Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective Approaches to QCD   In this lecture I will explain the established pictures of the QCD vacuum
and, in particular, the underlying confinement mechanism. These are: the
magnetic monopole condensation (dual Mei\ss ner effect), the center vortex
picture and the Gribov--Zwanziger picture. I will start by giving a survey of
the common order and disorder parameters of confinement: the temporal and
spatial Wilson loop, the Polyakov loop and the 't Hooft loop. Next the dual
Mei\ss ner effect, which assumes a condensate of magnetic monopoles, will be
explained as a picture of confinement. I will also show how magnetic monopoles
arises in QCD after the so-called Abelian projection. The second lecture is
devoted to the center vortex picture of confinement. Center vortices will be
defined both on the lattice and in the continuum. Within the center vortex
picture the emergence of the area law for the Wilson loop as well as the
deconfinement phase transition at finite temperature will be explained.
Furthermore, lattice evidence for the center vortex picture will be provided.
Finally, I will discuss the topological properties of center vortices and their
relation to magnetic monopoles. I will provide evidence from lattice
calculations that center vortices are not only responsible for confinement but
also for the spontaneous breaking of chiral symmetry. In the last lecture I
will present the Hamiltonian approach to QCD in Coulomb gauge, which is then
used to establish the Gribov--Zwanziger picture of confinement. Furthermore, I
will also relate this scenario to the dual Mei\ss ner effect and the center
vortex picture. Finally, I will study QCD at finite temperature within the
Hamiltonian approach in a novel way by compactifying one spatial dimension. The
Polyakov loop and the dual and chiral quark condensates will be evaluated as
function of the temperature.

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The categories of this paper are: math
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
1
The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: stat