org/10.1002/andp.19975090403

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