Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New polynomially exact integration rules on U(N) and SU(N)   In lattice Quantum Field Theory, we are often presented with integrals over
polynomials of coefficients of matrices in U(N) or SU(N) with respect to the
Haar measure. In some physical situations, e.g., in presence of a chemical
potential, these integrals are numerically very difficult since their
integrands are highly oscillatory which manifests itself in form of the sign
problem. In these cases, Monte Carlo methods often fail to be adequate,
rendering such computations practically impossible. We propose a new class of
integration rules on U(N) and SU(N) which are derived from polynomially exact
rules on spheres. We will examine these quadrature rules and their efficiency
at the example of a 0+1 dimensional QCD for a non-zero quark mass and chemical
potential. In particular, we will demonstrate the failure of Monte Carlo
methods in such applications and that we can obtain polynomially exact,
arbitrary precision results using the new integration rules.

30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn