Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Second Order Langevin Equation and Definition of Quantum Gravity By
  Stochastic Quantisation   Euclidean quantum gravity might be defined by stochastic quantisation that is
governed by a higher order Langevin equation rather than a first order
stochastic equation. In a transitory phase where the Lorentz time cannot be
defined, the parameter that orders the evolution of quantum gravity phenomena
is the stochastic time. This changes the definition of causality in the period
of primordial cosmology. The prediction of stochastically quantised gravity is
that there will a transition from an oscillating quantum phase to a
semi-classical one, when the Lorentz time emerges. The end of the transition,
as it can be observed from now and described by inflation models, is a diluted
Universe, following the inflation phenomenological evolution. It is filled at
the beginning with scattered classical primordial black holes. The smallest
ones will quickly decay in matter, with a standard quantum field theory
evolution till our period. The stable heavier black holes will remain, forming
a good fraction of the dark matter and the large black holes observed in the
galaxies. In a theoretically related way, this framework suggests the
possibility of a gravitational parton content for "point-like" particles, in
the same five dimensional quantum field theory context as in the primordial
cosmology, with a (+----) signature for the 5d metrics. The very precise and
explicit result expressed in this paper is actually far more modest than its
motivation. We compute explicitly the meaning of a second order Langevin
equation in zero dimensions and define precisely what is second order
stochastic quantisation in a soluble case.

31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess