Structure of the plane waves for a spin 3/2 particle, massive and massless cases, gauge symmetry

The structure of the plane waves solutions for a relativistic spin 3/2 particle described by 16-component vector-bispinor is studied. In massless case, two representations are used: Rarita – Schwinger basis, and a special second basis in which the wave equation contains the Levi-Civita tensor. In the second representation it becomes evident the existence of gauge solutions in the form of 4-gradient of an arbitrary bispinor. General solution of the massless equation consists of six independent components, it is proved in an explicit form that four of them may be identified with the gauge solutions, and therefore may be removed. This procedure is performed in the Rarita – Schwinger basis as well. For the massive case, in Rarita – Schwinger basis four independent solutions are constructed explicitly.

Gauge Symmetries in Physical Fields (Review)

Gauge invariance is one of the fundamental symmetries in theoretical physics. In this paper, the gauge symmetry is reviewed to see how it is working in fundamental physical fields: Electromagnetism, Quantum Electro Dynamics and Geometric Theory of Gravity. In the 19th century, the gauge invariance was recognized as a mathematical non-uniqueness of the electromagnetic potentials. Real recognition of the gauge symmetry and its physical significance required two new fields developed in the 20th century: the relativity theory for physics of the world structure of linked 4d-spacetime and the quantum mechanics for the new dimension of a phase factor in complex representation of wave function. Finally the gauge theory was formulated on the basis of the gauge principle which played a role of guiding principle in the study of physicalfields such as Quantum Electrodynamics, Particle Physics and Theory of Gravitation. Fluid mechanics of a perfect fluid can join in this circles, which is another motivation of the present review. There is a hint of fluid gauge theory in the general representation of rotational flows of an ideal compressible fluid satisfying the Euler’s equation, found in 2013 by the author. In fact, law of mass conservation can be deduced from the gauge symmetry equipped in the new system of fluid-flow field combined with a gauge field, rather than given a priori.

A chiral model for sterile neutrino

A model, which extends the standard model with a new chiral U(1)′ gauge symmetry sector, for the eV-mass sterile neutrino is constructed. It is basically fixed by anomaly free conditions. The lightness of the sterile neutrino has a natural explanation. As a by product, this model provides a WIMP-like dark matter candidate.

Gravitational waves from the phase transition in the B-LSSM

Based on the gauge symmetry group SU(3)C ⨂ SU(2)L ⨂ U(1)Y ⨂ U(1)B–L, the minimal supersymmetric extension of the SM with local B-L gauge symmetry(B-LSSM) has been introduced. In this model, we study the Higgs masses with the one-loop zero temperature effective potential corrections. Besides, the finite temperature effective potentials connected with two U(1)B-L Higgs singlets are deduced specifically. Then we can obtain the gravitational wave spectrums generated from the strong first-order phase transition. In the B-LSSM, with the fine-tuned parameter regions, we can obtain the strength parameter αθ ~ 0.14 and the ratio of speed to Hubble rate β/Hn ~ 5 at nucleation temperature, and then obtain observable gravitational wave signals. The gravitational wave signals can be as strong as h2ΩGW ~ 10–9, which may be detectable in the future experiments.

Spontaneously stabilised dark matter from a fermiophobic U(1)′ gauge symmetry

We consider the possibility that dark matter is stabilised by a discrete Z2 symmetry which arises from a subgroup of a U(1)′ gauge symmetry, spontaneously broken by integer charged scalars, and under which the chiral quarks and leptons do not carry any charges. A chiral fermion χ with half-integer charge is odd under the preserved Z2, and hence becomes a stable dark matter candidate, being produced through couplings to right-handed neutrinos with vector-like U(1)′ charges, as in the type Ib seesaw mechanism. We calculate the relic abundance in such a low energy effective seesaw model containing few parameters, then consider a high energy renormalisable model with a complete fourth family of vector-like fermions, where the chiral quark and lepton masses arise from a seesaw-like mechanism. With the inclusion of the fourth family, the lightest vector-like quark can contribute to the dark matter production, enlarging the allowed parameter space that we explore.

Symmetric Mass Generation in Lattice Gauge Theory

We construct a four-dimensional lattice gauge theory in which fermions acquire mass without breaking symmetries as a result of gauge interactions. Our model consists of reduced staggered fermions transforming in the bifundamental representation of an SU(2)×SU(2) gauge symmetry. This fermion representation ensures that single-site bilinear mass terms vanish identically. A symmetric four-fermion operator is however allowed, and we give numerical results that show that a condensate of this operator develops in the vacuum.

Study of phases in a holographic QCD model

Witten–Sakai–Sugimoto model is used to study Yang–Mills theory with flavors and large number of colors at finite temperature and in the presence of chemical potential for baryon number and isospin. Sources for [Formula: see text] and [Formula: see text] gauge fields on the flavor 8-branes are D4-branes wrapped on [Formula: see text] part of the background. Here, gauge symmetry on the flavor branes has been decomposed as [Formula: see text] and [Formula: see text] is within [Formula: see text] and generated by the diagonal generator. We show various brane configurations, along with the phases in the boundary theory they correspond to, and explore the possibility of phase transition between various pairs of phases.