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In quantum field theory, it is generally assumed that there is a lower boundto the energy, which is normally assumed to the the vacuum state. While thismay be a reasonable assumption for a free field it is not necessarily the casefor interacting fields. In this paper I will examine a "toy" model of a neutralscalar field interacting with a charged scalar field and show that there is nolower bound to the energy in this case.

A "toy" model in QFT with no lower bound to the energy