Abstract
We construct a consistent model of Galileon scalar electrodynamics. The model satisfies three essential requirements: (1) The action contains higher-order derivative terms, and obey the Galilean symmetry, (2) Equations of motion also satisfy Galilean symmetry and contain only up to second-order derivative terms in the matter fields and, hence do not suffer from instability, and (3) local U(1) gauge invariance is preserved. We show that the non-minimal coupling terms in our model are different from that of the real scalar Galileon models; however, they match with the Galileon real scalar field action. We show that the model can lead to an accelerated expansion in the early Universe. We discuss the implications of the model for cosmological inflation.
Highlights
The standard relativistic field theories describing physical phenomena contain the second-order time and spatial derivatives
The perturbative approach of these field theories is highly successful in explaining the experiments and observations. These field theories have ultraviolet divergences, and higher-derivative terms were introduced in an attempt to remove the ultraviolet divergence [1,2,3]
The interaction between π and φ will pump out energy from π, leading to a runaway situation. These negative energy states can be traded by negative norm states, leading to nonunitary theories [6] and, unsuitable to describe physical phenomena
Summary
The standard relativistic field theories describing physical phenomena contain the second-order time and spatial derivatives. Like Galileon scalars, these theories of gravity are exceptional in that the resulting equations of motion are no more than the second order They are free of ghosts when expanded about the flat space-time. It was shown that the electromagnetic action breaks conformal invariance and has the following three properties: model is described by vector potential Aμ and its derivatives, Gauge invariance is preserved, and equations of motion are linear in second derivatives of the vector potential This is an essential result as earlier it was proven that such an action could not be constructed in flat space-time [19]. [25], Heisenberg et al studied scalarvector Galileon models that do not preserve gauge invariance.) In this work, we bridge this gap by constructing a higher-derivative action of interacting fields (complex scalar Galileons interacting with a vector field), which do not lead to ghosts.
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