219,708 research outputs found
Generalized BRST Quantization and Massive Vector Fields
A previously proposed generalized BRST quantization on inner product spaces
for second class constraints is further developed through applications. This
BRST method involves a conserved generalized BRST charge Q which is not
nilpotent but which satisfies Q=\delta+\delta^{\dagger}, \delta^2=0, and by
means of which physical states are obtained from the projection
\delta|ph>=\delta^{\dagger}|ph>=0. A simple model is analyzed in detail from
which some basic properties and necessary ingredients are extracted. The method
is then applied to a massive vector field. An effective theory is derived which
is close to the one of the Stueckelberg model. However, since the scalar field
here is introduced in order to have inner product solutions, a massive
Yang-Mills theory with polynomial interaction terms might be possible to
construct.Comment: 19 pages,Latexfil
The coupled-cluster approach to quantum many-body problem in a three-Hilbert-space reinterpretation
The quantum many-body bound-state problem in its computationally successful
coupled cluster method (CCM) representation is reconsidered. In conventional
practice one factorizes the ground-state wave functions which live in the "physical" Hilbert space using
an elementary ansatz for plus a formal expansion of in an
operator basis of multi-configurational creation operators. In our paper a
reinterpretation of the method is proposed. Using parallels between the CCM and
the so called quasi-Hermitian, alias three-Hilbert-space (THS), quantum
mechanics, the CCM transition from the known microscopic Hamiltonian (denoted
by usual symbol ), which is self-adjoint in , to its
effective lower-case isospectral avatar , is assigned a
THS interpretation. In the opposite direction, a THS-prescribed, non-CCM,
innovative reinstallation of Hermiticity is shown to be possible for the CCM
effective Hamiltonian , which only appears manifestly non-Hermitian in
its own ("friendly") Hilbert space . This goal is achieved via
an ad hoc amendment of the inner product in , thereby yielding
the third ("standard") Hilbert space . Due to the resulting
exact unitary equivalence between the first and third spaces, , the indistinguishability of predictions
calculated in these alternative physical frameworks is guaranteed.Comment: 15 page
Cardinality Estimation in Inner Product Space
This article addresses the problem of cardinality estimation in inner product spaces. Given a set of high-dimensional vectors, a query, and a threshold, this problem estimates the number of vectors such that their inner products with the query are not less than the threshold. This is an important problem for recent machine-learning applications that maintain objects, such as users and items, by using matrices. The important requirements for solutions of this problem are high efficiency and accuracy. To satisfy these requirements, we propose a sampling-based algorithm. We build trees of vectors via transformation to a Euclidean space and dimensionality reduction in a pre-processing phase. Then our algorithm samples vectors existing in the nodes that intersect with a search range on one of the trees. Our algorithm is surprisingly simple, but it is theoretically and practically fast and effective. We conduct extensive experiments on real datasets, and the results demonstrate that our algorithm shows superior performance compared with existing techniques.Hirata K., Amagata D., Hara T.. Cardinality Estimation in Inner Product Space. IEEE Open Journal of the Computer Society 3, 208 (2022); https://doi.org/10.1109/OJCS.2022.3215206
Homogeneous Ricci solitons in low dimensions
In this article we classify expanding homogeneous Ricci solitons up to
dimension 5, according to their presentation as homogeneous spaces. We obtain
that they are all isometric to solvsolitons, and this in particular implies
that the generalized Alekseevskii conjecture holds in these dimensions. In
addition, we prove that the conjecture holds in dimension 6 provided the
transitive group is not semisimple.Comment: 20 pages, 3 tables; Appendix by Jorge Laure
On the Representation Theory of Negative Spin
We construct a class of negative spin irreducible representations of the
su(2) Lie algebra. These representations are infinite-dimensional and have an
indefinite inner product. We analyze the decomposition of arbitrary products of
positive and negative representations with the help of generalized characters
and write down explicit reduction formulae for the products. From the
characters, we define effective dimensions for the negative spin
representations, find that they are fractional, and point out that the
dimensions behave consistently under multiplication and decomposition of
representations.Comment: 21 pages, no figures, Latex2
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