Related papers: A Bundle-Theoretic Formulation of Phonons in Cryst…
The first part of the series formulates the Einstein-Cartan theory in the covariant hamiltonian framework. The first section revises the general multisymplectic approach and introduces the notion of the d-jet bundles. Since the whole…
A large class of phononic crystals and mechanical metamaterials exhibit glide symmetry that dictates their functionality or exceptional performance. The glide symmetry gives rise to a number of intriguing phenomena like sticking-bands and…
This paper addresses martensitic precursor phenomena from new theoretical and experimental perspectives. Driven by a phonon domain hypothesis, based on the premise of incomplete phonon softening, and employing Born's dynamical approach to…
We provide a comprehensive classification of isotropic solid and fluid holographic models with broken translational invariance. We describe in detail the collective modes in both the transverse and longitudinal sectors. First, we discuss…
We present a geometric algorithm for obtaining consistent solutions to systems of partial differential equations, mainly arising from singular covariant first-order classical field theories. This algorithm gives an intrinsic description of…
Crystallographic groups describe the symmetries of crystals and other repetitive structures encountered in nature and the sciences. These groups include the wallpaper and space groups. We derive linear and nonlinear representations of…
We theoretically elucidate the transfer of phonon angular momentum by acoustic modes across a smooth interface between crystals. We analyze this process, which is difficult to describe with the conventional acoustic mismatch model, using a…
We propose a fibre bundle formulation of the mathematical base of relativistic quantum mechanics. At the present stage the bundle form of the theory is equivalent to its conventional one, but it admits new types of generalizations in…
We introduce horizontal holonomy groups, which are groups defined using parallel transport only along curves tangent to a given subbundle $D$ of the tangent bundle. We provide explicit means of computing these holonomy groups by deriving…
In this paper, we show that a simple generalization of the holographic axion model can realize spontaneous breaking of translational symmetry by considering a special gauge-axion higher derivative term. The finite real part and imaginary…
The discrete rotational symmetry of crystals leads to the conservation of quantized angular momentum in solids. While the exchange of energy and linear momentum between lattice vibrations (phonons) via anharmonic coupling is a cornerstone…
Some mathematical aspects of using the translation group as an internal symmetry group in a gauge field theory are presented and discussed. The traditional manner in which gravitation can be accounted for by the introduction of a global…
Let $\mathfrak{X}$ be a smooth connected $p$-adic formal scheme. Based on the prismatic description of crystalline local systems, we prove an analogue of Fontaine's conjecture for torsion crystalline local systems on the generic fiber of…
We analyze the concomitant spontaneous breaking of translation and conformal symmetries by introducing in a CFT a complex scalar operator that acquires a spatially dependent expectation value. The model, inspired by the holographic…
We describe some applications of group- and bundle-theoretic methods in solid state physics, showing how symmetries lead to a proof of the localization of electrons in gapped crystalline solids, as e.g. insulators and semiconductors. We…
A very important class of homogeneous Riemannian manifolds are the so-called normal homogeneous spaces, which have associated a canonical connection. In this work we obtain geometrically the (connected component of the) group of affine…
For moduli space of stable parabolic bundles on a compact Riemann surface, we derive an explicit formula for the curvature of its canonical line bundle with respect to Quillen's metric and interpret it as a local index theorem for the…
F-bundle is a formal/non-archimedean version of variation of nc-Hodge structures which plays a crucial role in the theory of atoms as birational invariants from Gromov-Witten theory. In this paper, we establish the spectral decomposition…
We define a notion of connection in a fibre bundle that is compatible with a singular foliation of the base. Fibre bundles equipped with such connections are in plentiful supply, arising naturally for any Lie groupoid-equivariant bundle,…
Affine hamiltonians are defined in the paper and their study is based especially on the fact that in the hyperregular case they are dual objects of lagrangians defined on affine bundles, by mean of natural Legendre maps. The variational…