Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A representation of the wave function on the three-dimensional space   One of the major concerns of Schr\"odinger, Lorentz, Einstein, and many
others about the wave function is that it is defined on the
$3\mathbf{N}$-dimensional configuration space, rather than on the
$3$-dimensional physical space. This gives the impression that quantum
mechanics cannot have a three-dimensional space or spacetime ontology, even in
the absence of quantum measurements. In particular, this seems to affect
interpretations which take the wave function as a physical entity, in
particular the many worlds and the spontaneous collapse interpretations, and
some versions of the pilot wave theory.
  Here, a representation of the many-particle states is given, as multi-layered
fields defined on the $3$-dimensional physical space. This representation is
equivalent to the usual representation on the configuration space, but it makes
it explicit that it is possible to interpret the wave functions as defined on
the physical space. As long as only unitary evolution is involved, the
interactions are local. I intended this representation to capture and formalize
the non-explicit and informal intuition of many working quantum physicists,
who, by considering the wave function sometimes to be defined on the
configuration space, and sometimes on the physical space, may seem to
researchers in the foundations of quantum theory as adopting an inconsistent
view about its ontology. This representation does not aim to solve the
measurement problem, and it allows for Schr\"odinger cats just like the usual
one. But it may help various interpretations to solve these problems, through
inclusion of the wave function as (part of) their primitive ontology.
  In an appendix, it is shown how the multi-layered field representation can be
extended to quantum field theory.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-fin