Electromagnetism as an emergent phenomenon: a step-by-step guide

Abstract

We give a detailed description of electrodynamics as an emergent theory from condensed-matter-like structures, not only per se but also as a warm-up for the study of the much more complex case of gravity. We concentrate on two scenarios that, although qualitatively different, share some important features with the idea of extracting the basic generic ingredients that give rise to emergent electrodynamics and, more generally, to gauge theories. We start with Max-wellʼs mechanical model for electrodynamics, where Maxwellʼs equations appear as dynamical consistency conditions. We next take a superfluid 3 He-like system as representative of a broad class of fermionic quantum systems whose low-energy physics reproduces classical electrodynamics (Dirac and Maxwell equations as dynamical low-energy laws). An important lesson that can be derived from both analyses is that the vector potential has a microscopic physical reality and only in the low-energy regime is this physical reality blurred in favor of gauge invariance, which in addition turns out to be secondary to effective Lorentz invariance. 4 New J. Phys. 16 (2014) 123028 C Barceló et al −   ( ) B J J J D t ;.T T Q 0 6 New J. Phys. 16 (2014) 123028 C Barceló et al New J. Phys. 16 (2014) 123028 C Barceló et al New J. Phys. 16 (2014) 123028 C Barceló et al

BeyondΛCDM: Problems, solutions, and the road ahead

“…2, so we will simply mention that some attempts to solve (or at least alleviate) it have resorted to modifying GR, e.g. IR modifications exhibiting degravitating solutions [169,86,170,171], or the presence of a Weyl symmetry [172,173,174]. The existence of black hole or big bang singularities indicate a failure of GR in the high-curvature regime.…”

Longitudinal diffeomorphisms obstruct the protection of vacuum energy

“…The nonlinear completions of these theories can be motivated by symmetry considerations [8,9] or through the self-coupling problem of gravitons [10,13,15]. A detailed analysis shows that these ways are not independent but are intimately related [13].…”

“…A detailed analysis shows that these ways are not independent but are intimately related [13]. The nonlinear completion of Fierz-Pauli theory leads to general relativity, or more precisely to Rosen's reformulation of Einstein's theory as a nonlinear field theory over a flat background (see [12,13] for a thorough discussion of the history of the subject and the different assumptions needed to obtain the result). On the other hand, the solution to the self-coupling problem of gravitons which has as non-interacting limit the free Weyl transverse theory is given by the action of Weyl transverse gravity [9,10] …”

From physical symmetries to emergent gauge symmetries

“…First, it makes easier to compare the present discussion with the features of the theory of spinor electrodynamics that has been briefly discussed previously in section 2.1. On the other hand, the theory with Lagrangian density L = L A + L D has been shown to arise as an emergent theory in specific condensed-matter-like systems [13], which gives to this example further physical relevance.…”

“…From an emergent perspective, one could identify physical quanties underneath an effective low-energy electromagnetic field. As Maxwell himself did with his mechanical model of electromagnetism (see the discusion in [13] and references therein), one could identify some physical quantities playing the role of magnetic and electric fields. However, there is an even simpler description for the electromagnetic phenomena in terms of just one Galilean vector field.…”