On the nonrelativistic limit of the Dirac theory

The relation between a “nonrelativistic” Hamiltonian of the formH ^∞=(A+B)²+C and a corresponding family of “Dirac-Hamiltonians”H(c) in the limitc → ∞ is investigated. It is shown that the resolvent (z ?H(c))^?1 and the relativistic perturbation of isolated eigenvalues ofH ^∞ are analytic in 1/c for sufficiently large |c|.     

The long-time behaviour of the electric-field autocorrelation function in a finite photon gas

We investigate an autocorrelation function of a soluble three-dimensional system, namely the temporal coherence functionC _E(t)∝<E(0)E(t)> of the thermal radiation field in a cube-shaped cavity for the stochastic electrical fieldE. In the thermodynamic limit,C _E(t) relaxes exponentially at intermediate times, but a “long-tail” behaviourC ₀(t)=At^?4 withA<0 is predominant for long times. In the case of a finite, but not too small, cavity lengthL obeyingΛ=hc/k _BT?L and at timest withct?L, C _E(t) is described by an asymptotic expansion in powers ofL ^?1 using generalized Riemann zeta functions. Surface-and shape-effects enhance the long-tail. In the case of very small cavities withL«Λ, we calculate an expansion ofC _E(t) in terms of exp(?L ^?1) and cosines. An oscillatory, but not strictly periodic, long-time behaviour is observed in this case.     

Algebraic approach to supergravity in superspace

The methods of algebraic geometry are used to construct supergravity theories in a homogeneous superspace OSp(N|4) with structure group Sl(2C) ? O_N and base supermanifold the coset space OSp(N|4)/(Sl(2C)? O_N). The nature and origin of the supersymmetry transformations is completely elucidated. The equations of motion for O₁ and O₂ supergravity are obtained, as the realization of this symmetry on the space-time components h_μ of the “supervierbein”.     

W-algebras and superalgebras from constrained WZW models: A group theoretical classification

We present a classification ofW algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with anSl(2) subalgebra (resp.OSp(1/2) superalgebra) of a simple Lie algebra (resp. superalgebra)G. However, the determination of anU(1) _Y factor, commuting withSl(2) (resp.OSp(1/2)), appears, when it exists, particularly useful to characterize the correspondingW algebra. The (super) conformal spin contents of eachW (super) algebra is performed. The class of all the superconformal algebras (i.e. with conformal spinss<=2) is easily obtained as a byproduct of our general results.     

On the fragmentation functions of heavy quarks into hadrons

An explicit form for the charmed quark fragmentation function D^C_c(z) into hadrons has been obtained with the help of the “reciprocity relation” and the c-quark distribution function in charmed mesons (the function calculated in terms of the Kuti-Weisskopf model). D^C_c(z) turns out to peak mainly at z close to 1. The analysis of new data on muon pair production in neutrino reactions points to such a behaviour of the D^C_c(z) function. The obtained fragmentation function, contrary to those, used earlier, leads to a charmed particle (average) multiplicity in e⁺e^?-annihilation independent of energy.     

Retardation effects: Localized excitations of a soliton in a model of a one-dimensional electron-phonon (Peierls) system

A set of localized mixed electron-phonon excitations has been found in the “quantum” regime M < K²/2C(g²+2KB) = M_c. We suggest that the spectrum is related to possible bound states of ions in the Coulomb field of the charge soliton for sufficiently light ions.     

Low-temperature contribution to the resonant tunneling conductance of a disordered N–I–N junction

A formula for the contribution ΔG ^res(T) to the resonant tunneling conductance of the N–I–N junction (where N is a normal metal and I is an insulator) with a weak (low impurity concentrations) structural disorder in the I layer from the low-temperature “smearing” electron Fermi surfaces in its N shores is obtained. It is shown that the temperature dependence ΔG ^res(T) in such a “dirty” junction qualitatively differs from the corresponding dependence ΔG ₀(T) in a “pure” (without resonant impurities in the I layer) junction: ΔG ^res(T) < 0, d(ΔG ^res)/dT < 0; ΔG ₀(T) > 0, d(ΔG ₀)/dT > 0, which can serve as an experimental test of the presence of impurity tunneling resonances in the disordered I layer.     

Relativmessung integrierter Wirkungsquerschnitte für den Kernphotoeffekt: Die Reaktion O16(γ, n)O15

Li₂CO₃ and Na₂C₄H₈O₈ have been irradiated by 34 MeV bremsstrahlung. The yield of the induced O¹⁵ activity has been measured relative to the yield of the C¹²(γ, n)C¹¹ resp. Cu⁶³(γ, n)Cu⁶² reaction by detecting the annihilation quanta. Additional yield measurements with the bremsstrahlung beam attenuated by 18 mm of lead were made to determine the ratio of the integrated cross sections for the reactions O¹⁶(γ, n)O¹⁵ and C¹²(γ, n)C¹¹ resp. Cu⁶³(γ, n)Cu⁶². Using the cross section ofBarber et al. for C¹²(γ, n)C¹¹, the cross section integrated up to 33 MeV for O¹⁶(γ, n)O¹⁵ was obtained to 61±7 MeVmb.     

Super Riemann surfaces: Uniformization and Teichmüller theory

Teichmüller theory for super Riemann surfaces is rigorously developed using the supermanifold theory of Rogers. In the case of trivial topology in the soul directions, relevant for superstring applications, the following results are proven. The super Teichmüller space is a complex super-orbifold whose body is the ordinary Teichmüller space of the associated Riemann surfaces with spin structure. For genusg>1 it has 3g-3 complex even and 2g-2 complex odd dimensions. The super modular group which reduces super Teichmüller space to super moduli space is the ordinary modular group; there are no new discrete modular transformations in the odd directions. The boundary of super Teichmüller space contains not only super Riemann surfaces with pinched bodies, but Rogers supermanifolds having nontrivial topology in the odd dimensions as well. We also prove the uniformization theorem for super Riemann surfaces and discuss their representation by discrete supergroups of Fuchsian and Schottky type and by Beltrami differentials. Finally we present partial results for the more difficult problem of classifying super Riemann surfaces of arbitrary topology.Enrico Fermi Fellow. Research supported by the NSF (PHY 83-01221) and DOE (DE-AC02-82-ER-40073).     

Six bits for nine colored quarks

The hypercomplex number system of the Dirac equation is used to generalizeSU(2) to the covering group ofSO(4). The basic representations in this number language suggest a parton model of 6 “bits” and 6 “antibits”; one with spin 0, two with spin 1/2, and three with spin 1. The relationship of this to the special relativity group is also considered.     

On the Energy of a “One-Dimensional” Two-Electron Atom

Based on the perturbation theory and variational method long known for a “three-dimensional” atom, the ground and first excited state energies are calculated for a “one-dimensional” two-electron atom in the “one-dimensional ortho-helium” configuration, which can be obtained experimentally in principle, as has been already done for a Na Bose condensate, or produced in a super strong magnetic field B ? (2α)²B₀ (B₀ = m²c³/e? ≈ 4.41 × 10¹³ G). The “screening constant” σ for this atom in the ground and excited states was about 0.20 and 0.17, 0.18, respectively, depending on the relative parity PP' of the electronic states, which is somewhat smaller than in “two-dimensional” and “three-dimensional” variants (in these cases, this constant in the ground state is almost the same and about 0.3). The frequencies of the main spectral lines of a “onedimensional” He atom representing a doublet split over the relative parity PP' are found. The presence of the close lines of this doublet in the emission spectrum of magnetars at frequencies ω_{1, 2} ≈ {1.15; 1.17}α²(c/λC) (α = e²/?c, λ_C =?/mc) corresponding to the “one-dimensional ortho-helium” would suggest the existence of a superstrong magnetic field in such astrophysical objects.     

Lattice (Φ 4)4 effective potential giving spontaneous symmetry breaking and the role of the Higgs mass

We present a critical reappraisal of the available results on the broken phase ofλ(Φ ⁴)₄ theory, as obtained from rigorous formal analyses and from lattice calculations. All the existing evidence is compatible with Spontaneous Symmetry Breaking but dictates a trivially free shifted field that becomes controlled by a quadratic hamiltonian in the continuum limit. As recently pointed out, this implies that the simple one-loop effective potential should become effectively exact. Moreover, the usual naive assumption that the Higgs mass-squaredm _h ² is proportional to its “renormalized” self-couplingλ _R is not valid outside perturbation theory: the appropriate continuum limit hasm _h finite and vanishingλ _R . A Monte Carlo lattice computation of theλ(Φ ⁴)₄ effective potential, both in the single-component and in theO(2)-symmetric cases, is shown to agree very well with the one-loop prediction. Moreover, its perturbative leading-log improvement (based on the concept ofλ _R ) fails to reproduce the Monte Carlo data. These results, while supporting in a new fashion the peculiar “triviality” of theλ(Φ ⁴)₄ theory, also imply that, outside perturbation theory, the magnitude of the Higgs mass does not give a measure of the observable interactions in the scalar sector of the standard model.     

The forgotten 1D2 level of charmonium

The standard “charmonium” picture predicts four C=+1 states (³P₀, ³P₁, ³P₂, 2 ¹S₀) between ψ and ψ′. If these are identified with the four experimentally observed levels, serious difficulties arise. We remark that a ,,forgotten” ¹D₂ level (J^PC=2^?) is likely to be around 3.5 GeV. It may be identified with χ(2.45) or χ(3.50), avoiding the above above difficulties. The 2 ¹S₀ level has then yet to be discovered.     

The classification of superconductors using muon spin rotation

In this paper we explore the role of muon spin rotation (μSR) techniques in the characterization and classification of superconducting materials. In particular we focus upon the Uemura classification scheme which considers the correlation between the superconducting transition temperature,T _c, and the effective Fermi temperature,T _F, determined from μSR measurements of the penetration depth. Within this scheme strongly correlated “exotic” superconductors, i.e, hightT _C cuprates, heavy fermions, Chevrel phases and the organic superconductors, form a common but distinct group, characterized by a universal scaling ofT _C withT _F such that 1/100 <T _C/T _F<1/10. For conventional BCS superconductorsT _C/T _F<1/1000. The results of new μSR measurements of the penetration depth in superconducting Y(Ni_1?x Co _x )₂B₂C and YB₆ are also presented. In Y(Ni_1?x Co _x )₂B₂C the decrease ofT _C with increasing Co concentration is linked to a marked decrease in the carrier density from 2.9·10²⁸ m^?3 atx=0 to 0.6·10²⁸ m^?3, atx=0.1, while the carrier mass enhancement remains almost constant at approximately 10. For YB₆ we find evidence of a modest enhancement of the carrier mass (m ^*/m=3), and a relatively low carrier density of 0.24·10²⁸ m^?3. These results are discussed within the Uemura classification scheme. It is found that neither Y(Ni_1?x Co _x )₂B₂C withT _c/T _F>>1/250 nor YB₆ withT _C/T _F>>1/340 can be definitively classified as either “exttic” or “conventional”, but instead the compounds display behavior which interpolates between the two regimes.     

On some geometrical consequences of physical symmetries

It is shown that there exists only one submanifold O^(4,m)₂ of the representation space C^4m of the group GL(4,C)×GL(m,C) which admits a unique projection onto Minkowski space, consistent with the group. We describe the decomposition of this manifold O^4,m)₂ when the group is restricted to the physical symmetry group SU (2,2)× ×SU(m) or P×SU(m). We consider also representations of SU(2,2)×SU(m) in the resulting submanifolds and in the Hilbert space of functions over these manifolds.     

Invariant states and conditional expectations of the anticommutation relations

The groupG of unitary elements of a maximal abelian von Neumann algebra on a separable, complex Hilbert spaceH acts as a group of automorphisms on the CAR algebraA(H) overH. It is shown that the set ofG-invariant states is a simplex, isomorphic to the set of regular probability measures on aw*-compact setS ofG-invariant generalized free states. The GNS Hilbert space induced by an arbitraryG-invariant state onA(H) supports a *-representation ofC(S); the canonical map ofA(H) intoC(S) can then be locally implemented by a normal,G-invariant conditional expectation.     

Infrared contribution to the double-logarithmic small-x asymptotics of structure functions

The role playing by the “soft” (κ _T < 1 GeV/c) region in the small-x behaviour ofg ₁(x,Q ²) and the non-singlet structure functionf _{1, NS}(x, Q²) has been studied with the help of the effective QCD Lagrangian which takes into account the lightest degrees of freedom — the constituent quarks and the π-mesons (Goldstone bosons). It has been shown that the quark-quark interaction due to the pion exchange has a negative couplingg for the isovector component (I = 1 in thet-channel) off ₁(x,Q ²) and isosinglet component ofg ₁(x, Q²). Here the pion induced interaction changes mainly the normalization of the quark distribution (it decreasesf _1,NS ^{I = 1} (x,Q ²) two times atx < 3·10^?3) and changes slightly the effective exponents λ (?_1,NS ,g ₁ ～x ^?λ atx → 0). On the other hand due to a positive value of couplingg the value of λ increases by 15% for the isovector part ofg ₁ (x,Q ²) and up to λ ≈ 0.5 (instead of λ ≈ 0.2 without the pion contribution) for the isoscalar non-singlet structure functionf _1,NS ^{I = 0} (x,Q ²).     

String ghost number violation in the operator formalism

A systematic procedure of incorporating b−c zero modes into an operator formalism on arbitrary Riemann surfaces is presented. It is demonstrated that transition amplitudes on Riemann surfaces must contain certain fermionic δfunctions to ensure analyticity of the “classical” ghost coordinates. A transition amplitude on a Riemann surface of Euler characteristic χ violates ghost number conservation by −3χ units.     

Integration by parts: The algorithm to calculate β-functions in 4 loops

The following statement is proved: the counterterm for an arbitrary 4-loop Feynman diagram in an arbitrary model is calculable within the minimal subtraction scheme in terms of rational numbers and the Riemann ζ-function in a finite number of steps via a systematic “algebraic” procedure involving neither integration of elementary, special, or any other functions, nor expansions in and summation of infinite series of any kind. The number of steps is a rapidly increasing function of the complexity of the diagram. To demonstrate further possibilities offered by the technique we compute the 5-loop diagram contributing to the anomalous field dimension γ₂(g) in the ?⁴ model, that defied, heretofore, analytical calculation by other methods.