On the structure of the canonical tensor operators in the unitary groups. I. An extension of the pattern calculus rules and the canonical splitting in U(3)

1972 ◽  
Vol 13 (12) ◽  
pp. 1957-1984 ◽  
Author(s):  
L. C. Biedenharn ◽  
J. D. Louck ◽  
E. Chacón ◽  
M. Ciftan
Keyword(s):  
Unitary Groups ◽  
Calculus Rules ◽  
Canonical Splitting ◽  
Tensor Operators

scholarly journals A pattern calculus for tensor operators in the unitary groups

1968 ◽  
Vol 8 (2) ◽  
pp. 89-131 ◽  
Author(s):  
L. C. Biedenharn ◽  
J. D. Louck
Keyword(s):  
Unitary Groups ◽  
Tensor Operators

On the Symmetric Tensor Operators of the Unitary Groups

1972 ◽  
Vol 13 (9) ◽  
pp. 1329-1333 ◽  
Author(s):  
S. J. Ališauskas ◽  
A.‐ A. A. Jucys ◽  
A. P. Jucys
Keyword(s):  
Symmetric Tensor ◽  
Unitary Groups ◽  
Tensor Operators

scholarly journals Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties

2018 ◽  
Vol 2020 (13) ◽  
pp. 3902-3926
Author(s):  
Réda Boumasmoud ◽  
Ernest Hunter Brooks ◽  
Dimitar P Jetchev
Keyword(s):  
Vertical Distribution ◽  
Three Dimensional ◽  
Complex Multiplication ◽  
Horizontal Distribution ◽  
Unitary Groups ◽  
Shimura Varieties ◽  
Heegner Points ◽  
Universal Norm

Abstract We consider cycles on three-dimensional Shimura varieties attached to unitary groups, defined over extensions of a complex multiplication (CM) field $E$, which appear in the context of the conjectures of Gan et al. [6]. We establish a vertical distribution relation for these cycles over an anticyclotomic extension of $E$, complementing the horizontal distribution relation of [8], and use this to define a family of norm-compatible cycles over these fields, thus obtaining a universal norm construction similar to the Heegner $\Lambda $-module constructed from Heegner points.

scholarly journals An improved holographic nodal line semimetal

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Yan Liu ◽  
Xin-Meng Wu
Keyword(s):  
Mass Term ◽  
Nodal Line ◽  
Duality Relation ◽  
Strongly Coupled ◽  
Nodal Lines ◽  
Form Field ◽  
Improved Model ◽  
Fermionic Spectrum ◽  
Chern Simons ◽  
Tensor Operators

Abstract We study an improved holographic model for the strongly coupled nodal line semimetal which satisfies the duality relation between the rank two tensor operators $$ \overline{\psi}{\gamma}^{\mu v}\psi $$ ψ ¯ γ μv ψ and $$ \overline{\psi}{\gamma}^{\mu v}{\gamma}^5\psi $$ ψ ¯ γ μv γ 5 ψ . We introduce a Chern-Simons term and a mass term in the bulk for a complex two form field which is dual to the above tensor operators and the duality relation is automatically satisfied from holography. We find that there exists a quantum phase transition from a topological nodal line semimetal phase to a trivial phase. In the topological phase, there exist multiple nodal lines in the fermionic spectrum which are topologically nontrivial. The bulk geometries are different from the previous model without the duality constraint, while the resulting properties are qualitatively similar to those in that model. This improved model provides a more natural ground to analyze transports or other properties of strongly coupled nodal line semimetals.

scholarly journals The time-dependent angular analysis of Bd → KSℓℓ, a new benchmark for new physics

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Sébastien Descotes-Genon ◽  
Martín Novoa-Brunet ◽  
K. Keri Vos
Keyword(s):  
Time Evolution ◽  
Form Factors ◽  
New Physics ◽  
Time Dependent ◽  
Angular Analysis ◽  
Time Dependent Analysis ◽  
Tensor Operators

Abstract We consider the time-dependent analysis of Bd→ KSℓℓ taking into account the time-evolution of the Bd meson and its mixing into $$ {\overline{B}}_d $$ B ¯ d . We discuss the angular conventions required to define the angular observables in a transparent way with respect to CP conjugation. The inclusion of time evolution allows us to identify six new observables, out of which three could be accessed from a time-dependent tagged analysis. We also show that these observables could be obtained by time-integrated measurements in a hadronic environment if flavour tagging is available. We provide simple and precise predictions for these observables in the SM and in NP models with real contributions to SM and chirally flipped operators, which are independent of form factors and charm-loop contributions. As such, these observables provide robust and powerful cross-checks of the New Physics scenarios currently favoured by global fits to b → sℓℓ data. In addition, we discuss the sensitivity of these observables with respect to NP scenarios involving scalar and tensor operators, or CP-violating phases. We illustrate how these new observables can provide a benchmark to discriminate among the various NP scenarios in b → sμμ. We discuss the extension of these results for Bs decays into f0, η or η′.

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