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We consider the covariant gauge field theory of fractons, which describes a new type of quasiparticles exhibiting novel and non-trivial properties. In particular, we focus on the field theoretical peculiarities which characterize this theory, starting from the fact that, if we accept the paradigm that quantum field theories are defined by their symmetries, fractons unavoidably come together with linearized gravity. The standard Faddeev–Popov procedure to gauge fix the theory leads to a scalar gauge condition, which has two important drawbacks: it is frozen in the Landau gauge and linearized gravity cannot be obtained as a limit. In this paper, we adopt a tensorially alternative gauge fixing, which avoids both problems. In particular, this allows to show that important physical features, such as counting of the degrees of freedom, do not depend on a particular gauge choice, as expected. Moreover, the resulting gauge fixed theory contains both fractons and linearized gravity as a limit, differently from the standard scalar choice. [ABSTRACT FROM AUTHOR]

We consider the theory of a symmetric tensor field in 4D, invariant under a subclass of infinitesimal diffeomorphism transformations, where the vector diff parameter is the 4-divergence of a scalar parameter. The resulting gauge symmetry characterizes the “fracton” quasiparticles and identifies a theory which depends on a dimensionless parameter, which cannot be reabsorbed by a redefinition of the tensor field, despite the fact that the theory is free of interactions. This kind of “electromagnetic gauge symmetry” is weaker that the original diffeomorphism invariance, in the sense that the most general action contains, but is not limited to, linearized gravity, and we show how it is possible to switch continuously from linearized gravity to a mixed phase where both gravitons and fractons are present, without changing the degrees of freedom of the theory. The gauge fixing procedure is particularly rich and rather peculiar, and leads to the computation of propagators which in the massive case we ask to be tachyonic-free, thus constraining the domain of the parameter of the theory. Finally, a closer contact to fractons is made by the introduction of a parameter related to the “rate of propagation”. For a particular value of this parameter the theory does not propagate at all, and we guess that, for this reason, the resulting theory should be tightly related to the fracton excitations.

We show that, contrary to the statements made by many authors, the backflow is not a nonclassical effect. The backflow is a characteristic feature of solutions of the wave equations: quantum and classical. We present simple solutions of the Dirac equation, Maxwell equations and equations of linearized gravity where the backflow phenomenon is clearly seen. In this work we describe backflow in relativistic theories but this phenomenon can occur in the solutions of all kinds of wave equations: quantum and classical. [ABSTRACT FROM AUTHOR]

In this manuscript, we study the nearly flat approximation of a conformally invariant gravitational theory in metric measure space (MMS). In addition, we investigate the transformation of the energy–momentum tensor in this context and obtain the vacuum solution of MMS and its weak field limit in the spherically symmetric coordinates. We show that while it is already a vacuum solution, it can simulate dark matter when restricted to the framework of general relativity, i.e., a symmetry-broken conformal frame. This is done by employing a density function which is an essential part of MMS. We derive an equation for the density function for a general profile of a rotation curve obtained from observations. Specifically, the density function corresponding to two well-known profiles PSS and NFW are provided. [ABSTRACT FROM AUTHOR]