Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some aspects of positive kernel method of quantization   We discuss various aspects of positive kernel method of quantization of the
one-parameter groups $\tau_t \in \mbox{Aut}(P,\vartheta)$ of automorphisms of a
$G$-principal bundle $P(G,\pi,M)$ with a fixed connection form $\vartheta$ on
its total space $P$. We show that the generator $\hat{F}$ of the unitary flow
$U_t = e^{it \hat{F}}$ being the quantization of $\tau_t $ is realized by a
generalized Kirillov-Kostant-Souriau operator whose domain consists of sections
of some vector bundle over $M$, which are defined by suitable positive kernel.
  This method of quantization applied to the case when $G=GL(N,\mathbb{C})$ and
$M$ is a non-compact Riemann surface leads to quantization of the arbitrary
holomorphic flow $\tau_t^{hol} \in \mbox{Aut}(P,\vartheta)$. For the above
case, we present the integral decompositions of the positive kernels on
$P\times P$ invariant with respect to the flows $\tau_t^{hol}$ in terms of
spectral measure of $\hat{F}$. These decompositions generalize the ones given
by Bochner theorem for a positive kernels on $\mathbb{C} \times \mathbb{C}$
invariant with respect to the one-parameter groups of translations of complex
plane.

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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex