Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum knots and knotted zeros   In this paper we show how to place Michael Berry's discovery of knotted zeros
in the quantum states of hydrogen in the context of general knot theory and in
the context of our formulations for quantum knots. Berry gave a time
independent wave function for hydrogen, as a map from three space to the
complex plane and such that the inverse image of zero in the complex plane
contains a knotted curve in three space. We show that for knots in three space
this is a generic situation in that every smooth knot K in three space has a
smooth classifying map f from three space to the complex plane such that the
inverse image of zero is the knot K. This leaves open the question of
characterizing just when such f are wave-functions for quantum systems. One can
compare this result with the work of Mark Dennis and his collaborators, with
the work of Daniel Peralta-Salas and his collaborators, and with the work of
Lee Rudolph. Our approach provides great generality to the structure of knotted
zeros of a wavefunction and opens up many new avenues for research in the
relationships of quantum theory and knot theory. We show how this classifying
construction can be related our previous work on two dimensional and three
dimensional mosaic and lattice quantum knots.

19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th