Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ultraviolet dimensional reduction of spacetime with zero-point length   Among the many disparate approaches towards quantum gravity, the reduction of
spacetime dimension in the ultraviolet regime is expected to be a common
thread. The dimensionality of spacetime can be defined in various contexts. The
spectral dimension of spacetime is defined in the context of diffusion
processes on a manifold. We show that a spacetime with zero-point length has
spectral dimension $3.5$ when the characteristic diffusion time has the size of
the zero-point length. The spectral dimension (negatively) diverges for an even
shorter diffusion time, thus preventing any reliable physical interpretation in
the deep ultraviolet regime. The thermodynamic dimension is defined by
realizing that the free energy $F(\beta)$ of a free field or ideal gas at
finite temperature ($\beta^{-1}$) in $D$ dimensions scales as $F\sim
\beta^{-D}$. Using Schwinger's proper time formalism at finite temperature, we
show that for spacetime incorporating a zero-point length, the thermodynamic
dimension reduces to $1.5$ near the Planck scale and then to $1$ in the deep
ultraviolet regime. This signifies a "phase-transition" in which a (massless)
bosonic ideal gas in four dimensions essentially behaves like radiation
($w=1/3$) at low energies, whereas near the Planck scale, it behaves
equivalently to having an equation of state parameter $w=2$. Furthermore,
dimension can be deduced from the potential $V_D(r)$ of interaction between two
point-like sources separated at a distance $r$ as its scaling depends on $D$.
Comparing with the scaling behavior of conventional Yukawa-like potentials at
short distances, we show that the zero-point length spacetime's ultraviolet
dimension appears to be either $2$ or $3$ depending on the use of massive or
massless force carriers as probes.

33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
2
The categories of this paper are: math
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga