A Note on the Faddeev–Popov Determinant and Chern–Simmons Perturbation Theory

A refined expression for the Faddeev–Popov determinant is derived for gauge theories quantised around a reducible classical solution. We apply this result to Chern–Simons perturbation theory on compact spacetime 3-manifolds with quantisation around an arbitrary flat gauge field isolated up to gauge transformations, pointing out that previous results on the finiteness and formal metric-independence of perturbative expansions of the partition function continue to hold.     

Exotic Yang–Mills Dilaton Gauge Theories

An exotic class of nonlinear p-form non-Abelian gauge theories is studied, arising from the most general allowed covariant deformation of linear Abelian gauge theory for a set of massless 1-form fields and 2-form fields in four dimensions. These theories combine a Chapline–Manton type coupling of the 1-forms and 2-forms, along with a Yang–Mills coupling of the 1-forms, a Freedman–Townsend coupling of the 2-forms, and an extended Freedman–Townsend type coupling between the 1-forms and 2-forms. It is shown that the resulting theories have a geometrically interesting dual formulation that is equivalent to an exotic Yang–Mills dilaton theory involving a nonlinear sigma field. In particular, the nonlinear sigma field couples to the Yang–Mills 1-form field through a generalized Chern class 4-form term.     

Direct measurement of dipole-dipole/CSA cross-correlated relaxation by a constant-time experiment

Relaxation rates in NMR are usually measured by intensity modulation as a function of a relaxation delay during which the relaxation mechanism of interest is effective. Other mechanisms are often suppressed during the relaxation delay by pulse sequences which eliminate their effects, or cancel their effects when two data sets with appropriate combinations of relaxation rate effects are added. Cross-correlated relaxation (CCR) involving dipole-dipole and CSA interactions differ from auto-correlated relaxation (ACR) in that the signs of contributions can be changed by inverting the state of one spin involved in the dipole-dipole interaction. This property has been exploited previously using CPMG sequences to refocus CCR while ACR evolves. Here we report a new pulse scheme that instead eliminates intensity modulation by ACR and thus allows direct measurement of CCR. The sequence uses a constant time relaxation period for which the contribution of ACR does not change. An inversion pulse is applied at various points in the sequence to effect a decay that depends on CCR only. A 2-D experiment is also described in which chemical shift evolution in the indirect dimension can share the same constant period. This improves sensitivity by avoiding the addition of a separate indirect dimension acquisition time. We illustrate the measurement of residue specific CCR rates on the non-myristoylated yeast ARF1 protein and compare the results to those obtained following the conventional method of measuring the decay rates of the slow and fast-relaxing (15)N doublets. The performances of the two methods are also quantitatively evaluated by simulation. The analysis shows that the shared constant-time CCR (SCT-CCR) method significantly improves sensitivity.     

Multiple Existence of the Multivortex Solutions of the Self-Dual Chern–Simons CP(1) Model on a Doubly Periodic Domain

In this Letter, we investigate multiple existence of the multivortex solutions of the self-dual Chern–Simons CP(1) model on a flat torus for each range of the symmetry breaking parameter. We also study asymptotics of solutions as the Chern–Simons coupling constant goes to zero.     

Solitons of the Self-dual Chern–Simons Theory on a Cylinder

We study the self-dual Chern–Simons Higgs theory on an asymptotically flat cylinder. A topological multivortex solution is constructed and the fast decaying property of solutions is proved.     

In Vivo Detection of N-Coupled Protons in Rat Brain by ISIS Localization and Multiple-Quantum Editing

Three-dimensional image-selected in vivo spectroscopy (ISIS) was combined with phase-cycled ¹H–¹⁵N heteronuclear multiple-quantum coherence (HMQC) transfer NMR for localized selective observation of protons J-coupled to ¹⁵N in phantoms and in vivo. The ISIS–HMQC sequence, supplemented by jump–return water suppression, permitted localized selective observation of 2–5 μmol of [¹⁵N_indole]tryptophan, a precursor of the neurotransmitter serotonin, through the ¹⁵N-coupled proton in 20–40 min of acquisition in vitro at 4.7 T. In vivo, the amide proton of [5-¹⁵N]glutamine was selectively observed in the brain of spontaneously breathing ¹⁵NH₄⁺-infused rats, using a volume probe with homogeneous ¹H and ¹⁵N fields. Signal recovery after three-dimensional localization was 72–82% in phantoms and 59 ± 4% in vivo. The result demonstrates that localized selective observation of ¹⁵N-coupled protons, with complete cancellation of all other protons except water, can be achieved in spontaneously breathing animals by the ISIS–HMQC sequence. This sequence performs both volume selection and heteronuclear editing through an addition/subtraction scheme and predicts the highest intrinsic sensitivity for detection of ¹⁵N-coupled protons in the selected volume. The advantages and limitations of this method for in vivo application are compared to those of other localized editing techniques currently in use for non-exchanging protons.     

Application of solid-state NMR restraint potentials in membrane protein modeling

We have developed a set of orientational restraint potentials for solid-state NMR observables including (15)N chemical shift and (15)N-(1)H dipolar coupling. Torsion angle molecular dynamics simulations with available experimental (15)N chemical shift and (15)N-(1)H dipolar coupling as target values have been performed to determine orientational information of four membrane proteins and to model the structures of some of these systems in oligomer states. The results suggest that incorporation of the orientational restraint potentials into molecular dynamics provides an efficient means to the determination of structures that optimally satisfy the experimental observables without an extensive geometrical search.     

Theory of particle transport phenomena during fatigue and time-dependent fracture of materials based on mesoscale dynamics and their practical applications

In this work, the mesoscale mechanics of metals, which links their microscopic physics and macroscopic mechanics, was established. For practical applications, the laws for quantitatively predicting life of cycle and time-dependent fracture behavior such as fatigue, hydrogen embrittlement, and high-temperature creep were derived using particle transport phenomena theories such as dislocation group dynamics, hydrogen diffusion, and vacancy diffusion. Furthermore, these concepts were also applied for estimating the degree of viscoelastic deterioration of blood vessel walls, which is dominated by a time-dependent mechanism, and for the diagnosis of aneurysm accompanied by the viscoelastic deterioration of the blood vessel wall. In these theories, new mechanical indexes were derived as dominant factors for predicting the life of fatigue crack growth and the time-dependent fracture of notched specimens of materials such as hydrogen embrittlement and high-temperature creep. Furthermore, as an example of a practical application, these theories were applied to estimate the degree of viscoelastic deterioration and chaotic motions of blood vessel walls, which are closely related to blood vessel diseases such as atherosclerosis and aneurysm. Moreover, new indexes to diagnose them were also proposed for clinical applications.     

The Equations of Grand Unified Field Theory in Terms of the Maurer-Cartan Structure Relations of Differential Geometry

The first and second Maurer-Cartan structure relations are combined with the Evans field equation [1] for differential forms to build a grand unified field theory based on differential geometry. The tetrad or vielbein plays a central role in this theory, and all four fields currently thought to exist in nature can be described by the same equations, the tangent space index of the tetrad in general relativity being identified with the tetrad's internal (gauge group) index guage theory.     

Derivation of the B (3) Field and Concomitant Vacuum Energy Density from the Sachs Theory of Electrodynamics

The archetypical and phaseless vacuum magnetic flux density of O(3) electrodynamics, the B ⁽³⁾ field, is derived from the irreducible representation of the Einstein group and is shown to be accompanied by a vacuum energy density which depends directly on the square of the scalar curvature R of curved spacetime. The B ⁽³⁾ field and the vacuum energy density are obtained respectively from the non-Abelian part of the field tensor F and the non-Abelian part of the metrical field equation. Both of these terms are given by Sachs [5].     

Loop Observables for BF Theories in Any Dimension and the Cohomology of Knots

A generalization of Wilson loop observables for BF theories in any dimension is introduced within the Batalin–Vilkovisky framework. The expectation values of these observables are cohomology classes of the space of imbeddings of a circle. One of the resulting theories discussed in the Letter has only trivalent interactions and, irrespective of the actual dimension, looks like a three-dimensional Chern–Simons theory.     

Simple suppression of spurious peaks in TROSY experiments

In (1)H-(15)N TROSY experiments of proteins and nucleic acids, where the second coherence transfer delay time tau' has been fixed as 5.6 ms, 1/(2(1)J(NH)), in order to achieve complete spin-state selection, spurious negative peaks are observed along the (15)N axes. These peaks are often annoyingly large, especially for nucleic acids. A simple product operator calculation, however, indicated that the shortening of the second delay time tau', which is next to the t1 period, would efficiently suppress these spurious peaks, without sacrificing the sensitivities of the TROSY peaks too much. We have shown for three systems, two 11- and 17-kDa proteins and one 8-kDa DNA duplex, that these spurious peaks can be effectively suppressed with delay times of 3.3 ms for the two proteins and 2.3 ms for the DNA. These delay times, optimized by trial and error, for the spurious peak suppression did not depend on the magnetic field strength and the temperature very much. Although the shortened tau' delay times attenuate the TROSY peak intensities by about 10 and 20% for the two proteins and the DNA, respectively, this simple modification will be useful for the quantitative uses of TROSY peaks and will result in cleaner spectra for various TROSY-based multiple resonance experiments.     

From dilute to dense self-avoiding walks on hypercubic lattices

A field-theoretic representation is presented to count the number of configurations of a single self-avoiding walk on a hypercubic lattice ind dimensions with periodic boundary conditions. We evaluate the connectivity constant as a function of the fractionf of sites occupied by the polymer chain. The meanfield approximation is exact in the limit of infinite dimensions, and corrections to it in powers ofd ^–1 can be systematically evaluated. The connectivity constant and the site entropy calculated throughout second order compare well with known results in two and three dimensions. We also find that the entropy per site develops a maximum atf1–(2d)^–1. Ford=2 (d=3), this maximum occurs atf~0.80 (f~0.86) and its value is about 50% (30%) higher than the entropy per site of a Hamiltonian walk (f=1).     

Evidence for a dipolar-coupled AM system in carnosine in human calf muscle from in vivo 1H NMR spectroscopy

Spin systems with residual dipolar couplings such as creatine, taurine, and lactate in skeletal muscle tissue exhibit first-order spectra in in vivo 1H NMR spectroscopy at 1.5 T because the coupled protons are represented by (nearly) symmetrized eigenfunctions. The imidazole ring protons (H2, H4) of carnosine are suspected to form also a coupled system. The ring's stiffness could enable a connectivity between these anisochronous protons with the consequence of second-order spectra at low field strength. Our purpose was to study whether this deviation from the Paschen-Back condition can be used to detect the H2-H4 coupling in localized 1D 1H NMR spectra obtained at 1.5 T (64 MHz) from the human calf in a conventional whole-body scanner. As for the hydrogen hyperfine interaction, a Breit-Rabi equation was derived to describe the transition from Zeeman to Paschen-Back regime for two dipolar-coupled protons. The ratio of the measurable coupling strength (Sk) and the difference in resonance frequencies of the coupled spins (Deltaomega) induces quantum-state mixing of various degree upon definition of an appropriate eigenbase of the coupled spin system. The corresponding Clebsch-Gordan coefficients manifest in characteristic energy corrections in the Breit-Rabi formula. These additional terms were used to define an asymmetry parameter of the line positions as a function of Sk and Deltaomega. The observed frequency shifts of the resonances were found to be consistent with this parameter within the accuracy achievable in in vivo NMR spectroscopy. Thus it was possible to identify the origin of satellite peaks of H2, H4 and to describe this so far not investigated type of residual dipolar coupling in vivo.     

Validity of the equivalent-photon approximation for the production of massive spin-1 particles

We point out that the equivalent-photon approximation (EPA) for processes with massive spin-1 particles in the final state would have validity in a more restricted kinematic domain than for processes where it is commonly applied, viz., those with spin-1/2 or spin-0 particles in the final state. We obtain the criterion for the validity ofEPA for the two-photon production of a pair of charged, massive, point-like spin-1 particlesV ^±, each of massM and with a standard magnetic moment (κ=1). In a process in which one of the photons is real and the other virtual with four-momentumq, the condition for the validity ofEPA is |q ²|≪M ², in addition to the usual condition |q ²|≪W ²,W being theV ⁺ V ⁻ invariant mass. In a process in which both photons are virtual (with four-momentaq andq′), our condition is |q ²||q′²|W ⁴ ≪ 16M ⁸, in addition to |q ²| ≪M ², |q′²| ≪M ² and |q ²| ≪W ², |q′²| ≪W ². Even when these extra conditions permitting the use ofEPA are not fulfilled, convenient approximate expressions may still be obtained assuming merely |q ²| ≪W ² and |q′²| ≪W ². We also discuss how the extra conditions are altered when the vector bosons are incorporated in a spontaneously broken gauge theory. Examples ofW boson production in Weinberg-Salam model are considered for which the condition |q ²||q′²|W ⁴ ≪ 16M ⁸ is shown to be removed.     

New observation of the , 1Δg, and 2Πg states and molecular constants with all Li2, Li2, and LiLi data

This paper reports our new observation of the , 1³Δ_g (v = 2–4), and 2³Π_g (v = 2–8) states of ⁶Li⁷Li by continuous wave perturbation facilitated optical–optical double resonance spectroscopy. Combining our new experimental term values of ⁶Li⁷Li with the available experimental data of ⁶Li₂ and ⁷Li₂, molecular constants and potential energy curves by Rydberg–Klein–Rees and direct-potential-fit techniques have been determined. Born-Oppenheimer breakdown parameters of the Li₂ 1³Δ_g and 2³Π_g states are calculated.     

The limitimg behaviour of the well width of a quantum two-dimensional metal–insulator transition

Metal–Insulator transition using an exact two-dimensional (2D) dielectric function is investigated for a shallow donor in an isolated well of a GaAs/Ga_1−xAl_sAs superlattice system within the effective mass approximation. Vanishing of the donor ionization energy as a function of well width and the donor concentration suggests that a phase transition is not possible even below a well width of 10 Å, supporting the scaling theory of localization. The effects of Anderson localization, exchange and correlation in the Hubbard model are included in a simple way. The relationship between the present model and the Mott criterion in terms of Hubbard model is also brought out. The critical concentration appears to be enhanced when a random distribution of impurities is considered. The limiting behaviour of the well width for a quantum 2D well is brought out. A simple expression is derived for a Mott constant in 2D, a*N_c^1/2 exp (9.86 exp (−L/a*))=0.123, where N_c is the critical concentration per area. Results are compared with the existing data available and discussed in the light of existing literature.