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Effective Hamiltonian for scalar theories in the Gaussian approximation
Author(s) -
Naus H. W. L.,
Gasenzer T.,
Pirner H.J.
Publication year - 1997
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19975090403
Subject(s) - hamiltonian (control theory) , physics , massless particle , gaussian , mathematical physics , scalar (mathematics) , ground state , spontaneous symmetry breaking , quantum mechanics , symmetry breaking , mathematics , mathematical optimization , geometry
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.