Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reflection positivity on spheres   In this article we specialize a construction of a reflection positive Hilbert
space due to Dimock and Jaffe--Ritter to the sphere $\mathbb{S}^n$. We
determine the resulting Osterwalder--Schrader Hilbert space, a construction
that can be viewed as the step from euclidean to relativistic quantum field
theory. We show that this process gives rise to an irreducible unitary
spherical representation of the orthochronous Lorentz group $G^c =
\mathrm{O}_{1,n}(\mathbb{R})^{\uparrow}$ and that the representations thus
obtained are the irreducible unitary spherical representations of this group. A
key tool is a certain complex domain $\Xi$, known as the crown of the
hyperboloid, containing a half-sphere $\mathbb{S}^n_+$ and the hyperboloid
$\mathbb{H}^n$ as totally real submanifolds. This domain provides a bridge
between those two manifolds when we study unitary representations of $G^c$ in
spaces of holomorphic functions on $\Xi$. We connect this analysis with the
boundary components which are the de Sitter space and the Lorentz cone of
future pointing light like vectors.

37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex