Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discrete history of the Lorentzian path integral   In these lecture notes, I describe the motivation behind a recent formulation
of a non-perturbative gravitational path integral for Lorentzian (instead of
the usual Euclidean) space-times, and give a pedagogical introduction to its
main features. At the regularized, discrete level this approach solves the
problems of (i) having a well-defined Wick rotation, (ii) possessing a
coordinate-invariant cutoff, and (iii) leading to_convergent_ sums over
geometries. Although little is known as yet about the existence and nature of
an underlying continuum theory of quantum gravity in four dimensions, there are
already a number of beautiful results in d=2 and d=3 where continuum limits
have been found. They include an explicit example of the inequivalence of the
Euclidean and Lorentzian path integrals, a non-perturbative mechanism for the
cancellation of the conformal factor, and the discovery that causality can act
as an effective regulator of quantum geometry.

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The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
2
The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph