The structure of the Yang–Mills spectrum for arbitrary simple gauge algebras

The mass spectrum of pure Yang–Mills theory in 3+1 dimensions is discussed for an arbitrary simple gauge algebra within a quasigluon picture. The general structure of the low-lying gluelump and two-quasigluon glueball spectrum is shown to be common to all algebras, while the lightest C=− three-quasigluon glueballs only exist when the gauge algebra is A _r≥2, that is, in particular, \mathfraksu(N 3 3)\mathfrak{su}(N\geq3). Higher-lying C=− glueballs are shown to exist only for the A _r≥2, D_odd−r≥4 and E₆ gauge algebras. The shape of the static energy between adjoint sources is also discussed assuming the Casimir scaling hypothesis and a funnel form; it appears to be gauge-algebra dependent when at least three sources are considered. As a main result, the present framework’s predictions are shown to be consistent with available lattice data in the particular case of an \mathfraksu(N)\mathfrak{su}(N) gauge algebra within ’t Hooft’s large-N limit.     

An invitation to higher gauge theory

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge ‘2-group’. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincaré 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a ‘tangent 2-group’, which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an ‘inner automorphism 2-group’, which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an ‘automorphism 2-group’, which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a ‘string 2-group’. We also touch upon higher structures such as the ‘gravity 3-group’, and the Lie 3-superalgebra that governs 11-dimensional supergravity.     

Cross sections and other parameters ofe − − H2O scattering (E i⩾50 eV)

Our previous theoretical work one ⁻ − H₂O scattering has been modified and extended to intermediate and high energiesE _i. Using the Bethe plot, we compare the present inelastic cross-sections with the experimental ionization cross sections. Total cross-sections are analytically represented asQ _TOT(cm²)=a.(E _ieV) ^−b and the parameters ‘a’ and ‘b’ are discussed for molecules H₂O, NH₃ and CH₄ in the rangeE _i=100–1000eV.     

The influence of free quintessence on gravitational frequency shift and deflection of light with 4D momentum

On the basis of the 4D momentum, the influence of quintessence on the gravitational frequency shift and the deflection of light are examined in modified Schwarzschild space. We find that the frequency of a photon depends on the state parameter of the quintessence w _q: the frequency increases for −1<w _q<−1/3 and decreases for −1/3<w _q<0. Meanwhile, we adopt an integral power number a (a=3ω _q+2) to solve the orbital equation of photon. The photon’s potentials become higher with the decrease of ω _q. The behavior of the bending light sensitively depends on the state parameter ω _q. In particular, for the case of ω _q=−1, there is no influence on the deflection of light by quintessence. Furthermore, according to the H-masers of the GP-A redshift experiment and long-baseline interferometry, the constraints on the quintessence field in the solar system are presented here.     

Genesis of Dark Energy: Dark Energy as Consequence of Release and Two-Stage Tracking of Cosmological Nuclear Energy

Recent observations on Type-Ia supernovae and low density (Ω _m =0.3) measurement of matter including dark matter suggest that the present-day universe consists mainly of repulsive-gravity type ‘exotic matter’ with negative-pressure often said ‘dark energy’ (Ω _x =0.7). But the nature of dark energy is mysterious and its puzzling questions, such as why, how, where and when about the dark energy, are intriguing. In the present paper the authors attempt to answer these questions while making an effort to reveal the genesis of dark energy and suggest that ‘the cosmological nuclear binding energy liberated during primordial nucleo-synthesis remains trapped for a long time and then is released free which manifests itself as dark energy in the universe’. It is also explained why for dark energy the parameter w=-\frac23w=-\frac{2}{3} . Noting that w=1 for stiff matter and w=\frac13w=\frac{1}{3} for radiation; w=-\frac23w=-\frac{2}{3} is for dark energy because “−1” is due to ‘deficiency of stiff-nuclear-matter’ and that this binding energy is ultimately released as ‘radiation’ contributing “ +\frac13+\frac{1}{3} ”, making w=-1+\frac13=-\frac23w=-1+\frac{1}{3}=-\frac{2}{3} . When dark energy is released free at Z=80, w=-\frac23w=-\frac{2}{3} . But as on present day at Z=0 when the radiation-strength-fraction (δ), has diminished to δ→0, the w=-1+d\frac13=-1w=-1+\delta\frac{1}{3}=-1 . This, almost solves the dark-energy mystery of negative pressure and repulsive-gravity. The proposed theory makes several estimates/predictions which agree reasonably well with the astrophysical constraints and observations. Though there are many candidate-theories, the proposed model of this paper presents an entirely new approach (cosmological nuclear energy) as a possible candidate for dark energy.     

Einsteinian gravity from a topological action

The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However, exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only Einstein’s equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of ‘dark energy’ as well as ‘dark matter’ modeled by a torsion induced quintaxion.     

Electrical transport study of potato starch-based electrolyte system

A biopolymer electrolyte system having conductivity ∼1.3 × 10⁻⁴ S cm⁻¹ has been prepared using potato starch, NaI, glutaraldehyde and poly(ethylene glycol) (PEG; molecular weight = 300). High ionic transference numbers (∼0.99) of the material confirmed its electrolytic behaviour. Conductivity and dielectric behaviour as a function of frequency has been studied. Conductivity follows ‘universal power law’ (σ = σ ₀ + Aω ⁿ ) with exponent ‘n’ varying from 0.94 to 1.18. Cross-linking and plasticization increases long pathways motion of charge carriers, comparable to sample dimension. Humidity-independent behaviour (up to 80% relative humidity), of impedance and water intake by the system, indicates the system’s potentiality as a promising candidate for humidity immune device fabrication. The addition of PEG has a twofold effect on the material’s conductivity. It not only increases conductivity but also improves the material’s immunity towards humid atmosphere.     

GUT precursors and fixed points in higher-dimensional theories

Within the context of traditional logarithmic grand unification atM _GUT ≈ 10¹⁶ GeV, we show that it is nevertheless possible to observe certain GUT states such asX andY gauge bosons at lower scales, perhaps even in the TeV range. We refer to such states as ‘GUT precursors’. Such states offer an interesting alternative possibility for new physics at the TeV scale, even when the scale of gauge coupling unification remains high, and suggest that it may be possible to probe GUT physics directly even within the context of high-scale gauge coupling unification. More generally, our results also suggest that it is possible to construct self-consistent ‘hybrid’ models containing widely separated energy scales, and give rise to a Kaluza-Klein realization of non-trivial fixed points in higher-dimensional gauge theories.     

Tunneling of trapped-atom Bose condensates

We obtain the dynamics in number and phase difference, for Bose condensates that tunnel between two wells of a double-well atomic trap, using the (nonlinear) Gross-Pitaevskii equation. The dynamical equations are of the canonical form for the two conjugate variables, and the Hamiltonian corresponds to that of a momentum-shortened pendulum, supporting a richer set of tunneling oscillation modes than for a superconductor Josephson junction, that has a fixed-length pendulum as a mechanical model. Novel modes include ‘inverted pendulum’ oscillations with an average angle of π; and oscillations about a self-maintained population imbalance that we term ‘macroscopic quantum self-trapping’. Other systems with this phase-number nonlinear dynamics include two-component (interconverting) condensates in a single harmonic trap, and He³B superfluids in two containers connected by micropores.     

Ferromagnetism of the electron gas

The ground-state energy of the ferromagnetic electron gas is calculated for the relative polarizationζ=0−1 and the interelectron separationr _s =5−12. The method consists in describing the electron gas approximately by a quadratic boson Hamiltonian, and contains the random-phase approximation as a special case. Numerical studies show that in both the random-phase and the present approximations the paramagnetic state has the lowest energy: the energy increases withζ for all values ofr _s considered. In the present approximation instabilities are found to occur forr _s above a critical value, due to exchange processes of finite momentum transfers. Forζ=0 this critical value ofr _s is 9.4; it decreases with increasingζ. However, the fully-polarized state (ζ=1), which lies above the rest, is always stable. The conclusions are as follows: (1) Forr _s <9.4 the electron gas is paramagnetic. (2) Atr _s =9.4 it goes over to the fully-polarized ferromagnetic state. (3) This phase transition requires an energy absorption of 0.03 rydberg per electron. (4) The fully-polarized state is not obtainable as the limitζ→1.     

Many-body study of van der Walls interaction involving lithium and rare-gas atoms and its contribution to hyperfine shifts

Using linked cluster many-body perturbation theory, the frequency-dependent dipole polarizabilitiesa(ω) has been calculated for the lithium atom. The value ofa(ω) at the static limit (169.04a ₀ ³ ) matches well with other available theoretical values and experimental results. These values have been used to calculate the van der Waals constants for interactions of lithium, helium and neon atoms. The values of the van der Waals constants for dipole-dipole interaction in atomic units are −22.9, −44.8, −1465.8, 184950.0, 2011.8, 3896.5, 30.3, 59.0 and 115.1 for Li-He, Li-Ne, Li-Li, Li-Li-Li, Li-Li-He, Li-Li-Ne, Li-He-He, Li-He-Ne and Li-Ne-Ne interactions respectively. Obtaining the suitable response functions for lithium and helium atoms, the long range contribution to Δa(r)/a ₀ in the study of fractional frequency shift in hyperfine pressure and temperature shift measurements is obtained as −541 atomic units.     

Nonlocality Without Nonlocality

Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ (SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all. This paper is dedicated to the memory of John A. Wheeler.     

Experimental determination of the difference of the beta-decay constants for atomic and molecular tritium

The results of an experiment measuring the difference Δλ=λ_a−λ _m of the beta-decay constants of atomic and molecular tritium are reported. The difference Δλ is determined by comparing the rates of growth of the relative content of radiogenic helium-3 in samples containing atomic and molecular tritium. The result Δλ=(4.6±0.8)×10⁻¹²s⁻¹ corresponds to a relative change of the decay constant by ∼0.26%. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 167–170 (10 August 1998)     

Renormalization of a gauge theory in a nonlinear gauge

We discuss renormalization of an O(3) gauge model with the gauge fixing term given by ℒ_g.f.=-1/ζ|(∂_μ-igA ₃ ^μ )W ^+μ|²-(1/2α)(∂A ³)². We utilize earlier results on the general theory of renormalization of gauge theories in quadratic gauges to prove multiplicative renormalizability of the theory together with a subtractive renormalization of gauge fixing and ghost terms. We show that this model has a double BRS invariance and that it is preserved under renormalization.     

Static Extra Dimension and Acceleration of the Universe

We study a five dimensional FLRW type Kaluza-Klein cosmological model with static extra dimension. Accelerated expansion is found by assuming a linear relationship p _b =mp _a between pressures ‘p _a ’ corresponding to the usual four dimension, and ‘p _b ’ corresponding to the extra dimension. The field equations are obtained and solved, for different values of m, to analyse the cosmological consequences of the present model. It is found that m has the value between 2 and 3 to match with the present observational findings for the accelerated expansion of the universe.     

A unified theory of weak interactions

A gauge model for the weak interactions of the leptons (v _e, e, μ, ν_μ) and the quarks (q _p, q_n,qλ,q _p′) is presented in which deviations from universality, such as the Cabibbo suppression, are explicitly and spontaneously generated. The gauge group is, to begin with SU(4). There are three quartets of Higgs scalars with suitable vacuum expectation values, sufficient and necessary to give masses to all gauge bosons. It turns out that this gauge group is too ‘large’ and fails to account for many observed symmetries of weak interactions, especially electron-muon symmetry. This symmetry corresponds to a discrete transformationR which is an element of SU(4). To accommodate it, the gauge group is restricted to the subgroup of SU(4) which commutes withR. There are now 7 gauge bosons, 4 charged and 3 neutral. One pair of charged bosons is necessarily heavier than the other pair (denotedW ^±) and two neutrals are necessarily heavier than the third (W ⁰). The electron and the muon become massive while the neutrinos and the quark fields remain massless. The dominant charged weak currents coupling toW ^± havee-μ universality and Cabibbo universality for both of whichR-symmetry is essential—the Cabibbo angle is a simple function of the vacuum expectation values. The same symmetry ensurese-μ symmetry and the absence of flavour-changing components in the neutral currents. The currents coupling to the heavier gauge bosons break all these symmetries but these bosons can be made arbitrarily heavy and so are relevant only in the domain of ‘ultraweak’ interactions. The Cabibbo angleϑ _c itself is determined by minimising a very general class of Higgs potentials, leading to a numerical valueϑ _c = ±π/8, | tanϑ _c | = √2 − 1 (an alternative solution | tanϑ _c | = (√2+1) is rejected), independent of the parameters and of the precise form of the potential. This is the ‘bare’ϑ _c; in low energy/momentum transfer processes, this value is renormalised by the structure of the hadrons. A model is given for this renormalisation which reduces the renormalised value of | tanϑ _c | to about 0.2–0.3 from the bare value 0.41. Recent data on highly inelastic neutrino interactions are shown to be not inconsistent with | tanϑ _c | = 0.4.     

Lagrangian instanton for the Kraichnan model

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism, we find the scaling exponents ζ_n of the structure functions S _n for n≫1 under the additional condition dζ₂≫1 (where d is the dimensionality of space).At n<n _c (where n _c =dζ₂/[2(2−ζ₂)]) the exponents are ζ_n=(ζ ₂/4)(2n−n ²/n _c ), while at n>n _c they are n-independent: ζ _n=ζ₂ n _c /4. We also estimate the n-dependent factors in S _n . Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 588–593 (10 October 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

D-dimensional massless particle with extended gauge invariance

We propose the model ofD-dimensional massless particle whose Lagrangian is given by theN-th extrinsic curvature of world-line. The system hasN+1 gauge degrees of freedom constitutingW-like algebra; the classical trajectories of the model are space-like curves which obey the conditionsk _N+a=k_N−a, k_2N =0,a=1, ...,N−1,N≤[(D−2)/2], while the firstN curvaturesk _i remain arbitrary. We show that the model admits consistent formulation on the anti-DeSitter space. The solutions of the system are the massless irreducible representations of Poincaré group withN nonzero helicities, which are equal to each other. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Some issues in a gauge model of unparticles

We address in a recent gauge model of unparticles the issues that are important for consistency of a gauge theory, i.e., unitarity and the Ward identity of the physical amplitudes. We find that non-integrable singularities arise in physical quantities like the cross section and the decay rate from the gauge interactions of unparticles. We also show that the Ward identity is violated due to the lack of a dispersion relation for charged unparticles although the Ward–Takahashi identity for general Green functions is incorporated in the model. A previous observation that the contribution of the unparticle (with scaling dimension d) to the gauge boson self-energy is a factor (2−d) of the particle’s self-energy has been extended to the Green function of triple gauge bosons. This (2−d) rule may be generally true for Green functions for any number of points of the gauge bosons. This implies that the model would be trivial even as one that mimics certain dynamical effects on gauge bosons in which unparticles serve as an interpolating field.     

Periodicity and the Determinant Bundle

The infinite matrix ‘Schwartz’ group G ^−∞ is a classifying group for odd K-theory and carries Chern classes in each odd dimension, generating the cohomology. These classes are closely related to the Fredholm determinant on G ^−∞. We show that while the higher (even, Schwartz) loop groups of G ^−∞, again classifying for odd K-theory, do not carry multiplicative determinants generating the first Chern class, ‘dressed’ extensions, corresponding to a star product, do carry such functions. We use these to discuss Bott periodicity for the determinant bundle and the eta invariant. In so doing we relate two distinct extensions of the eta invariant to self-adjoint elliptic operators and to elliptic invertible suspended families and show that the corresponding τ invariant is a determinant in this sense. The first author acknowledges the support of the National Science Foundation under grant DMS0408993, the second author acknowledges support of the Fonds québécois sur la nature et les technologies and NSERC while part of this work was conducted.