Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extension of Quantum Mechanics to Individual Systems   The Copenhagen Interpretation describes individual systems, using the same
Hilbert space formalism as does the statistical ensemble interpretation (SQM).
This leads to the well-known paradoxes surrounding the Measurement Problem. We
extend this common mathematical structure to encompass certain natural bundles
with connections over the Hilbert sphere S. This permits a consistent extension
of the statistical interpretation to interacting individual systems, thereby
resolving these paradoxes.
  Suppose V is a physical system in interaction with another system W. The
state vector of V+W has a set of polar decompositions with a vector q of
complex coefficients. These are parameterized by the right toroid T of
amplitudes q, and comprise a singular toroidal bundle over S, which comprises
the enlarged state space of V+W. We prove that each T has a unique natural
convex partition yielding the correct SQM probabilities. In the extended theory
V and W synchronously assume pure spectral states according to which member of
the partition contains q. The apparent indeterminism of SQM is thus
attributable to the effectively random distribution of initial phases.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph