## Making a Wavefunctional Representation of Physical States Congruent with the False Vacuum Hypothesis of Sidney Coleman

**Authors:** Andrew Beckwith

We examine quantum decay of the false vacuum in the driven sine-Gordon
system and show how both together permit construction of a Gaussian wave
functional. This is due to changing a least action integral to be similar with
respect to the WKB approximation. In addition we find that the soliton-antisoliton
(S-S') separation distance obtained from the Bogomol'nyi inequality permits after
rescaling a dominant &phi^{2} contribution to the least action integrand. This is from an
initial scalar potential characterized by a tilted double well potential construction.

**Comments:** 15 pages. Mathematical / condensed matter joint piece designed to explain
the congruence of the Bogomol’nyi inequality with the fate of the false vacuum hypothesis as given by Sidney Coleman.
Foundational issue involved which was key to up dates as to my PhD dissertation, and subsequent work in terms of the
tunneling Hamiltonian, and I-E curves in laboratory data taking. Note , the Bogomol’nyi inequality is a key work horse
as to PARTICLE/ Astro physics, as is the false vacuum hypothesis

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### Submission history

[v1] 28 Sep 2009

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