Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Total Angular Momentum Waves for Scalar, Vector, and Tensor Fields   Most calculations in cosmological perturbation theorydecompose those
perturbations into plane waves (Fourier modes). However, for some calculations,
particularly those involving observations performed on a spherical sky, a
decomposition into waves of fixed total angular momentum (TAM) may be more
appropriate. Here we introduce TAM waves, solutions of fixed total angular
momentum to the Helmholtz equation, for three-dimensional scalar, vector, and
tensor fields. The vector TAM waves of given total angular momentum can be
decomposed further into a set of three basis functions of fixed orbital angular
momentum (OAM), a set of fixed helicity, or a basis consisting of a
longitudinal (L) and two transverse (E and B) TAM waves. The symmetric
traceless rank-2 tensor TAM waves can be similarly decomposed into a basis of
fixed OAM or fixed helicity, or a basis that consists of a longitudinal (L),
two vector (VE and VB, of opposite parity), and two tensor (TE and TB, of
opposite parity) waves. We show how all of the vector and tensor TAM waves can
be obtained by applying derivative operators to scalar TAM waves. This operator
approach then allows one to decompose a vector field into three covariant
scalar fields for the L, E, and B components and symmetric-traceless-tensor
fields into five covariant scalar fields for the L, VE, VB, TE, and TB
components. We provide projections of the vector and tensor TAM waves onto
vector and tensor spherical harmonics. We provide calculational detail to
facilitate the assimilation of this formalism into cosmological calculations.
As an example, we calculate the power spectra of the deflection angle for
gravitational lensing by density perturbations and by gravitational waves. We
comment on an alternative approach to CMB fluctuations based on TAM waves. Our
work may have applications elsewhere in field theory and in general relativity.

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat