Narrow Results

We study the time variation of the fine structure constant driven by quintessential dark energy which is coupled to electromagnetism. By employing phenomenological quintessential models which provide the scalar field with maximal dynamics and satisfy the constraints from SNIa observations and the WMAP, we show that the fifth force experiments restrict the variation of the value of α at the decoupling epoch with respect to the present-day value from being less than about 0.1%.

We present a new physical model that links the maximum speed of light with the minimal Planck scale into a maximal-acceleration relativity principle in the space–time tangent bundle and in phase spaces (cotangent bundle). The maximal proper-acceleration bound is a = c²/Λ in full agreement with the old predictions of Caianiello, the Finslerian geometry point of view of Brandt and more recent results in the literature. The group transformation laws of this maximal-acceleration phase space relativity theory under velocity and acceleration boosts are analyzed in full detail. For pure acceleration boosts it is shown why the minimal Planck-areas (maximal string tension) are universal invariant quantities in any frame of reference. Inspired by the maximal-acceleration corrections to the Lamb shifts of one-electron atoms by Lambiase, Papini and Scarpetta, we derive the exact integral equation that governs the renormalization-group-like scaling dependence of the fractional change of the fine structure constant as a function of the cosmological redshift factor and a cutoff scale L_c, where the maximal acceleration relativistic effects are dominant. A particular physical model exists dominated entirely by the vacuum energy, when the cutoff scale is the Planck scale, with Ω_Λ = 1. The cosmological implications of this extreme case scenario are studied.

This paper presents the current status of the theory of electron anomalous magnetic moment a_e ≡(g-2)/2, including a complete evaluation of 12,672 Feynman diagrams in the tenth-order perturbation theory. To solve this problem, we developed a code-generator which converts Feynman diagrams automatically into fully renormalized Feynman-parametric integrals. They are evaluated numerically by an integration routine VEGAS. The preliminary result obtained thus far is 9.16 (58) (α/π)⁵, where (58) denotes the uncertainty in the last two digits. This leads to a_e(theory) = 1.159 652 181 78 (77) ×10^-3, which is in agreement with the latest measurement a_e (exp:2008) = 1.159 652 180 73 (28) ×10^-3. It shows that the Feynman–Dyson method of perturbative QED works up to the precision of 10^-12.

The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the Hall conductance is derived and is used for the proof of the integer quantum Hall effect in the realistic situation. Anisotropic quantum Hall gas is investigated based on the Hartree–Fock approximation in the same formalism. Thermodynamic properties, transport properties, and unusual response under external modulations are found. Implications for the integer quantum Hall effect in the finite systems are also studied and a new quantum Hall regime with non-zero longitudinal resistance is shown to exist.

We consider a dark energy model with a relation between the equation of state parameter w and the energy density parameter Ω_ϕ derived from thawing scalar field models. Assuming the variation of the fine structure constant is caused by dark energy, we use the observational data of the variation of the fine structure constant to constrain the current value of w₀ and Ω_ϕ0 for the dark energy model. At the 1σ level, the observational data excluded some areas around w₀ = –1, which explains the positive detection of the variation of the fine structure constant at the 1σ level, but ΛCDM model is consistent with the data at the 2σ level.

There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang–Mills fields, and fermions. The definition of spin in this theory leads us to an eight-dimensional octonionic spacetime. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low-energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.

The Higgs mechanism for imparting masses to gauge bosons and matter particles is obviated by showing that Yang–Mills gauge bosons have intrinsic nonzero masses (rest-frame energies) from self-interactions. Electroweak (EW) mixing is ruled out because it produces a photon field that is massive, carries EW charge, and does not satisfy Maxwell's equations. Other fundamental difficulties of the Standard Model are identified. A new gauge theory of electromagnetic, weak and strong interactions is derived from the Dirac equation with no other postulates and no free parameters. The three forces are intrinsically unified, the photon field is Maxwellian, weak interactions derive from spin (not isospin), and the weak and strong bosons are naturally massive and chiral. Charge is naturally quantized to integral values. Three generations of lepton pairs and elementary-hadron pairs, all with integral charges, are predicted, contradicting the phenomenology of fractional quark charges, but in full accord with experimental data on weak and strong processes and composite hadrons. Neutrinos are massive. The Dirac masses, the fine structure constant, neutrino oscillations and Cabibbo mixing are shown to have a common origin in the gravitational field. The new theory leads to a new interpretation of "negative energies" with cosmological implications. Finally, it is shown that key expressions of the EW formalism agree with those of the new theory and with experiments only if the mixing angle θ is given by sin² θ = 0.25, which accounts for the EW model's successes.

In this paper we use the Generalized Uncertainty Principle in order to obtain the corrections to the fine structure constant in (D + 1)-dimensional global monopole spacetime. We also discuss the case D = 3 corresponding to the (3+1)-dimensional global monopole spacetime.

A measurement reported in 2008 uses a one-electron quantum cyclotron to determine the electron magnetic moment in Bohr magnetons, g/2 = 1.001 159 652 180 73 (28) [0.28 ppt], with an uncertainty 2.7 and 15 times smaller than for previous measurements in 2006 and 1987. The electron is used as a magnetometer to allow lineshape statistics to accumulate, and its spontaneous emission rate determines the correction for its interaction with a cylindrical trap cavity. The new measurement and QED theory determine the fine structure constant, with α^-1 = 137.035 999 084(51) [0.37 ppb], and an uncertainty 20 times smaller than for any independent determination of α.

We use Bloch oscillations to coherently transfer many photon momenta to atoms. Then we can measure accurately the recoil velocity ħk/m and deduce the fine structure constant α. The velocity variation due to Bloch oscillations is measured using atom interferometry. This method yields a value of the fine structure constant α^-1 = 137.035 999 45 (62) with a relative uncertainty of about 4.5 × 10^-9.

This paper presents the current status of the theory of electron anomalous magnetic moment 𝝰_e ≡ (g − 2)/2, including a complete evaluation of 12,672 Feynman diagrams in the tenth-order perturbation theory. To solve this problem, we developed a code-generator which converts Feynman diagrams automatically into fully renormalized Feynman-parametric integrals. They are evaluated numerically by an integration routine VEGAS. The preliminary result obtained thus far is 9.16 (58) (α/π)⁵, where (58) denotes the uncertainty in the last two digits. This leads to 𝝰_e (theory) = 1.159 652 181 78 (77) × 10⁻³, which is in agreement with the latest measurement 𝝰_e (exp:2008) = 1.159 652 180 73 (28) × 10⁻³. It shows that the Feynman–Dyson method of perturbative QED works up to the precision of 10⁻¹².