Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A framework for nonrelativistic isotropic models based on generalized
  uncertainty principles   The existence of a fundamental length scale in Nature is a common prediction
of distinct quantum gravity models. Discovery of such would profoundly change
current knowledge of quantum phenomena and modifications to the Heisenberg
uncertainty principle may be expected. Despite the attention given to this
possibility in the past decades, there has been no common framework for a
systematic investigation of so called generalized uncertainty principles (GUP).
In this work we provide such framework in the context of nonrelativistic
quantum mechanics. Our approach is based on very few assumptions: there is a
fundamental length scale, space isotropy, invariance under parity and time
reversal transformations, and symmetricity of the position and momentum
operators. We show simple dimensional analysis allows for building a unified
framework containing any isotropic generalized uncertainty principle (iGUP) and
discuss some popular GUP models in this context after elaborating on relevant
theoretical aspects of the framework. At last, we translate current bounds on
three often investigated GUP models into bounds on parameters of such unified
iGUP framework.

26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
2
The categories of this paper are: math
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol