Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The role of dilations in diffeomorphism covariant algebraic quantum
  field theory   The quantum analogue of general relativistic geometry should be implementable
on smooth manifolds without an a priori metric structure, the kinematical
covariance group acting by diffeomorphisms.
  Here I approach quantum gravity (QG) in the view of constructive, algebraic
quantum field theory (QFT). Comparing QG with usual QFT, the algebraic approach
clarifies analogies and peculiarities. As usual, an isotonic net of *-algebras
is taken to encode the quantum field operators. For QG, the kinematical
covariance group acts via diffeomorphisms on the open sets of the manifold, and
via algebraic isomorphisms on the algebras. In general, the algebra of
observables is covariant only under a (dynamical) subgroup of the general
diffeomorphism group.
  After an algebraic implementation of the dynamical subgroup of dilations,
small and large scale cutoffs may be introduced algebraically. So the usual a
priori conflict of cutoffs with general covariance is avoided. Even more, these
cutoffs provide a natural local cobordism for topological quantum field theory.
  A new commutant duality between the minimal and maximal algebra allows to
extract the modular structure from the net of algebras. The outer modular
isomorphisms are then again related to dilations, which (under certain
conditions) may provide a notion of time.

24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph