Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Affine connection representation of gauge fields   There are two ways to unify gravitational field and gauge field. One is to
represent gravitational field as principal bundle connection, and the other is
to represent gauge field as affine connection. Poincar\'{e} gauge theory and
metric-affine gauge theory adopt the first approach. This paper adopts the
second. In this approach:
  (i) Gauge field and gravitational field can both be represented by affine
connection; they can be described by a unified spatial frame.
  (ii) Time can be regarded as the total metric with respect to all dimensions
of internal coordinate space and external coordinate space. On-shell can be
regarded as gradient direction. Quantum theory can be regarded as a geometric
theory of distribution of gradient directions. Hence, gauge theory,
gravitational theory, and quantum theory all reflect intrinsic geometric
properties of manifold.
  (iii) Coupling constants, chiral asymmetry, PMNS mixing and CKM mixing arise
spontaneously as geometric properties in affine connection representation, so
they are not necessary to be regarded as direct postulates in the Lagrangian
anymore.
  (iv) The unification theory of gauge fields that are represented by affine
connection can avoid the problem that a proton decays into a lepton in theories
such as $SU(5)$.
  (v) There exists a geometric interpretation to the color confinement of
quarks.
  In the affine connection representation, we can get better interpretations to
the above physical properties, therefore, to represent gauge fields by affine
connection is probably a necessary step towards the ultimate theory of physics.

8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th