Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Approach to Quantising Space-Time: III. State Vectors as Functions
  on Arrows   In two recent papers by the author, a new approach was suggested for
quantising space-time, or space. This involved developing a procedure for
quantising a system whose configuration space--or history-theory analogue--is
the set of objects, $\Ob\Q$, in a (small) category $\Q$. The quantum states in
this approach are cross-sections of a bundle $A\leadsto\K[A]$ of Hilbert spaces
over $\Ob\Q$. The Hilbert spaces $\K[A]$, $A\in\Ob\Q$, depend strongly on the
object $A$, and have to be chosen so as to get an irreducible, faithful,
representation of the basic `category quantisation monoid'. In the present
paper, we develop a different approach in which the state vectors are
complex-valued functions on the set of {\em arrows} in $\Q$. This throws a new
light on the Hilbert bundle scheme: in particular, we recover the results of
that approach in the, physically important, example when $\Q$ is a small
category of finite sets.

15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn