Legendre transforms and r-particle irreducibility in quantum field theory: The formal power series framework

We study the higher Legendre transforms Γ^(r) {A } of the generating functional G for connected Green's functions in Euclidean boson field theories. To analyze Γ^(r) {A } rigorously even when it does not make sense as an ordinary functional, we develop the framework of formal power series in A. For r = 1, 2 we isolate regularity conditions on G that ensure the existence of Γ^(r) as a formal power series and we verify these conditions for the weakly coupled P(φ)₂ model. We also establish the improved regularity of the functional Φ^(r) obtained by subtracting from Γ^(r) its trivial singular part.     

On the separation of initial and final state effects in photoelectron spectroscopy using an extension of the auger-parameter concept

First, we show that the quantity Δβ(i) = ΔE_A(kii) + 2ΔE_B(i) — ΔE_B(k) is directly related to the final state relaxation contribution ΔE_R(i) of the binding energy shift ΔE_B(i). ΔE_A(kii) is the kinetic energy shift of the Auger transition which corresponds to the decay of a hole state with a hole in level k into a final state with two holes in level i. The shift parameter Δβ(i), which is based on information on two binding energies, is conceptually similar to Wagner's Auger parameter. To establish the relation between Δβ(i) and ΔR(i) one needs, however, less drastic approximations than in the case of Auger parameter shifts. The only approximation necessary is the assumption that ΔR(i) is determined by coulomb contributions.Secondly, we use Δβ (i) to analyse the experimental data of eighteen gaseous phosphorus-containing compounds obtained by Sodhi and Cavell¹. It is shown that ΔR(P_2p) is strongly related to changes in the polarizability of the ligands. The initial state effects derived from our study deviate from those expected on the basis of simple electronegativity considerations.     

On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

Legendre transforms and r-particle irreducibility in quantum field theory: The formalism for r = 1, 2

We analyze the first and second Legendre transforms Γ^(r) (r = 1, 2) of the generating functional G for connected Green's functions in Euclidean boson field theories. By using Spencer's idea of t-lines we define and prove irreducibility properties independently of perturbation theory. In particular we prove that Γ^(r) generates r-irreducible vertex functions, r-irreducible expectations and r-field projectors; moreover, Γ⁽²⁾ generates (generalized) Bethe-Salpeter kernels with 2-cluster-irreducibility properties.     

Generalized density expansion in the kinetic theory and the resistivity of liquid metals

For the system of electrons and immovable interacting centers an exact equation for averaged electron Green's function is formulated. The expansion of self-energy part over the one-particle t-matrices and explicit Green's functions is derived. It represents a kind of a generalized density series containing the correlation functions of the centres. In the low approximation over t-matrix, the transition probability (t)²S in the kinetic equation is obtained (S = the structure factor of centers).     

On determination of the analytical formulas for reduction matrices of tetrahedral-symmetry molecules

The formulas for the elements of ^(J)G matrices (J = 0, 1, 2 ?) determining reduction of irreducible representations D^(Jg) of the group 0(3) to the irreducible representations D^(Γ) of the T_d group have been obtained in an analytical form. It was shown how the transition was made from the G matrices of this paper to those determined by Moret-Bailly's basis [Cah. Phys., 15, 237–314 (1961)].     

A fixed point approach to the Green's functions of Φ24: Local existence of the Borel transforms

We prove the existence at small μ of a unique solution of the system $\text{B =}\text{M}\text{(B)}$ to be satisfied by the set of Borel transformed euclidean Green's functions of a Φ₂⁴ theory, μ being the Borel conjugate variable of the coupling λ. As a byproduct, a new proof of convergence of the Borel transformed perturbative series is obtained.     

Correlation between band structure and hydride formation in dilute palladium alloys

Data on the free energy change ΔG, following solution of hydrogen in dilute Pd-alloys Pd_1?xM_x have been reviewed for different concentrations of M (M = Au, Ag, Pt, Ir, Rh, V, Cu, Ni, Pb, Sn and Ti) in both the α and β phases. The dependence of ΔG values upon the nature of the substituents (transition metals) is consistently explained within the framework of a metal-hydrogen bonding mechanism in the hydrides. For the β-hydride the ΔG values can be calculated on the basis of the equation ΔG = ΔG_pd + a(T)(〈?^M_LB〉 ? 〈?^Pd_LB〉)x, where $\text{ΔG}{}_{\mathrm{<mtext>Pd</mtext>}}\text{= ? 0.0489}\text{eV}\text{H}$ atom and is the free energy change of solution of hydrogen in pure Pd, a(T) = 0.194 at T = 298 K, 〈?^m_LB〉 and 〈?^pd_LB〉 are the average energies of the lowest band of the pure constituents ($\text{〈?}{}^{\mathrm{<mtext>Pd</mtext>}}{}_{\mathrm{<mtext>LB</mtext>}}\text{〉 = ?9.15}\text{eV}\text{atom}$). The stability of the palladium-hydrogen bond in dilute Pd-alloys depends on the value of 〈?^M_LB〉; for substituents having lower 〈?^M_LB〉 values than Pd the bond will strengthen, while for those having higher 〈?^M_LB〉 values it will weaken. This behaviour agrees well with the general trend of the stability of the stoichiometric hydrides predicted by Gelatt, Ehrenreich and Weiss using band structure results.     

Defect modes due to H− - D− pair impurities in KCl and KBr

Localised modes due to H^? - D^? pair impurities aligned in the [110] direction in KCl and KBr have been computed using a Green's function approach. The defect space used consists of 12 particles; the two defect ions (H^? and D^?) and their ten nearest neighbours (K⁺ ions). The system has C_2ν site symmetry around the defect ions, and this property has been used to block diagonalise the relevant 36 × 36 matrix by group theoretical techniques. Various irreducible representations thus obtained have been used to compute the defect modes. Numerical values of the various Green's functions computed on the basis of neutron-fitted shell model parameters were used. Mass changes as well as changes in the short range interactions were considered while forming the perturbation matrix. The localised modes computed are seen to be in good agreement with the experimentally observed values.     

Some rigorous results for electromagnetic mass splittings in QCD

Written proved recently that m_π⁺m_π⁰. We note that this result is a consequence of the Green's function inequalities generalized to include EM as background fields. We also suggest that all ΔI = 2EM mass splittings can be proved to be positive.     

The second Legendre transform of the P(φ)2 generating functional

We prove the existence of the second Legendre transform of the generating functional of connected Green's functions for even weakly coupled P(φ)₂ models. The transformed functional is the generator of two particle irreducible graphs.     

Spin autocorrelation of Ni in K2Mn0.975Ni0.025F4 studied by nuclear spin-lattice relaxation

From the nuclear spin-lattice relaxation of the out-of-layer ¹⁹F nuclei in magnetic fields perpendicular to the c-axis the low-frequency component of the autocorrelation function 〈S^z(t)S^z(O)〉 of Ni in ordered K₂Mn_0.975Ni_0.025F₄ is found to be substantially reduced relative to the Mn host. The experimental rates vs temperature are in accord with those for relaxation involving two spin excitations calculated with local Green's functions.     

Etude en fonction du temps de l'oxydation des magnetites substituees a l'aluminium et au chrome au moyen de la conductivite electrique

The oxidation of substituted magnetites (Fe²⁺Fe_2?x³⁺M_x³⁺O₄^2?(O < x < 2) into the lacunar phase γ(Fe_1?z³⁺M_z³⁺)O₃^{2 ?} (x = 3z) was followed over time by electrical conductivity over the temperature r Curves σ = f(t) are different according to whether we deal with an n or p-type spinel. However, for intermediate substitution rates (1,1 < x < 1,8), n-type ferrichromites are oxidized after an initial period in the same way as p-type semi-conductors.For the initial period, the chemisorption kinetics of oxygen upon these n-type samples, reduced under vacuum, was found to follow Elovich's law with an activation energy depending on the degree of coverage.     

On the role of the higgs mechanism in present electroweak precision tests

Based on the observablesM _W, Γ _l ,s _W ^?2 (M _Z ² ), we evaluate the parameters Δx, Δy and ε at one-loop level within an electroweak massive vector-boson theory, which does not employ the Higgs mechanism. The theoretical results are consistent with the experimental ones on Δx, Δy, ε. The theoretical prediction for Δy coincides with the standard-model one (apart from numerically irrelevant terms which vanish forM _H→∞). Nonrenormalizability only affects Δx and ε, which differ from the standard-model results by the replacement logM _H→log Λ for a heavy Higgs mass,M _H (where Λ denotes an effective UV cut-off).     

Spin-dependence and glueball mixing with θ(1640) in ordinary meson spectroscopy

It is shown from a fairly general point of view that meson spectroscopy implies that the spin-spin and tensor forces are due to very short-ranged interactions. The (Q₁, Q₂) ? (Q_A, Q_B) mixing of axial vector $\text{I =}\text{1}\text{2}$ mesons implies the presence of a substantial repulsive Thomas term as well as an attractive short-ranged spin-orbit force of comparable magnitude. This analysis makes no reference to detailed potentials or wave functions. Inverted multiplets are predicted as a consequence of the large repulsive Thomas term. The spin-dependent potentials can be interpreted as effective exchanges dominated by short-ranged vector exchange and a confining potential transforming as a Lorentz scalar, although small amounts of other exchanges are also possible. A model-dependent analysis of the gluon annihilation contribution to the mass matrix and two-body decays of the I = 0 2⁺⁺ mesons indicates significant gluon mixing in these states. The presence of a $\text{non-q}\text{q}$ state (glueball?) which mixes with f'(1514) and another I = 0 2⁺⁺ state is required by the mixing model. The possibility that this additional state is θ(1640) is considered. The mass of such a state satisfies f'(1514)<M(G₀)<θ(1640). The model predicts $\text{0.01 < Λ(θ → ηη)/Λ(θ →}\text{K}\text{K}\text{)<0.18}$, with the actual widths sensitive to the details of singlet-octet mixing in the η wave function.     

Synthesis and characterisation of Cr3+-containing NASICON-related phases

Chromium-containing NASICON-related phosphates of the type Na_(1+x)Cr_xM_(2−x)P₃O₁₂) (M = Ti, Hf, Zr) have been synthesised by solid state reaction and structurally characterised by Rietveld refinement of the powder X-ray diffraction data. Materials of composition A_(1+x)/2Cr_xZr_(2−x)P₃O₁₂ (A = Cd, Ca, Sr), have also been prepared and characterised. The crystal structure of Na_(1+x)Cr_xM_(2−x)P₃O₁₂ corresponds to R-3c symmetry for x values ranging from 0.15 to 2.00, whereas compounds of composition A_(1+x)/2Cr_xZr_(2−x)P₃O₁₂ corresponding to R-3c are obtained when x ≤ 1.00 for Sr²⁺ and Ca²⁺, and x ≤ 1.50 for Cd²⁺. The polarizing effect of the two different metal ions A and M on the phosphorus atom and the P–O bond was studied by both ³¹P MAS NMR and infrared spectroscopy and shows that the electron density on the phosphorus, and thus the strength of the P–O bonds, are affected by both the interstitial (A) and the structural (M) metal ions.     

Some exact solutions of the local induction equation for the motion of a vortex in a Bose–Einstein condensate with a Gaussian density profile

The dynamics of a vortex filament in a Bose–Einstein condensate whose equilibrium density in the reference frame rotating at the angular velocity Ω is Gaussian with the quadratic form r·D?r has been considered. It has been shown that the equation of motion of the filament in the local-induction approximation permits a class of exact solutions in the form R(β, t) = βM(t) + N(t) of a straight vortex, where β is the longitudinal parameter and is the time. The vortex slips over the surface of an ellipsoid, which follows from the conservation laws N · D?N=C ₁ and M · D?N=C ₀=0. The equation of the evolution of the tangential vector M(t) appears to be closed and has integrals of motion M ·D?M=C ₂ and (|M| ? M· G?Ω) = C, with the matrix G? = 2(I?TrD? ? D?)^?1. Crossing of the respective isosurfaces specifies trajectories in the phase space.     

Application of the Green's function method to lattice vibrations in thin films

The Green's function method is used to investigate the lattice vibrations in a simple cubic thin film with nearest neighbour interactions. Appropriate Green's functions for the study of the surface waves for (001) and (011) orientations of the surface are determined. For a thin film with two parallel (001) free surfaces the atomic force tensors at the surface are modified in order to satisfy the rotational invariance condition. The surface waves are determined and a detailed discussion is made for the long wave-length limit k_y = 0 and k_x ? 1. For a given k_x there is a critical thickness below which only an antisymmetrical solution can exist. For the (011) orientation only the case of a single free surface is discussed.     

Low-temperature specific heat study of Ni85.5PxB18.5−x (0 ⩽ x ⩽ 18.5) metallic glasses

The low-temperature specific heat (LTSH) of the melt-quenched Ni_81.5P_x^- B_18.5?x amorphous alloy system, with 0 ? x ? 18.5, is presented. The decomposition of the LTSH into magnetic, lattice and electronic contributions shows that both Debye temperature θ_D and electronic specific heat coefficient decrease when the concentration of P increases.The electronic density of states N(E_F), deduced from γ for various Ni-metalloid alloys, is plotted as a function of the average electronic concentration xZ^M, where x is the metalloid concentration and Z^M is the chemical valence of M. Following Malozemoff et al.'s work, this plot is considered as a representation of the band structure and yields the change of the Fermi level with alloying.