Axial Anomaly and the Triality Symmetry of Leptons and Hadrons

We apply the supersymmetric model of É. Cartan to the pseudoscalar meson decay into two photons, \({\pi_0\to\gamma\gamma}\) , \({\eta\to\gamma\gamma}\) and \({\eta'\to\gamma\gamma}\) . In the book of É. Cartan published in 1966, Dirac spinors ^t (A, B) and ^t (C, D) and vector fields E and E′ were introduced and five supersymmetric transformations G ₂₃, G ₁₂, G ₁₃, G ₁₂₃ and G ₁₃₂ were considered. The Pauli spinor is treated as a quaternion and the Dirac spinor is treated as an octonion. In the pseudoscalar meson decay, when the two final vector fields belong to the same group (EE or E′E′), we call the diagram rescattering diagram. When they belong to different groups (EE′), the diagram is called twisted diagram. Assuming the triality selection rules of octonions, dark matter is interpreted as matter emitting photons in a different triality sector than that of electromagnetic probes in our world.     

Geometry of multidimensional universes

LetG be a compact group of transformation (global symmetry group) of a manifoldE (multidimensional universe) with all orbits of the same type (one stratum). We studyG invariant metrics onE and show that there is one-to-one correspondence between those metrics and triples (g _μv,A _μ ^ä ,h _αβ), whereg _μv is a (pseudo-) Riemannian metric on the space of orbits (space-time),A _μ ^ä is a Yang-Mills field for the gauge groupN|H, whereN is the normalizer of the isotropy groupH inG, andh _αβ are certain scalar fields characterizing geometry of the orbits (internal spaces). The scalar curvature ofE is expressed in terms of the component fields onM. Examples and model building recipes are also given. The results generalize those of non-abelian Kaluza-Klein theories to the case where internal spaces are not necessarily group manifolds.     

S Q E D 4 and Q E D 4 on the Null-Plane

We study the scalar electrodynamics (S Q E D ₄) and the spinor electrodynamics (Q E D ₄) in the null-plane formalism. We follow Dirac’s technique for constrained systems to analyze the constraint structure in both theories in detail. We impose the appropriate boundary conditions on the fields to fix the hidden subset first class constraints that generate improper gauge transformations and obtain a unique inverse of the second-class constraint matrix. Finally, choosing the null-plane gauge condition, we determine the generalized Dirac brackets of the independent dynamical variables, which via the correspondence principle give the (anti)-commutators for posterior quantization.     

Infinite-parameter symmetries and the Higgs effect in gravity-coupled sigma models in D+4 dimensions

We compute the mass spectra of small fluctuations of four-dimensional fields for Kaluza-Klein models in which the compactification from D+4 to 4 (flat) dimensions is induced by the scalar fields of a nonlinear sigma model defined on an S^N or CP^N manifold. The compactifications are stable for all values of N. The fact that the spectra contain no massless vector fields is traced to the absence of a local gauge invariance for the sigma-model action. We introduce a complete basis for the infinite-parameter symmetries that arise from the harmonic analysis of the higher-dimensional dynamical invariances. The spectrum of spin-one and spin-two fields is consistent with the Higgs effect associated with the breaking of the local symmetries corresponding to these generators. The commutation relations of the infinite parameter algebra for the case of CP¹ are also given. The algebra includes the spectrum-generating algebra SO(1,3) of Salam and Strathdee.     

Local-potential approximation for the Brueckner G matrix and problem of optimally choosing model subspace

The validity of the local-potential approximation, which was proposed previously for the singlet-pairing problem in semi-infinite nuclear matter, is investigated in the Bethe-Goldstone equation for the Brueckner G matrix. For this purpose, use is made of the method developed earlier for solving this equation for a planar slab of nuclear matter in the case of a separable form of NN interaction. The ¹ S ₀ singlet and the ³ S ₁+³ D ₁ triplet channel are considered. The complete two-particle Hilbert space is split into a model and the complementary subspace that are separated by an energy E ₀. The two-particle propagator is calculated precisely in the first subspace, and the local-potential approximation is used in the second subspace. With an eye to subsequently employing the G matrix to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at E=2μ, where μ is the chemical potential of the system under consideration. Specific numerical calculations are performed at μ=?8 MeV. The applicability of the local-potential approximation is investigated versus the cutoff energy E ₀. It is shown that, in either channel being considered, the accuracy of the local-potential approximation is rather high for E ₀≥10 MeV.     

Chiral fermion generations from higher-dimensional gravity

We discuss a six-dimensional SO(12) gauge theory which can be obtained from pure gravity in 18 dimensions coupled to a Majorana-Weyl spinor, if the ground state is characterized by a noncompact internal space without boundary with small finite volume. The six-dimensional SO(12) theory spontaneously compactifies to a four-dimensional SO(10) theory with local generation group SU(2)_G × U(1)_G. We obtain an even number of chiral fermion generations transforming as ($\text{16, k, ±}\text{1}\text{2}$) under SO(10) × SU(2)_G × U(1)_G. Adding a scalar field to the six-dimensional theory provides us with fields carrying all the quantum numbers needed for a realistic spontaneous symmetry breakdown to SU(3)_c × U(1)_e.m.     

Matter fields and metric deformations in multidimensional unified theories

This paper describes a first study of the effects due to including matter fields in generalized Kaluza-Klein (KK) theories with nonabelian compact gauge group G and nontrivial fibres $\text{V}$^K. The approach is based on the first-order Einstein-Cartan (EC) general relativity in (4 + K) dimensions. In the EC theory there are two basic mechanisms which can lead to a spontaneously compactified KK background geometry R⁴ × $\text{V}$^K: (A) a particular kind of energy-momentum density matter condensate in the quantized ground state, or (B) a particular kind of spin-density matter condensate. If (A) or (B) are operating, the inconsistencies usually found between the KK ansatz and the matter-free EC theory are avoided. Mechanism (B) works only when $\text{V}$^K is parallelizable. It is shown that the expansion of matter fields in normal modes on $\text{V}$^K implies that one must include deformations of the Yang-Mills (YM) potentials contained in the usual KK metrics. We discuss and characterize one class of such deformations. As a case study, we consider fibres $\text{V}$^K ～ G′, where G′ is a semisimple compact Lie group. We allow for the “maximal” YM gauge group G_L′ × G_R′. We carry out the harmonic analysis for spinor fields and study the mass spectrum and YM quantum numbers of the normal modes. We rely on mechanism (B) to provide a curvature-free connection (“parallelization”) on $\text{V}$^KG′ by means of a suitable vertical constant torsion. Minimal YM couplings are of size $\text{l}\text{L}\text{≡ g}$, where l is the Planck length and L is the length of the fibre; nonminimal YM couplings are of size L. Nonzero masses are of size L^?1. The massless modes are found and discussed. There would be no massless modes if the parallelizing vertical torsion were absent. This torsion also implies the vanishing of the cosmological constant. When the theory is restricted to massless modes, the YM deformations disappear and the dimensional reduction to four dimensions yields an effective YM theory, which is renormalizable at energies far below L^?1: the effective theory is obtained by letting L → 0 with g ? 1 fixed and by neglecting all masses of order L^?1; g corresponds to the bare YM coupling constant. The surviving effective YM gauge group is G_L′ and the matter fields are in a particular representation of G_L′ × G_R′, corresponding to the zero mass eigenvalue. Explicit examples are discussed for G′ = SU(2) and G′ = SU(3).     

Vector-spinor space and field equations

Generalizing the work of Einstein and Mayer, it is assumed that at each point of space-time there exists a vector-spinor space with N_v vector dimensions and N_s spinor dimensions, where N_v=2k and N_s=2 ^k, k3. This space is decomposed into a tangent space with4 vector and4 spinor dimensions and an internal space with N_v–4 vector and N_s–4 spinor dimension. A variational principle leads to field equations for geometric quantities which can be identified with physical fields such as the electromagnetic field, Yang-Mills gauge fields, and wave functions of bosons and fermions.     

Electrostriction in a uniaxial ferroelectric with second order phase transition

The electrostriction constant γ(m²V^?2) of a uniaxial ferroelectric with a second order phase transition has been calculated as a function of the dielectric constant (?P/?E)₀. The results have been experimentally verified on triglycine sulphate (TGS) by measuring γ and (?P/?E)₀. A sign reversal of γ above the Curie temperature is presented.     

Chiral fermions on complex Kaluza-Klein manifolds

The four-dimensional fermion zero modes, arising in the presence of a monopole solution, from a higher dimensional spinor or vector-spinor are studied for the manifoldsCP _N . Twelve-dimensional Kaluza-Klein theories, some of which haveCP _N factors in the compact manifold, are also discussed.     

Standard model Higgs field and energy scale of gravity

The effective potential of the Higgs scalar field in the Standard Model may have a second degenerate minimum at an ultrahigh vacuum expectation value. This second minimum then determines, by radiative corrections, the values of the top-quark and Higgs-boson masses at the standard minimum corresponding to the electroweak energy scale. An argument is presented that this ultrahigh vacuum expectation value is proportional to the energy scale of gravity, E _Planck ≡ √?c ⁵/G _N, considered to be characteristic of a spacetime foam. In the context of a simple model, the existence of kink-type wormhole solutions places a lower bound on the ultrahigh vacuum expectation value and this lower bound is of the order of E _Planck.     

Assortativity of complementary graphs

Newman's measure for (dis)assortativity, the linear degree correlationρ _D , is widely studied although analytic insight into the assortativity of an arbitrary network remains far from well understood. In this paper, we derive the general relation (2), (3) and Theorem 1 between the assortativity ρ _D (G) of a graph G and the assortativityρ _D (G ^c) of its complement G ^c. Both ρ _D (G) and ρ _D (G ^c) are linearly related by the degree distribution in G. When the graph G(N,p) possesses a binomial degree distribution as in the Erd?s-Rényi random graphs G _p (N), its complementary graph G _p ^c (N) = G _{1- p} (N) follows a binomial degree distribution as in the Erd?s-Rényi random graphs G _{1- p} (N). We prove that the maximum and minimum assortativity of a class of graphs with a binomial distribution are asymptotically antisymmetric: ρ _max(N,p) = -ρ _min(N,p) for N → ∞. The general relation (3) nicely leads to (a) the relation (10) and (16) between the assortativity range ρ _max(G)–ρ _min(G) of a graph with a given degree distribution and the range ρ _max(G ^c)–ρ _min(G ^c) of its complementary graph and (b) new bounds (6) and (15) of the assortativity. These results together with our numerical experiments in over 30 real-world complex networks illustrate that the assortativity range ρ _max–ρ _min is generally large in sparse networks, which underlines the importance of assortativity as a network characterizer.     

Fermions and stability in quantum Kaluza-Klein theories

The effective action for spinor fields propagating in a time-dependent Kaluza-Klein background geometry is calculated explicitly to one-loop order in an adiabatic approximation. This result is used in a stability analysis of the Candelas-Weinberg model. It is found that the “internal” space (which we choose to be an odd-dimensional sphere S_N) is stable against small, uniform oscillations only if the ratio of the number of scalar fields to the number of spinor fields is greater than a certain minimum value.It is also shown that oscillations of the internal space produce conformal gravity waves in the four-dimensional space.     

Can the superstring inspire the standard model?

We discuss general features of models in which the E₈ × E′₈ heterotic superstring is compactified on a specific Calabi-Yau manifold. The gauge group of rank-6 in four dimensions is supposed to be broken down at an intermediate scale m_I to the standard model group SU(3)_C × SU(2)_L × U(1)_Y, as a result of two neutral scalar fields acquiring large vacuum expectations (vev's) in one of many flat directions of the effective potential. We find that it is difficult to generate such an intermediate scale by radiative symmetry breaking, whilst such models have prima facie problems with baryon decay mediated by massive particles and with non-perturbative behaviour of the gauge couplings, unless m_I ≳ 10¹⁶ GeV. Rapid baryon decay mediated by light particles, large neutrino masses, other Δ L ≠ 0 processes and flavour-changing neutral currents are generic features of these models. We illustrate these observations with explicit calculations in a number of different models given by vev's in different flat directions.     

The geometry of N = 2 Maxwell-Einstein supergravity and Jordan algebras

We construct the general coupling of nN = 2 Maxwell super-multiplets to N = 2 supergravity in five spacetime dimensions. In the case that the scalar field manifold is symmetric we find a complete classification based on Jordan algebras. Apart from the generic case there are also four “exceptional” cases associated with the Jordan algebras J₃^$\text{A}$ of 3 × 3 hermitian matrices over the division algebras $\text{A}\text{=}\text{R}\text{,}\text{C}\text{,}\text{H}\text{,}\text{O}$. Similar results follow for four dimensions, by dimensional reduction.     

Effect of antiferromagnetic ordering on the optical transitions in MnF2

Two optical absorption bands (viz. C and F) in MnF₂, whose line positions are nearly temperature-independent above T_N = 67.3 K, are investigated for the effect of magnetic ordering. Both bands are blue-shifted by ΔE (≌90 cm^?1 for C and 120 cm^?1 for F at 10 K) and the lines show additional narrowing on cooling through T_N. It is found that ΔE varies as the sublattice lattice magnetization below T_N and nearly as the magnetic energy above T_N.     

The effect of interface states, excess capacitance and series resistance in the Al/SiO2/p-Si Schottky diodes

The current-voltage (I-V) characteristics of Al/SiO₂/p-Si metal-insulator-semiconductor (MIS) Schottky diodes were measured at room temperature. In addition the capacitance-voltage (C-V) and conductance-voltage (G-V) measurements are studied at frequency range of 10 kHz-1 MHz. The higher value of ideality factor of 3.25 was attributed to the presence of an interfacial insulator layer between metal and semiconductor and the high density of interface states localized at Si/SiO₂ interface. The density of interface states (N_ss) distribution profile as a function of (E_ss − E_v) was extracted from the forward bias I-V measurements by taking into account the bias dependence of the effective barrier height (Φ_e) at room temperature for the Schottky diode on the order of ≅4 × 10¹³ eV⁻¹ cm⁻²_. These high values of N_ss were responsible for the non-ideal behaviour of I-V and C-V characteristics. Frequency dispersion in C-V and G-V can be interpreted only in terms of interface states. The N_ss can follow the ac signal especially at low frequencies and yield an excess capacitance. Experimental results show that the I-V, C-V and G-V characteristics of SD are affected not only in N_ss but also in series resistance (R_s), and the location of N_ss and R_s has a significant on electrical characteristics of Schottky diodes.     

The local potential approximation for the Brueckner G-matrix and a simple model of the scalar-isoscalar Landau-Migdal amplitude

The Brueckner G-matrix for a slab of nuclear matter is analyzed in the singlet ^1S and triplet ³ S + ³ D channels. The complete Hilbert space is split into two domains, the model subspace S₀, in which the two-particle propagator is calculated explicitly, and the complementary one, S', in which the local potential approximation is used. This kind of local approximation was previously found to be quite accurate for the ^1S pairing problem. A set of model spaces S ₀(E ₀) with different values of the energy E₀ is considered, E₀ being the upper limit for the single-particle energies of the states belonging to S₀. The independence of the G-matrix on E₀ is assumed as a criterion for the validity of the local potential approximation. It turns out that such an independence holds within few percents for E ₀ = 10-20 MeV, for both channels under consideration. The G-matrix within the local potential approximation is used for justifying a simple microscopic model for the coordinate-dependent scalar-isoscalar component f (r) of the Landau-Migdal amplitude in terms of the free T-matrix. Received: 2 November 2001 / Accepted: 4 January 2002     

Supergravity,the seven-sphere,and spontaneous symmetry breaking

N = 1 supergravity in d = 11 dimensions spontaneously compactifies on S⁷ to an N = 8 supergravity in d = 4 with a local SO(8) × SO(8) invariance, probably enlargeable to SO(8) × SU(8). Apart from group manifolds, S⁷ is the only compact manifold to admit an absolute parallelism. This permits (a) a “squashing” of S⁷ which gives expectation values to the scalar fields and (b) a parallelizing “torsion” which gives expectation values to the pseudoscalars. This correspondence between extrema of the d = 4 effective potential and solutions of the d = 11 field equations provides a Kaluza-Klein origin for the spontaneous breakdown of gauge symmetries, discrete symmetries, and supersymmetries. It also puts a new perspective on the puzzle of the cosmological constant.     

Brueckner G matrix for a planar slab of nuclear matter

The equation for the Brueckner G matrix is investigated for planar-slab geometry. A method for calculating the G matrix for a planar slab of nuclear matter is developed for a separable form of NN interaction. Actually, the separable version of the Paris NN potential is used. The singlet ¹ S ₀ and the triplet ³ S ₁–³ D ₁ channel are considered. The present analysis relies on the mixed momentum-coordinate representation, where use is made of the momentum representation in the slab plane and of the coordinate representation in the orthogonal direction. The full two-particle Hilbert space is broken down into the model subspace, where the two-particle propagator is considered exactly, and the complementary subspace, where the local-potential approximation is used, which was proposed previously for calculating the effective pairing potential. Specific calculations are performed for the case where the model subspace is constructed on the basis of negative-energy single-particle states. The G matrix is parametrically dependent on the total two-particle energy E and the total momentum P _⊥ in the slab plane. Since the G matrix is assumed to be further used to calculate the Landau-Migdal amplitude, the total two-particle energy is fixed at the value E=2μ, where μ is the chemical potential of the system under investigation. The calculations are performed predominantly for P _⊥=0. The role of nonzero values of P _⊥ is assessed. The resulting G matrix is found to depend greatly on μ in the surface region.