Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourth order wave equation in Bhabha-Madhavarao spin-$\frac{3}{2}$
  theory   Within the framework of the Bhabha-Madhavarao formalism, a consistent
approach to the derivation of a system of the fourth order wave equations for
the description of a spin-$\frac{3}{2}$ particle is suggested. For this purpose
an additional algebraic object, the so-called $q$-commutator ($q$ is a
primitive fourth root of unity) and a new set of matrices $\eta_{\mu}$, instead
of the original matrices $\beta_{\mu}$ of the Bhabha-Madhavarao algebra, are
introduced. It is shown that in terms of the $\eta_{\mu}$ matrices we have
succeeded in reducing a procedure of the construction of fourth root of the
fourth order wave operator to a few simple algebraic transformations and to
some operation of the passage to the limit $z \rightarrow q$, where $z$ is some
(complex) deformation parameter entering into the definition of the
$\eta$-matrices. In addition, a set of the matrices ${\cal P}_{1/2}$ and ${\cal
P}_{3/2}^{(\pm)}(q)$ possessing the properties of projectors is introduced.
These operators project the matrices $\eta_{\mu}$ onto the spins 1/2- and
3/2-sectors in the theory under consideration. A corresponding generalization
of the obtained results to the case of the interaction with an external
electromagnetic field introduced through the minimal coupling scheme is carried
out. The application to the problem of construction of the path integral
representation in parasuperspace for the propagator of a massive
spin-$\frac{3}{2}$ particle in a background gauge field within the
Bhabha-Madhavarao approach is discussed.

17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph