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Register a new userBaryonic sources using irreducible representations of the double-covered octahedral group
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Irreducible representations (IRs) of the double-covered octahedral group are used to construct lattice source and sink operators for three-quark baryons. The goal is to achieve a good coupling to higher spin states as well as ground states. Complete sets of local and nonlocal straight-link operators are explicitly shown for isospin 1/2 and 3/2 baryons. The orthogonality relations of the IR operators are confirmed in a quenched lattice simulation.
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We have developed a Mathematica program package SpaceGroupIrep which is a database and tool set for irreducible representations (IRs) of space group in BC convention, i.e. the convention used in the famous book The mathematical theory of symmetry in solids by C. J. Bradley & A. P. Cracknell. Using this package, elements of any space group, little group, Herring little group, or central extension of little co-group can be easily obtained. This package can give not only little-group (LG) IRs for any k-point but also space-group (SG) IRs for any k-stars in intuitive table form, and both single-valued and double-valued IRs are supported. This package can calculate the decomposition of the direct product of SG IRs for any two k-stars. This package can determine the LG IRs of Bloch states in energy bands in BC convention and this works for any input primitive cell thanks to its ability to convert any input cell to a cell in BC convention. This package can also provide the correspondence of k-points and LG IR labels between BCS (Bilbao Crystallographic Server) and BC conventions. In a word, the package SpaceGroupIrep is very useful for both study and research, e.g. for analyzing band topology or determining selection rules.
Using the entropic inequalities for Shannon and Tsallis entropies new inequalities for some classical polynomials are obtained. To this end, an invertible mapping for the irreducible unitary representation of groups $SU(2)$ and $SU(1,1)$ like Jacoby polynomials and Gauss hypergeometric functions, respectively, are used.
We provide a new tableau model from which one can easily deduce the characters of irreducible polynomial representations of the orthogonal group $mathrm{O}_n(mathbb{C})$. This model originates from representation theory of the $imath$quantum group of type AI, and is equipped with a combinatorial structure, which we call AI-crystal structure. This structure enables us to describe combinatorially the tensor product of an $mathrm{O}_n(mathbb{C})$-module and a $mathrm{GL}_n(mathbb{C})$-module, and the branching from $mathrm{GL}_n(mathbb{C})$ to $mathrm{O}_n(mathbb{C})$.
We prove that various subgroups of the mapping class group $Mod(Sigma)$ of a surface $Sigma$ are at least exponentially distorted. Examples include the Torelli group (answering a question of Hamenstadt), the point-pushing and surface braid subgroups, and the Lagrangian subgroup. Our techniques include a method to compute lower bounds on distortion via representation theory and an extension of Johnson theory to arbitrary subgroups of $H_1(Sigma;mathbb{Z})$.
Thermal radiation of photons and dileptons from hadronic matter plays an essential role in understanding electromagnetic emission spectra in high-energy heavy-ion collisions. In particular, baryons and anti-baryons have been found to be strong catalysts for electromagnetic radiation, even at collider energies where the baryon chemical potential is small. Here, we conduct a systematic analysis of $pi$- and $omega$-meson-induced reactions off a large set of baryon states. The interactions are based on effective hadronic Lagrangians where the parameters are quantitatively constrained by empirical information from vacuum decay branchings and scattering data, and gauge invariance is maintained by suitable regularization procedures. The thermal emission rates are computed using kinetic theory but can be directly compared to previous calculations using hadronic many-body theory. The comparison to existing calculations in the literature reveals our newly identified contributions to be rather significant.
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