.png){kind=icon}
.png){kind=icon}
Return
From elasticity tetrads to rectangular vielbein
.png){kind=icon}
OA
AI
DOI：10.1016/j.aop.2022.168998.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
The paper is devoted to the memory of Igor E. Dzyaloshinsky. In our common paper Dzyaloshinskii and Volovick (1980), we discussed the elasticity theory described in terms of the gravitational field variables - the elasticity vielbein Ea mu. They come from the phase fields, which describe the deformations of crystal planes. The important property of the elasticity vielbein Ea mu is that in general they are not the square matrices. While the spacetime index mu takes the values mu = (0, 1, 2, 3), in crystals the index a = (1, 2, 3), in vortex lattices a = (1, 2), and in smectic liquid crystals there is only one phase field, a = 1. These phase fields can be considered as the spin gauge fields, which are similar to the gauge fields in Standard Model (SM) or in Grand Unification (GUT).On the other hand, the rectangular vielbein e mu a may emerge in the vicinity of Dirac points in Dirac materials. In particular, in the planar phase of the spin-triplet superfluid 3He the spacetime index mu = (0, 1, 2, 3), while the spin index a takes values a = (0, 1, 2, 3, 4). Although these (4 x 5) vielbein describing the Dirac fermions are rectangular, the effective metric g mu nu of Dirac quasiparticles remains (3+1)-dimensional. All this suggests the possible extension of the Einstein-Cartan gravity by introducing the rectangular vielbein, where the spin fields belong to the higher groups, which may include SM or even GUT groups.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open (http://creativecommons.org/licenses/by/4.0/).
Keywords:
Tetrad
Vielbein
Elasticity theory
Einstein-Cartan gravity
Dirac fermions
Superfluid3He
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.