219,708 research outputs found

    Generalized BRST Quantization and Massive Vector Fields

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    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

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    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 Ψ=eSΦ|\Psi\rangle= e^S |\Phi\rangle which live in the "physical" Hilbert space H(P){\cal H}^{(P)} using an elementary ansatz for Φ|\Phi\rangle plus a formal expansion of SS 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 HH), which is self-adjoint in H(P){\cal H}^{(P)}, to its effective lower-case isospectral avatar h^=eSHeS\hat{h}=e^{-S} H e^S, 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 h^\hat{h}, which only appears manifestly non-Hermitian in its own ("friendly") Hilbert space H(F){\cal H}^{(F)}. This goal is achieved via an ad hoc amendment of the inner product in H(F){\cal H}^{(F)}, thereby yielding the third ("standard") Hilbert space H(S){\cal H}^{(S)}. Due to the resulting exact unitary equivalence between the first and third spaces, H(P)H(S){\cal H}^{(P)}\sim {\cal H}^{(S)}, the indistinguishability of predictions calculated in these alternative physical frameworks is guaranteed.Comment: 15 page

    Cardinality Estimation in Inner Product Space

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    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

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    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

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    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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