Unification of Gravitational and Strong Interaction Fields Using Partial Gauge Symmetry

We propose the new field potential by maintaining both the symmetry of the scalar gauge and the conservation law keeping N?ether’s theorem, while disregarding the symmetry of the vector gauge. The new potential forms like the well-type potential where a particle behaves almost freely but is very hard to escape without external energy, which can be interpreted as local confinement and asymptotic freedom. By assuming a 2-dimensional metric tensor in 4-dimensional space-time, we suggest the existence of 3 kinds of particles that resemble QCD with 3 color charges. We also show that the mass term exists but comes to zero and derive the charge and spin values. We can regard the particle with this new potential as a gluon, and the interaction in this well-type potential as a strong interaction for the properties of mass, charge, spin, and its behavior. We suggest the eight-fold way with this new particle, which is similar to the existing method based on SU (3) symmetry. Even though the strong interaction has been analyzed in the standard model and string theory, we build a new consistent model based on the theory of relativity including Riemann geometry, and show the unification of gravitational and strong interactional field.

Unification of Gravitational and Electromagnetic Fields in Curved Space-Time Using Gauge Symmetry of Bianchi Identities

This paper deals with the generalization of the linear theory of the unification of gravitational and electromagnetic fields using 4-dimensional gauge symmetry in order to solve the contradictions from the Kaluza-Klein theory’s unification of the gravitational and electromagnetic fields. The unification of gravitational and electromagnetic fields in curved space-time starts from the Bianchi identity, which is well known as a mathematical generalization of the gravitational equation, and by using the existing gauge symmetry condition, equations for the gravitational and electromagnetic fields can be obtained. In particular, the homogeneous Maxwell’s equation can be obtained from the first Bianchi identity, and the inhomogeneous Maxwell’s equation can be obtained from the second Bianchi identity by using Killing’s equation condition of the curved space-time. This paper demonstrates that gravitational and electromagnetic fields can be derived from one equation without contradiction even in curved space-time, thus proving that the 4-dimensional metric tensor using the gauge used for this unification is more complete. In addition, geodesic equations can also be derived in the form of coordinate transformation, showing that they are consistent with the existing equations, and as a result, they are consistent with the existing physical equations.

Unification of Gravitational and Electromagnetic Fields Using Gauge Symmetry

A new method for the unification of gravitational and electromagnetic forces is proposed. Previously, Kaluza-Klein theory dealt with the unification, but it has not yet been established as a complete theory. The main reason for this is that Kaluza-Klein theory has various contradictions due to the use of a 5-dimensional metric tensor. In this paper, unlike the conventional method, various equations related to gravitational and electromagnetic force are derived without any contradiction by processing equations having gauge symmetry within a 4-dimensional range. In this process, we propose that Maxwell’s equations for the electromagnetic force are expressed more simply and implicitly than the existing tensor form. Using the gauge symmetry, it shows that electromagnetic force can exist in single metric tensor along with gravity. In addition, since geodesic equations can be derived in the form of coordinate transformation, it has been shown that they are consistent with the existing equations. As a result, it has shown that they are consistent with the existing physical equations without contradiction.

Erratum and Addendum： A unified model with a generalized gauge symmetry and its cosmological implications, （J. P. Hsu and K. O. Cottrell, Chin. Phys. C, 39（10）： 105101 （2015））

The phase Pw（x） defined by Eq. （3） in the paper as- sociated with the generalized U1b symmetry should be corrected and completely specified as follows：

Neutrino masses,leptonic flavor mixing,and muon(g−2)in the seesaw model with the U(1)L_(μ)-L_(r)gauge symmetry

The latest measurements of the anomalous muon magnetic moment a_(μ)≡(g_(μ)-2)/2show a 4:2σdiscrepancy between the theoretical prediction of the Standard Model and the experimental observations.To account for such a discrepancy,we consider a possible extension of the type-(I+II)seesaw model for neutrino mass generation with a gauged L_(μ)-L_(r)symmetry.By explicitly constructing an economical model with only one extra scalar singlet,we demonstrate that the gauge symmetry U(1)L_(μ)-L_(r)and its spontaneous breaking are crucial not only for explaining the muon result but also for generating the neutrino masses and leptonic flavor mixing.Various phenomenological implications and experimental constraints on the model parameters are also discussed.

Critical Behavior of Dynamical Chiral Symmetry Breaking with Gauge Boson Mass in QED3

Since the massless quantum electrodynamics in 2＋1 dimensions （QEDa） with nonzero gauge boson mass ζ can be used to explain some important traits of high-Tc superconductivity in planar cuprates, it is worthwhile to apply this model to analyze the nature of chiral phase transition at the critical value ζ. Based on the feature of chiral susceptibility, we show that the system at ζ exhibits a second-order phase transition which accords with the nature of appearance of the high-To superconductivity, and the estimated critical exponents around ζ are illustrated.

Proposal of a New Scalar Gauge in Relativity Field Equation

In this paper we propose a new gauge term in addition to the conventional gauge to acquire complete solution for the linear approximated gravitational equation. The calculation to make general form for the linear gravitational equation uses the well-known N?ether’s theorem saying that gauge symmetry is equal to conservation law. The unsolved coefficients in the equation require another condition which is leading to new gauge term. This proposed new gauge is a tensor product by a scalar quantity with a metric tensor having the trace value of 2. The scalar component in the 5th row and column of Kaluza-Klein’s metric tensor can be found as 2 diagonal components in our proposed 4×4 metric tensor. We also show that only a constant scalar gauge can be allowed in the curved space-time although arbitrary gauge can exist in the linear space-time.

Structure-preserving geometric particle-in-cell methods for Vlasov-Maxwell systems

Recent development of structure-preserving geometric particle-in-cell （PIC） algorithms for Vlasov-Maxwell systems is summarized. With the arrival of 100 petaflop and exaflop computing power, it is now possible to carry out direct simulations of multi-scale plasma dynamics based on first-principles. However, standard algorithms currently adopted by the plasma physics community do not possess the long-term accuracy and fidelity required for these large-scale simulations. This is because conventional simulation algorithms are based on numerically solving the underpinning differential （or integro-differential） equations, and the algorithms used in general do not preserve the geometric and physical structures of the systems, such as the local energy-momentum conservation law, the symplectic structure, and the gauge symmetry. As a consequence, numerical errors accumulate coherently with time and long-term simulation results are not reliable. To overcome this difficulty and to harness the power of exascale computers, a new generation of structure-preserving geometric PIC algorithms have been developed. This new generation of algorithms utilizes modem mathematical techniques, such as discrete manifolds, interpolating differential forms, and non-canonical symplectic integrators, to ensure gauge symmetry, space-time symmetry and the conservation of charge, energy-momentum, and the symplectic structure. These highly desired properties are difficult to achieve using the conventional PIC algorithms. In addition to summarizing the recent development and demonstrating practical implementations, several new results are also presented, including a structure-preserving geometric relativistic PIC algorithm, the proof of the correspondence between discrete gauge symmetry and discrete charge conservation law, and a reformulation of the explicit non-canonical symplectic algorithm for the discrete Poisson bracket using the variational approach. Numerical examples are given to verify the advantages of the structure- preserving geometric PIC algorithms in comparison with the conventional PIC methods.

Geometrical Models of the Locally Anisotropic Space-Time

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.

A model with flavor-dependent gauged U(1)B-L1×U(1)B-L2-L3 symmetry

We propose a new model with flavor-dependent gauged U(1)B-L1×U(1)B-L2-L3symmetry in addition to the flavor-blind symmetry in the Standard Model. The model contains three right-handed neutrinos to cancel gauge anomalies and several Higgs bosons to construct the measured fermion masses. We show the generic features of the model and explore its phenomenology. In particular, we discuss the current bounds on the extra gauge bosons from the K and B meson mixings as well as the LEP and LHC data, and focus on their contributions to the lepton flavor violating processes of ?i+1→?iγ(i=1,2).

LEPTON MIXING-RIGHT SYMMETRY ELECTROWEAK GAUGE THEORY AND v_3 NEUTRINO DECAY

In this paper, we introduce four models for the discrete horizontal symmetry in the gauge theory of electroweak interactions with left-right symmetry （i. e., the SU（2）L × SU（2）R × U（1） model） to obtain four sets of the mixing angles among the different generations of leptons separately. In light of the corresponding mass relations obtained and the preliminary result for mv1 and mv2, we estimate the possible value of mv3 and discuss the various physical effects arising from the lepton mixing and non-vanishing mass of neutrinos in these four models, such as their influences on the determination of quark mixing angle and the representation of the μ-e universality, the neutrino oscillations and their applications in astrophysics and so on, with special emphasis on the life-time and various possible decay modes of v3 （its mass is about 2×102 Mev in Model B） so as to give a clue to experimental detection of v3.

Flavor non-universal gauge interactions and anomalies in B-meson decays

Motivated by flavor non-universality and anomalies in semi-leptonic B-meson decays, we present a general and systematic discussion about how to construct anomaly-free U（1）＇ gauge theories based on an extended standard model with only three right-handed neutrinos. If all standard model fermions are vector-like under this new gauge symmetry, the most general family non-universal charge assignments, （a,b,c） for three-generation quarks and （d,e,f） for leptons, need satisfy just one condition to be anomaly-free, a（a＋b＋c）= （d＋e＋f）. Any assignment can be linear combinations of five independent anomaly-free solutions. We also illustrate how such models can generally lead to ttavor-changing interactions and easily resolve the anomalies in B-meson decays. Probes with Bs-Bs mixing, decay into τ±, dilepton and dijet searches at colliders are also discussed.

Oblique parameters in gauged baryon and lepton numbers with a 125 GeV Higgs

In an extension of the standard model, where baryon number and lepton number are local gauge sym- metries, we analyze the effect of corrections from exotic fermions and scalars on the oblique parameters S, T, U. Because a light neutral Higgs h0 with mass around 12-126 GeV strongly constrains the corresponding parameter space of this model, we also investigate the gluon fusion process gg→h0 and two photon decay of the lightest neutral Higgs h0→yy at the Large Hadron Collider.

Gravidynamics,spinodynamics and electrodynamics within the framework of gravitational quantum field theory

By noticing the fact that the charged leptons and quarks in the standard model are chirality-based Dirac spinors since their weak interaction violates maximally parity symmetry though they behave as Dirac fermions in electromagnetic interaction,we show that such a chirality-based Dirac spinor possesses not only electric charge gauge symmetry U(1)but also inhomogeneous spin gauge symmetry WS(1,3)=SP(1,3)?W1,3,which reveals the nature of gravity and spacetime.The gravitational force and spin gauge force are governed by the gauge symmetries W1,3and SP(1,3),respectively,and a biframe spacetime with globally fiat Minkowski spacetime as base spacetime and locally fiat gravigauge spacetime as a fiber is described by the gravigauge field through emergent non-commutative geometry.The gauge-geometry duality and renormalizability in gravitational quantum field theory(GQFT)are carefully discussed.A detailed analysis and systematic investigation on gravidynamics and spinodynamics as well as electrodynamics are carried out within the framework of GQFT.A full discussion on the generalized Dirac equation and Maxwell equation as well as Einstein equation and spin gauge equation is made in biframe spacetime.New effects of gravidynamics as extension of general relativity are particularly analyzed.All dynamic equations of basic fields are demonstrated to preserve the spin gauge covariance and general coordinate covariance due to the spin gauge symmetry and emergent general linear group symmetry GL(1,3,R),so they hold naturally in any spinning reference frame and motional reference frame.

A multi-charged particle model with local U(1)_(μ-τ) to explain muon g-2,flavor physics,and possible collider signature

We consider a model with multi-charged particles,including vector-like fermions,and a charged scalar under a local U(1)_(μ−τ) symmetry.We search for an allowed parameter region explaining muon anomalous magnetic moment(muon g−2)and b→sℓ^(+)ℓ^(−) anomalies,satisfying constraints from the lepton flavor violations,Z boson decays,meson anti-meson mixing,and collider experiments.Via numerical analysis,we explore the typical size of the muon g−2 and Wilson coefficients to explain the b→sℓ^(+)ℓ^(−) anomalies in our model when all other experimental constraints are satisfied.Subsequently,we discuss the collider physics of the multicharged vectorlike fermions,considering a number of benchmark points in the allowed parameter space.

The radiative decay D^(0)→ K^(*0)γ with vector meson dominance

Motivated by the experimental measurements of D0 radiative decay modes, we have proposed a model to study the D0→ K＊0γ decay, by establishing a link with D0→ K＊0V （V=ρ0, ω） decays through the vector meson dominance hypothesis. In order to do this properly, we have used the Lagrangians from the local hidden gauge symmetry approach to account for Vγ conversion. As a result, we have found the branching ratio B[D0→ K＊0γ]=（1.55-3.44）×10-4, which is in fair agreement with the experimental values reported by the Belle and BaBar collaborations.