Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The minimum parameterization of the wave function for the many-body
  electronic Schr\"odinger equation. Theory and ansatz   The minimum parameterization of the wave function is derived for the
time-independent many-body problem. In this parameterization all electrons and
electron pairs are indistinguishable which eliminates the exponential scaling
with the number of particles plaguing all other correlation methods. An
exponential scaling shown to stem from the expansion of the wave function in
one-particle basis sets. It is demonstrated that using a geminal basis with a
skew-symmetric orthogonal coefficient matrix, which fulfill a Lie algebra, the
parameterization of the exact wave function becomes independent of the number
of particles and only scale quadratic with the number of basis functions in the
optimized basis and quartic in an arbitrary basis. The resulting
antisymmetrized geminal power wave function is shown to fulfill the necessary
and sufficient conditions for the exact wave function, treat all electrons and
electron pairs as indistinguishable and be the most compact representation of
the exact wave function possible. The number of parameters in the
antisymmetrized geminal power wave function is exactly the same number of
parameters as in the two-particle reduced density matrix thereby showing that
these representations are equivalent just like the representations for a
one-particle Hamiltonian. A detailed discussion of how the most compact wave
function can be derived in general is also presented along with different
geminal ans\"atze and sufficient closure relations. Due to the breaking of the
scaling wall for the exact wave function it is expected that, if a general set
of constraints can be found, even systems of biological relevance can be
treated exactly in the future.

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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg