Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Introduction to Spontaneous Symmetry Breaking   Perhaps the most important aspect of symmetry in physics is the idea that a
state does not need to have the same symmetries as the theory that describes
it. This phenomenon is known as spontaneous symmetry breaking. In these lecture
notes, starting from a careful definition of symmetry in physics, we introduce
symmetry breaking and its consequences. Emphasis is placed on the physics of
singular limits, showing the reality of symmetry breaking even in small-sized
systems. Topics covered include Nambu-Goldstone modes, quantum corrections,
phase transitions, topological defects and gauge fields. We provide many
examples from both high energy and condensed matter physics. These notes are
suitable for graduate students.

24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom