Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative Spectral Invariants and Black Hole Entropy   We consider an intrinsic entropy associated with a local conformal net A by
the coefficients in the expansion of the logarithm of the trace of the ``heat
kernel'' semigroup. In analogy with Weyl theorem on the asymptotic density
distribution of the Laplacian eigenvalues, passing to a quantum system with
infinitely many degrees of freedom, we regard these coefficients as
noncommutative geometric invariants. Under a natural modularity assumption, the
leading term of the entropy (noncommutative area) is proportional to the
central charge c, the first order correction (noncommutative Euler
characteristic) is proportional to log\mu_A, where \mu_A is the global index of
A, and the second spectral invariant is again proportional to c.
  We give a further general method to define a mean entropy by considering
conformal symmetries that preserve a discretization of S^1 and we get the same
value proportional to c.
  We then make the corresponding analysis with the proper Hamiltonian
associated to an interval. We find here, in complete generality, a proper mean
entropy proportional to log\mu_A with a first order correction defined by means
of the relative entropy associated with canonical states.
  By considering a class of black holes with an associated conformal quantum
field theory on the horizon, and relying on arguments in the literature, we
indicate a possible way to link the noncommutative area with the
Bekenstein-Hawking classical area description of entropy.

18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph