Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Role of Conservation Principles in the Abraham--Minkowski
  Controversy   The Abraham--Minkowski controversy refers to a long-standing inability to
adequately address certain issues involving the conservation of the momentum of
an electromagnetic field in a linear dielectric medium. We apply the usual
assumption of a material subsystem that couples to the electromagnetic
subsystem such that the total energy and total momentum are conserved. We then
construct the total energy--momentum tensor from the total energy density and
the total momentum density. Applying conservation principles to the total
energy--momentum tensor, we construct the tensor energy--momentum continuity
equation. We show that one of the components of the tensor energy--momentum
continuity equation, the energy continuity equation, is manifestly false. We
conclude that the Abraham--Minkowski controversy is unresolvable because the
extant principles of conservation are inconsistent in a simple linear
dielectric medium.

36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex