Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: To be unitary-invariant or not?: a simple but non-trivial proposal for
  the complexity between states in quantum mechanics/field theory   We make comments on some shortcomings of the non-unitary-invariant and
non-bi-invariant complexity in quantum mechanics/field theory and argue that
the unitary-invariant and bi-invariant complexity is still a competitive
candidate in quantum mechanics/field theory, contrary to quantum circuits in
quantum computation. Based on the unitary-invariance of the complexity and
intuitions from the holographic complexity, we propose a novel complexity
formula between two states. Our proposal shows that i) the complexity between
certain states in two dimensional CFTs is given by the Liouville action, which
is compatible with the path-integral complexity; ii) it also gives natural
interpretation for both the CV and CA holographic conjectures and identify what
the reference states are in both cases. Our proposal explicitly produces the
conjectured time dependence of the complexity: linear growth in chaotic
systems. Last but not least, we present interesting relations between the
complexity and the Lyapunov exponent: the Lyapunov exponent is proportional to
the complexity growth rate in linear growth region.

21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat