Related papers: $(k,n)$-fractonic Maxwell theory
Inspired by the Maxwell symmetry generalization of general relativity (Maxwell gravity), we have constructed the Maxwell extension of $f(R)$ gravity. We found that the semi-simple extension of the Poincare symmetry allows us to introduce…
The 2+1d continuum Lifshitz theory of a free compact scalar field plays a prominent role in a variety of quantum systems in condensed matter physics and high energy physics. It is known that in compact space, it has an infinite ground state…
We derive the full N=2 supergravity Lagrangian which contains a symplectic invariant scalar potential in terms of electric and magnetic charges. As shown in reference [1], the appearance of magnetic charges is allowed only if tensor…
The objective of the present work -- a literature review on both gapped and gapless fractonic theories -- is to pedagogically fill in the gaps between the research on fractons, and an undergraduate physics education (particularly quantum…
We outline here a simple mathematical introduction to the notions of multipoles for a general extensive property $\Pi$ from the point of view of continuum mechanics. Classically, $\Pi$ is the electric charge, but the theory is not limited…
We establish pointwise and distributional fractal tube formulas for a large class of compact subsets of Euclidean spaces of arbitrary dimensions. These formulas are expressed as sums of residues of suitable meromorphic functions over the…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
A new representation of the scalar electrodynamics is discovered which gives a more redundant description of electromagnetic theory and suitable to construct an appropriate matter action which contains two global symmetries . The symmetries…
The dispersionless longitudinal photon in Maxwell theory is thought of as a redundant degree of freedom due to the gauge symmetry. We find that when there exist exactly flat bands with zero energy in a condensed matter system, the fermion…
We consider the concept of fractons in the context of high-$T_{c}$ superconductivity. These objects, which carry rational or irrational quantum numbers, are classified into universal classes $h$ of particles or quasiparticles which obey…
Extensions of the gravity theory in order to obtain traceless field equations have been widely considered in the literature. The leading example of such class of theories is the unimodular gravity, but there are other possibilities like the…
The dynamics of the torsion field is analyzed in the framework of the Covariant Canonical Gauge Theory of Gravity (CCGG), a De~Donder-Weyl Hamiltonian formulation of gauge gravity. The action is quadratic in both, the torsion and the…
This paper develops a detailed lattice-continuum correspondence for all common examples of Abelian gauge theories, with and without matter. These rules for extracting a continuum theory out of a lattice one represent an elementary way to…
Motivated by recent discussions of fractons, we explore nonrelativistic field theories with a continuous global symmetry, whose charge is a spatial vector. We present several such symmetries and demonstrate them in concrete examples. They…
Fractons are anyons classified into equivalence classes and they obey a specific fractal statistics. The equivalence classes are labeled by a fractal parameter or Hausdorff dimension $h$. We consider this approach in the context of the…
Fractons are a type of emergent quasiparticle which cannot move freely in isolation, but can easily move in bound pairs. Similar phenomenology is found in boson-affected hopping models, encountered in the study of polaron systems and…
Michael Barnsley introduced a family of fractals sets which are repellers of piecewise affine systems. The study of these fractals was motivated by certain problems that arose in fractal image compression but the results we obtained can be…
We show that there exists a natural analogue of the Yang-Mills equations using the Fr\"olicher-Nijenhuis bracket between vector-valued differential forms. The gauge field is a rank-two tensor, and when one constrains it to be symmetric,…
Fractional Gaussian fields are scalar-valued random functions or generalized functions on an $n$-dimensional manifold $M$, indexed by a parameter $s$. They include white noise ($s = 0$), Brownian motion ($s=1, n=1$), the 2D Gaussian free…
Fascinating new phases of matter can emerge from strong electron interactions in solids. In recent years, a new exotic class of many-body phases, described by generalized electromagnetism of symmetric rank-2 electric and magnetic fields and…