Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Metric-Affine Gauge Theory of Gravity: Field Equations, Noether
  Identities, World Spinors, and Breaking of Dilation Invariance   In Einstein's gravitational theory, the spacetime is Riemannian, that is, it
has vanishing torsion and vanishing nonmetricity (covariant derivative of the
metric). In the gauging of the general affine group ${A}(4,R)$ and of its
subgroup ${GL}(4,R)$ in four dimensions, energy--momentum and hypermomentum
currents of matter are canonically coupled to the one--form basis and to the
connection of a metric--affine spacetime with nonvanishing torsion and
nonmetricity, respectively. Fermionic matter can be described in this framework
by half--integer representations of the $\overline{SL}(4,R)$ covering subgroup.
--- We set up a (first--order) Lagrangian formalism and build up the
corresponding Noether machinery. For an arbitrary gauge Lagrangian, the three
gauge field equations come out in a suggestive Yang-Mills like form. The
conservation--type differential identities for energy--momentum and
hypermomentum and the corresponding complexes and superpotentials are derived.
Limiting cases such as the Einstein--Cartan theory are discussed. In particular
we show, how the ${A}(4,R)$ may ``break down'' to the Poincar\'e (inhomogeneous
Lorentz) group. In this context, we present explicit models for a symmetry
breakdown in the cases of the Weyl (or homothetic) group, the ${SL}(4,R)$, or
the ${GL}(4,R)$.

12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat