Topological geometrodynamics and the solar neutrino problem

A solution of the solar neutrino problem based on certain differences between T(opological) G(eometro) D(ynamics) and the standard model of the electroweak interactions is proposed. First, TGD predicts the existence of a right-handed neutrino inert with respect to ordinary electroweak interactions. Second, the generalization of the massless Dirac equation contains terms mixing differentM ⁴ chiralities, unlike the ordinary massless Dirac equation. This and the observation of anticorrelations of the solar neutrino flux with sunspot number suggest that solar neutrinos are transformed to right-handed neutrinos on the convective zone of the Sun. Third, the compactness ofCP ₂ implies topological field quantization: space-time decomposes into regions, topological field quanta, characterized by a handful of vacuum quantum numbers. In particular, there are topological obstructions for the smooth global imbeddings of magnetic fields and the decomposition of the solar magnetic field into flux tubes is predicted. Finally, every electromagnetically neutral mass distribution is accompanied by a long-rangeZ ⁰ vacuum field. If the vacuum quantum numbers inside the flux tubes of the solar magnetic field are considerably smaller than in the normal phase, theZ ⁰ electric force becomes strong and implies Thomas precession for the spin of the lefthanded component of the neutrino. As a consequence, left-handed neutrinos are transformed to right-handed ones and the process is irreversible, since righthanded neutrinos do not couple toZ ⁰.     

LETTER: Neutrino Oscillations Induced by Gravitational Recoil Effects

Quantum gravitational fluctuations of the space-time background, described by virtual D branes, may induce the neutrino oscillations if a tiny violation of the Lorentz invariance (or a violation of the equivalence principle) is required. In this approach, the oscillation length of massless neutrinos turns out to be proportional to E ^–2 M, where E is the neutrino energy and M is the mass scale characterizing the topological fluctuations in the vacuum. Such a functional dependence on the energy is the same obtained in the framework of loop quantum gravity.     

Topics in the S-matrix theory of massless particles

We discuss how massless particle reactions may be incorporated into standard S-matrix theory. The crucial element for doing so is a low-energy zero. Examples of reactions where such zeros occur are weak interaction processes involving neutrinos, chirally symmetric massless pion scattering, and two-photon exchange between neutral systems. These zeros make two-body unitarity a good approximation for sufficiently low energy despite the coalescence of multiparticle thresholds. Through two-body unitarity, these zeros produce lines of zeros in the absorptive parts and double spectral functions. These lines of zeros are the S-matrix analog of the requirement of an infrared finite field theory. Not only do they produce finite total cross sections at finite energies, but they also allow both upper and lower bounds to be derived for these cross sections at high energies. This upper bound is our main result. If a plausible smoothness assumption is made, we find σ_tot <s^? (where ? is arbitrarily small). In particular, the experimentally observed linear rise of the neutrino proton cross section cannot continue indefinitely.     

Multi-loop Feynman integrals and conformal quantum mechanics

New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts and star-triangle relation methods, can be drastically simplified by using this algebraic approach. To demonstrate the advantages of the algebraic method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless φ³ theory. Using our algebraic approach we show that the problem of evaluation of special classes of Feynman diagrams reduces to the calculation of the Green functions for specific quantum mechanical problems. In particular, the integrals for ladder massless diagrams in the φ³ scalar field theory are given by the Green function for the conformal quantum mechanics.     

Solitonlike solutions for interacting fields with consideration of gravitation

Within the general theory of relativity the interaction between scalar and vector massless fields with interaction LagrangianF ^αβ F _αβ Ψ (?) is considered, where ψ is an arbitrary function of the scalar field. For six types of space-time symmetry (spherical, cylindrical, pseudospherical, planar, pseudoplanar, and toroidal) such interaction induces nonlinearity in the scalar field, which can be chosen in trigonometric (for example, sin-Gordon) or polynomial form. Exact solutions of the field equations are obtained for all six symmetries. The spherically symmetric solutions are studied in detail and solitionlike solutions are found.     

关于狭义相对论本质的十个论据(英文)

为寻找狭义相对论的本质,我们逐渐积累了10个论据,在量子力学基础上集中到一个基本假设:一个粒子总是不纯的,它总是包含着两个对立的场,φ(x,t)与χ(x,t),它们耦合在一起,并服从如下的对称性:φ(-x,-t)χ(x,t),χ(-x,-t)φ(x,t)。在一个粒子态中因|φ|>|χ|,φ占主导地位,但随着粒子速度增长,隐藏的χ场随之增大,这导致各种奇异的狭义相对论效应。在新定义的空一时反演(x-x,t-t)下,因φ(x,t)φ(-x,-t)=χc(x,t),　χ(x,t)χ(-x,-t)=φc(x,t)而|χc|>|φc|,于是粒子便变为它的反粒子,具有同样的动量与(正的)能量。上述对称性应当作为构造狭义相对论,相对论性量子力学,量子场论和粒子物理的出发点,其中关于中微子的超光速理论又是特别有兴趣的。     

Chiral phase structure of QCD with many flavors

We investigate QCD with a large number of massless flavors with the aid of renormalization group flow equations. We determine the critical number of flavors separating the phases with and without chiral symmetry breaking in SU(N_c) gauge theory with many fermion flavors. Our analysis includes all possible fermionic interaction channels in the pointlike four-fermion limit. Constraints from gauge invariance are resolved explicitly and regulator-scheme dependencies are studied. Our findings confirm the existence of an N_f window where the system is asymptotically free in the ultraviolet, but remains massless and chirally invariant on all scales, approaching a conformal fixed point in the infrared. Our prediction for the critical number of flavors of the zero-temperature chiral phase transition in SU(3) is N_f^cr=10.0±0.29 (fermion)^+1.55_-0.63 (gluon), with the errors arising from approximations in the fermionic and gluonic sectors, respectively. PACS 11.10.Hi, 11.15.Tk, 11.30.Rd     

Effective Field Theory Description of the Higher Dimensional Quantum Hall Liquid

We derive an effective topological field theory model of the four dimensional quantum Hall liquid state recently constructed by Zhang and Hu. Using a generalization of the flux attachment transformation, the effective field theory can be formulated as a U(1) Chern–Simons theory over the total configuration space CP₃, or as a SU(2) Chern–Simons theory over S⁴. The new quantum Hall liquid supports various types of topological excitations, including the 0-brane (particles), the 2-brane (membranes), and the 4-brane. There is a topological phase interaction among the membranes which generalizes the concept of fractional statistics.     

Plasma oscillations of edge Dirac fermions

The dispersion law of one-dimensional plasmons in a quasi-one-dimensional system of massless Dirac fermions has been calculated. Two model two-dimensional systems where bands of edge states filled with such Dirac fermions appear at the edge have been considered. Edge states in the first system, topological insulator, are due to topological reasons. Edge states in the second system, system of massive Dirac fermions, have Tamm origin. It has been shown that the dispersion laws of plasmons in both systems in the long-wavelength limit differ only in the definition of the parameters (velocity and localization depth of Dirac fermions). The frequency of plasmons is formally quantum (ω ∝ ? ^?1/2) and, in the case of the Coulomb interaction between electrons, depends slightly on the Fermi level E _F. The dependence on E _F is stronger in the case of short-range interaction. The quantum features of oscillations of massless one-dimensional Dirac fermions are removed by introducing the mass of Dirac fermions at the Fermi level and their density. Correspondence to the dispersion law of classical one-dimensional plasma oscillations in a narrow stripe of “Schrödinger” electrons has been revealed.     

Cosmological constant: a lesson from the effective gravity of topological weyl media

Topological matter with Weyl points, such as superfluid ³He-A, provide an explicit example where there is a direct connection between the properly determined vacuum energy and the cosmological constant of the effective gravity emerging in condensed matter. This is in contrast to the acoustic gravity emerging in Bose-Einstein condensates (S. Finazzi, S. Liberati, and L. Sindoni, Phys. Rev. Lett. 108, 071101 (2012); arXiv:1103.4841). The advantage of topological matter is that the relativistic fermions and gauge bosons emerging near the Weyl point obey the same effective metric and thus the effective gravity is more closely related to real gravity. We study this connection in the bi-metric gravity emerging in ³He-A, and its relation to the graviton masses, by comparison with a fully relativistic bi-metric theory of gravity. This shows that the parameter ??, which in ³He-A is the bi-metric generalization of the cosmological constant, coincides with the difference in the proper energy of the vacuum in two states (the nonequilibrium state without gravity and the equilibrium state in which gravity emerges) and is on the order of the characteristic Planck energy scale of the system. Although the cosmological constant ?? is huge, the cosmological term T _??? ^?? itself is naturally non-constant and vanishes in the equilibrium vacuum, as dictated by thermodynamics. This suggests that the equilibrium state of any system including the final state of the Universe is not gravitating.     

Neutrino radiative decay in external field and medium

The current state of the theory of massive neutrino radiative decay is reviewed. By extending our previous studies, we thoroughly analyze the process of radiative decay of a massive Dirac neutrino in the strong external magnetic field H ? H ⁰ = m _e ² c ³ / e? = 4.41 × 10¹³ G in the presence of medium (degenerate electron gas), and calculate its probability. It is shown that, in the presence of dense medium, the latter quantity becomes much larger than that in the magnetic field in the case of both relativistic and nonrelativistic neutrinos. Possible astrophysical applications of the obtained results are considered.     

Maximal symmetry and mass generation of Dirac fermions and gravitational gauge field theory in six-dimensional spacetime

The relativistic Dirac equation in four-dimensional spacetime reveals a coherent relation between the dimensions of spacetime and the degrees of freedom of fermionic spinors. A massless Dirac fermion generates new symmetries corresponding to chirality spin and charge spin as well as conformal scaling transformations. With the introduction of intrinsic W-parity, a massless Dirac fermion can be treated as a Majorana-type or Weyl-type spinor in a six-dimensional spacetime that reflects the intrinsic quantum numbers of chirality spin. A generalized Dirac equation is obtained in the six-dimensional spacetime with a maximal symmetry. Based on the framework of gravitational quantum field theory proposed in Ref. [1] with the postulate of gauge invariance and coordinate independence, we arrive at a maximally symmetric gravitational gauge field theory for the massless Dirac fermion in six-dimensional spacetime. Such a theory is governed by the local spin gauge symmetry SP(1,5) and the global Poincar′e symmetry P(1,5)= SO(1,5) P~(1,5) as well as the charge spin gauge symmetry SU(2). The theory leads to the prediction of doubly electrically charged bosons. A scalar field and conformal scaling gauge field are introduced to maintain both global and local conformal scaling symmetries. A generalized gravitational Dirac equation for the massless Dirac fermion is derived in the six-dimensional spacetime. The equations of motion for gauge fields are obtained with conserved currents in the presence of gravitational effects. The dynamics of the gauge-type gravifield as a Goldstone-like boson is shown to be governed by a conserved energy-momentum tensor, and its symmetric part provides a generalized Einstein equation of gravity. An alternative geometrical symmetry breaking mechanism for the mass generation of Dirac fermions is demonstrated.     

关于狭义相对论本质的十个论据

为寻找狭义相对论的本质,我们逐渐积累了10个论据,在量子力学基础上集中到一个基本假设:一个粒子总是不纯的,它总是包含着两个对立的场,φ(x,t)与χ(x,t),它们耦合在一起,并服从如下的对称性:φ(-x,-t)χ(x,t),χ(-x,-t)φ(x,t)。在一个粒子态中因|φ|>|χ|,φ占主导地位,但随着粒子速度增长,隐藏的χ场随之增大,这导致各种奇异的狭义相对论效应。在新定义的空一时反演(x-x,t-t)下,因φ(x,t)φ(-x,-t)=χc(x,t),　χ(x,t)χ(-x,-t)=φc(x,t)而|χc|>|φc|,于是粒子便变为它的反粒子,具有同样的动量与(正的)能量。上述对称性应当作为构造狭义相对论,相对论性量子力学,量子场论和粒子物理的出发点,其中关于中微子的超光速理论又是特别有兴趣的。     

The 2D effective field theory of interfaces derived from 3D field theory

The one-loop determinant computed around the kink solution in the 3D φ⁴ theory, in cylindrical geometry, allows one to obtain the partition function of the interface separating coexisting phases. The quantum fluctuations of the interface around its equilibrium position are described by a c = 1 two-dimensional conformal field theory, namely a 2D free massless scalar field living on the interface. In this way the capillary wave model conjecture for the interface free energy in its gaussian approximation is proved.     

Relativistic Point Dynamics and Einstein Formula as a Property of Localized Solutions of a Nonlinear Klein-Gordon Equation

Einstein’s relation E = Mc ² between the energy E and the mass M is the cornerstone of the relativity theory. This relation is often derived in a context of the relativistic theory for closed systems which do not accelerate. By contrast, the Newtonian approach to the mass is based on an accelerated motion. We study here a particular neoclassical field model of a particle governed by a nonlinear Klein-Gordon (KG) field equation. We prove that if a solution to the nonlinear KG equation and its energy density concentrate at a trajectory, then this trajectory and the energy must satisfy the relativistic version of Newton’s law with the mass satisfying Einstein’s relation. Therefore the internal energy of a localized wave affects its acceleration in an external field as the inertial mass does in Newtonian mechanics. We demonstrate that the “concentration” assumptions hold for a wide class of rectilinear accelerating motions.     

Gravitational radiation antennas using the Sagnac effect

A new class of gravitational antennas that utilize the general relativistic Sagnac effect is proposed. These antennas may be more efficient than the Weber bar by a factor of (c/v_s)⁴ 10¹⁹, wherev _sis the velocity of sound in the bar. A specific case of such an antenna consisting of a superfluid helium Josephson interferometer is considered. A general relativistic theory of the interaction of the superfluid with the gravitational field is given. Using this theory, the phase shift due to a gravitational plane wave on one such antenna is obtained. More generally, the proposed interferometer involves the interplay of general relativity and quantum theory and may afford the possibility of testing general relativity in the laboratory at the quantum mechanical level. The possibility of detecting gravitons, assuming nearly unit coupling efficiency for the antenna, is explored.This essay received the second award from the Gravity Research Foundation for the year 1981-Ed.Research was supported by NSF grant No. PHY 79-13146.Research was supported by NSF grant No. ECS-8009834.     

Perturbative approach to the hydrogen atom in a strong magnetic field

We consider states of the hydrogen atom with the principal quantum number n≤3 and zero magnetic quantum number in a constant homogeneous magnetic field ?. The perturbation theory series is summed using the Borel transformation and conformal mapping of the Borel variable. Convergence of the approximate energy eigenvalues and their agreement with the corresponding existing results are observed for external fields up to n³?/?₀～5, where ?₀ is the atomic magnetic field. The possibility of restoring the asymptotic behavior of energy levels using perturbation theory coefficients is also discussed.