Generalized Variational Principle for the Fractal (2 + 1)-Dimensional Zakharov–Kuznetsov Equation in Quantum Magneto-Plasmas

In this paper, we propose the fractal (2 + 1)-dimensional Zakharov–Kuznetsov equation based on He’s fractal derivative for the first time. The fractal generalized variational formulation is established by using the semi-inverse method and two-scale fractal theory. The obtained fractal variational principle is important since it not only reveals the structure of the traveling wave solutions but also helps us study the symmetric theory. The finding of this paper will contribute to the study of symmetry in the fractal space.

Bentuk Komposisi Musik Tradisional Balo-Balo Grup Kampung Tirang Di Kecamatan Tegal Barat Kota Tegal

The purpose of this study was to determine the composition of the traditional music Balo-balo group of Kampung Tirang in Tegal City. The research approach used by the author is descriptive qualitative. The research location is in Murareja Village, West Tegal District, Tegal City. Data collection techniques in this case use observation, interview and documentation techniques. The source of the data that is the focus of the author is the chairman and personnel of the Tirang Village group, who are then analyzed using analysis techniques according to the basic framework that has been prepared. The results of the study indicate that the traditional Balo-balo music of the Kampung Tirang group is an art that uses a pitchbled membranophone musical instrument, namely kencer or tambourine, main drum, kempling, kempyang and gong tambourine. In the lyrics, the group uses the original Tegal language or deles dialect, for example in the song entitled "Balo-balo Pitutur". The song is a three part song. Whereas in the main elements of the music, the Kampung Tirang group emphasizes the rhythmic patterns of the game which are very visible but still form harmony. In the main melody, the song Balo-balo Pitutur uses the Tegalan style with elements of pentatonic scales. The songs of the Kampung Tirang group are packaged with a humorous or joking concept, so that the expression in the music is very active, energetic but still structured, even though the song structure does not use a symmetrical scheme in general, but uses a three-part symmetric theory.

Neutrino mass, mixing and muon g − 2 explanation in $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ extension of left-right theory

We consider a gauged $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ U 1 L μ − L τ extension of the left-right symmetric theory in order to simultaneously explain neutrino mass, mixing and the muon anomalous magnetic moment. We get sizeable contribution from the interaction of the new light gauge boson Zμτ of the $$ \mathrm{U}{(1)}_{L_{\mu }-{L}_{\tau }} $$ U 1 L μ − L τ symmetry with muons which can individually satisfy the current bounds on muon (g − 2) anomaly (∆aμ). The other positive contributions to ∆aμ come from the interactions of singly charged gauge bosons WL, WR with heavy neutral fermions and that of neutral CP-even scalars with muons. The interaction of WL with heavy neutrino is facilitated by inverse seesaw mechanism which allows large light-heavy neutrino mixing and explains neutrino mass in our model. CP-even scalars with mass around few hundreds GeV can also satisfy the entire current muon anomaly bound. The results show that the model gives a small but non-negligible contribution to ∆aμ thereby eliminating the entire deviation in theoretical prediction and experimental result of muon (g − 2) anomaly. We have briefly presented a comparative study for symmetric and asymmetric left-right symmetric model in context of various contribution to ∆aμ. We also discuss how the generation of neutrino mass is affected when left-right symmetry breaks down to Standard Model symmetry via various choices of scalars.

On gauging finite subgroups

We study in general spacetime dimension the symmetry of the theory obtained by gauging a non-anomalous finite normal Abelian subgroup AA of a \GammaΓ-symmetric theory. Depending on how anomalous \GammaΓ is, we find that the symmetry of the gauged theory can be i) a direct product of G=\Gamma/AG=Γ/A and a higher-form symmetry \hat AÂ with a mixed anomaly, where \hat AÂ is the Pontryagin dual of AA; ii) an extension of the ordinary symmetry group GG by the higher-form symmetry \hat AÂ; iii) or even more esoteric types of symmetries which are no longer groups. We also discuss the relations to the effect called the H^3(G,\hat A)H3(G,Â) symmetry localization obstruction in the condensed-matter theory and to some of the constructions in the works of Kapustin-Thorngren and Wang-Wen-Witten.

Global monopole in a broken-symmetric theory of gravitation

We investigate global monopole solutions in a particular kind of scalar–tensor theory of gravity, viz. the broken-symmetric theory of gravity. Invoking the “hedgehog” ansatz for the scalar field, we derive the metric corresponding to global monopole solutions. The global monopole solutions found are independent of the scale of symmetry breaking unlike the Barriola–Vilenkin global monopoles in Einstein’s General Relativity (GR) which intrinsically depend on the symmetry breaking scale.