Abstract
We formulate the word-line approach of the field theory of fractons and their symmetries. The distinction between the different models is based on their dispersion relations for the energy. In order to study the sub-system symmetries, we construct the Routhians associated with the particle Lagrangians considered. We also construct the pseudoclassical description of spinning fractons.
Highlights
There has been recent interest in condensed matter physics to study lattice models with some peculiar properties, like the infinite degeneracy of the ground state and the existence of restricted motions along lines and planes
In order to study the subsystem symmetries, we construct the Routhian functionals associated with the particle Lagrangians considered
From the worldline approach point of view, this corresponds to considering the Routhian functionals, i.e., a partial Legendre transformation associated with the Lagrangian [12]
Summary
There has been recent interest in condensed matter physics to study lattice models with some peculiar properties, like the infinite degeneracy of the ground state and the existence of restricted motions along lines and planes. Standard lore is that the long-distance properties of a lattice can be described in terms of field theories. The fracton models that we will consider here are classified as ðmE; npÞ, where mE is the exponent of the energy in the dispersion relation, and np is the overall power of the space momenta [9]. We give the first steps towards constructing a worldline formulation of the field theory of some fracton models and their symmetries. As we shall see, using the dispersion relations of the field theory for the fractons will allow us to derive a Lagrangian describing the classical. The organization of the paper is as follows: in Sec. II, we will construct the particle Lagrangians associated with the (2,4) and (1,4) models, and we will study the related symmetries and subsymmetries.
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