# Exact solutions of classical scalar field equations

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Referee this paper: arXiv:0907.4053v2

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This paper presents a set of exact solutions for the classical field equation of a quartic massless scalar field. These solutions have the property to satisfy a dispersion relation of a massive field even if one started from a massless field. They can be used as the expectation value on the vacuum state of a quantum field theory representing oscillations around a constant vacuum expectation value. Indeed, such solutions can be used to describe a scalar field theory that develops a mass gap with a tower of oscillations, those of a harmonic oscillator, being completely trivial in the infrared limit. To understand the formation of the mass gap the Green function is also computed and it is shown that a zero mode appears. So, the theory is seen to break conformal invariance.

summarized
paper authored Jul 23, 2009
edited Aug 6, 2014

The paper is also published in the Journal of Nonlinear Mathematical Physics here.

Please note that since then (2009), I published a more extended version here published in the European Physical Journal C very recently (see here, it is open access). Also the preceding paper is open access and can be freely downloaded.

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