Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Einstein-Cartan-Dirac theory   There are various generalizations of Einstein's theory of gravity (GR); one
of which is the Einstein-Cartan (EC) theory. It modifies the geometrical
structure of manifold and relaxes the notion of affine connection being
symmetric. The theory is also called $U_4$ theory of gravitation; where the
underlying manifold is not Riemannian. The non-Riemannian part of the
space-time is sourced by the spin density of matter. Here mass and spin both
play the dynamical role. We consider the minimal coupling of Dirac field with
EC theory; thereby calling the full theory as Einstein-Cartan-Dirac (ECD)
theory. In the recent works by T.P Singh titled "A new length scale in quantum
gravity", the idea of new unified; mass dependent length scale $L_{cs}$ in
quantum gravity has been proposed. We discuss this idea and formulate ECD
theory in both - standard length scales as well as this new length scale. We
found the non-relativistic limit of ECD theory using WKB-like expansion in
$\sqrt{\hbar}/c$ of the ECD field equations with both the length scales. At
leading order, ECD equations with standard length scales give
Schr\"{o}dinger-Newton equation. With $L_{cs}$, in the low mass limit, it gives
source-free Poisson equation and for higher mass limit, it reduces to Poisson
equation with delta function source. Based on this, a falsifiable test of the
idea of $L_{cs}$ has been proposed. Next, we formulate ECD theory with both the
length scales (especially the Dirac equation (Hehl-Datta equation) and
Contorsion spin coefficients) in Newman-Penrose (NP) formalism. The idea of
$L_{cs}$ suggests a symmetry between small and large masses. Formulating ECD
theory with $L_{cs}$ in NP formalism is desirable because NP formalism happens
to be the common vocabulary for the description of low masses (Dirac theory)
and high masses (gravity theories). A duality between Curvature and torsion has
also been discussed.

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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: math
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys