Gribov vacuum copies and interpolation in the Coulomb and Landau gauges of SU(N) Yang-Mills theories

The problem of interpolation and Gribov vacuum copies in the Coulomb and Landau gauges is studied by exploiting the methods of harmonic maps. A Dirichlet formulation for seeking out vacuum copies is presented. In a patched space all differentiable vacuum copies are characterized by means of Dirichlet boundary value maps. In the global version connections with non-linear σ-models is emphasized. A complete family of vacuum copies is proposed both in the Coulomb and Landau gauges, and interpolation is studied by using the properties of these vacuum copies.     

Renormalizability of a generalized gauge fixing interpolating among the Coulomb, Landau and maximal Abelian gauges

A detailed discussion of the renormalization properties of a class of gauges which interpolates among the Landau, Coulomb and maximal Abelian gauges is provided in the framework of the algebraic renormalization in Euclidean Yang-Mills theories in four dimensions.     

Coulomb formation and evolution of muonium in vacuum

An exact calculation ofμ ⁺ e ^? Coulomb capture cross sections at various energies in the centre-of-mass system is reported. The population of 1s, 2s and 2p levels as function of the time elapsed after muonium formation is shown.     

Structure of the Yang-Mills vacuum in the Coulomb gauge

The non-uniqueness of Yang-Mills potential in the Coulomb gauge leads to a non-trivial vacuum structure featuring vacuum fields of both integer and half-integer topological charge. Instantons fit in consistently with this picture and their interpretation is not charged. Integer and half-integer vacua are connected by certain meron solutions and the existence of half-integer charged states appears to be important for the confinement properties of the theory.     

On the non-classical structure of the vacuum

Given any three causally separated space-time regions there are observables associated with these regions which do not possess a joint distribution in the vacuum state. This result extends to any state with the Reeh-Schlieder property. This non-classical structure of the vacuum implies, due to the vacuum asymptotic condition, the genericity of non-classical structure for all density matrices in the vacuum sector.     

On the Landau diamagnetism

The grand-canonical partition function of an assembly of free spinless electrons in a magnetic field enclosed in a box (Dirichlet boundary conditions) is shown to be an entire function of the fugacityz and the magnetic fieldH, as a consequence of the trace-norm convergence of the perturbation series for the statistical semigroup. This allows to derive analyticity properties of the pressure as a function ofz andH, and to express the coefficients of its power series expansion aroundz=H=0 by means of the unperturbed semigroup. Hence, the magnetic susceptibility at zero field and fixed density is expressed in terms of Green functions of the heat equation. Its asymptotic expansion for Λ→∞ (Fisher) along parallelepipedic domains is obtained up to 0 (S(Λ)/V(Λ)). The volume term of this expansion is the Landau diamagnetism.     

On the vacuum structure of gauge differential forms

We discuss the problem of the existence of -vacua for gauge differential forms.     

On the semi-classical vacuum structure of the electroweak interaction

It is shown that in the semi-classical approximation of the electroweak sector of the standard model the moduli space of vacua can be identified with the first de Rham cohomology group of space–time. This gives a slightly different physical interpretation of the occurrence of the well-known Ahoronov–Bohm effect. Moreover, when charge conjugation is taken into account, the existence of a non-trivial ground state of the Higgs boson is shown to be equivalent to the triviality of the electroweak gauge bundle. As a consequence, the gauge bundle of the electromagnetic interaction must also be trivial. Though derived at “tree level” the results presented here may also have some consequences for quantizing, e.g., electromagnetism on an arbitrary curved space–time.     

Uniqueness of Bounded Solutions for the Homogeneous Landau Equation with a Coulomb Potential

We prove the uniqueness of bounded solutions for the spatially homogeneous Fokker-Planck-Landau equation with a Coulomb potential. Since the local (in time) existence of such solutions has been proved by Arsen’ev–Peskov (Z. Vycisl. Mat. i Mat. Fiz. 17:1063–1068, 1977), we deduce a local well-posedness result. The stability with respect to the initial condition is also checked.     

The Landau domain structure in superconducting zinc

Experimental data are reported for the dependence of the periodicity of the Landau domain structure in zinc on the fraction of the sample surface in the normal state. The data show good agreement with a modified form of the Landau-Sharvin Theory.     

On the realization of Landau gauge

Starting with the determination of the two-points function in the Landau gauge given by Wightman and Strocchi, we build a more economic realization of this gauge, following the basic principles they have proposed.     

On the one-dimensional Coulomb problem

We analyse the one-dimensional Coulomb problem (1DCP) pointing out some mistaken beliefs on it. We show that no eigenstates of even or odd parity can represent states of the system. The 1DCP exhibits a sort of spontaneous breaking of parity. We also show that a superselection rule operates in the system. Such rule explains some of its peculiarities. We build the superpotential associated to the 1DCP.     

On the structure of the QCD vacuum in the large-N limit

We present an approximate QCD vacuum for SU(N → ∞). It is a generalization of the ferromagnetic vacuum first obtained by Savvidy for SU(2) and generalized by one of us to SU(3) and SU(4). Problems occuring for N ? 5 are handled in the large-Nlimit by a contnious formalism, and the vacuum obtained is characterized by N ? 1 constant, commuting, color magnetic fields with an isotropic distribution of spatial directions. The energy density of this vacuum is lower than of the perturbative vacuum by a number proportional to N², as expected from general large-N arguments. Like the Savvidy vacuum the large-N vacuum may decay into a variant of the domained Copenhagen vacuum. We give a lower limit on the domain size.     

On the Coulomb displacement energy

The Coulomb displacement energies of the $\text{T =}\text{1}\text{2}$ mirror nuclei (A = 15, 17, 27, 29, 31, 33, 39 and 41) are re-examined with the best available HF wave functions (the DME and the Skyrme II interaction), with the inclusion of all electromagnetic corrections. The results are compared with the experimental s.p. charge dependent energies extracted from the experimental data taking into account admixtures of core-excitation corrections with the help of present shell-model and co-existence model calculations. Although the so-called Nolen-Schiffer anomaly is not removed by these improvements, it is found that the remaining observed anomalies in the ground states of s.p. and s.h. systems can be resolved with the introduction of a simple, phenomenological charge symmetry breaking nucleon-nucleon force. This force can also account for the observed anomalies in the higher excited s.p. states, while those of the deeper s.h. states need further explanation.     

On the two-dimensional Coulomb gas

This is a sequel to a recent work of Gaudin, who studied the classical equilibrium statistical mechanics of the two-dimensional Coulomb gas on a lattice at a special value of the coupling constant such that the model is exactly solvable. This model is briefly reviewed, and it is shown that the correlation functions obey the sum rules that characterize a conductive phase. A related model in which the particles are constrained to move on an array of equidistant parallel lines has simpler mathematics, and the asymptotic behavior of its correlation functions is studied in some detail. In the low-density limit, the lattice model is expected to have the same properties as a system of charged, hard disks; the correlation functions, internal energy, and specific heat of the latter are discussed.this laboratory is associated with the Centre National de la Recherche Scientifique