Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-08-28
Phys.Lett. B358 (1995) 287-296
Physics
High Energy Physics
High Energy Physics - Theory
11 pages, latex
Scientific paper
10.1016/0370-2693(95)01007-D
For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional can be expanded as a sum of local functionals, however this does not satisfy the obvious form of the Schr\"odinger equation. For $\varphi^4$ theory we construct the appropriate equation that this expansion does satisfy. This reduces the eigenvalue problem for the Hamiltonian to a set of algebraic equations. We suggest two approaches to their solution. The first is equivalent to the usual semi-classical expansion whilst the other is a new scheme that may also be applied to theories that are classically massless but in which mass is generated quantum mechanically.
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