On Bogovski\u{\i} and regularized Poincar\'e integral operators for de Rham complexes on Lipschitz domains

We study integral operators related to a regularized version of the classical Poincar\'e path integral and the adjoint class generalizing Bogovski\u{\i}'s integral operator, acting on differential forms in $R^n$. We prove that these operators are pseudodifferential operators of order -1. The Poincar\'e-type operators map polynomials to polynomials and can have applications in finite element analysis. For a domain starlike with respect to a ball, the special support properties of the operators imply regularity for the de Rham complex without boundary conditions (using Poincar\'e-type operators) and with full Dirichlet boundary conditions (using Bogovski\u{\i}-type operators). For bounded Lipschitz domains, the same regularity results hold, and in addition we show that the cohomology spaces can always be represented by $C^\infty$ functions.Comment: 23 page

Perturbative and Nonperturbative Kolmogorov Turbulence in a Gluon Plasma

In numerical simulations of nonabelian plasma instabilities in the hard-loop approximation, a turbulent spectrum has been observed that is characterized by a phase-space density of particles $n(p)\sim p^{-\nu}$ with exponent $\nu\simeq 2$, which is larger than expected from relativistic $2\leftrightarrow 2$ scatterings. Using the approach of Zakharov, L'vov and Falkovich, we analyse possible Kolmogorov coefficients for relativistic $(m \ge 4)$-particle processes, which give at most $\nu=5/3$ perturbatively for an energy cascade. We discuss nonperturbative scenarios which lead to larger values. As an extreme limit we find the result $\nu=5$ generically in an inherently nonperturbative effective field theory situation, which coincides with results obtained by Berges et al.\ in large-$N$ scalar field theory. If we instead assume that scaling behavior is determined by Schwinger-Dyson resummations such that the different scaling of bare and dressed vertices matters, we find that intermediate values are possible. We present one simple scenario which would single out $\nu=2$.Comment: published versio

Ward identity and electrical conductivity in hot QED

We study the Ward identity for the effective photon-electron vertex summing the ladder diagrams contributing to the electrical conductivity in hot QED at leading logarithmic order. It is shown that the Ward identity requires the inclusion of a new diagram in the integral equation for the vertex that has not been considered before. The real part of this diagram is subleading and therefore the final expressions for the electrical conductivity at leading logarithmic order are not affected.Comment: 25 pages with 5 eps figures, discussion in section 3 improved; to appear in JHE

Shear viscosity of hot scalar field theory in the real-time formalism

Within the closed time path formalism a general nonperturbative expression is derived which resums through the Bethe-Salpter equation all leading order contributions to the shear viscosity in hot scalar field theory. Using a previously derived generalized fluctuation-dissipation theorem for nonlinear response functions in the real-time formalism, it is shown that the Bethe-Salpeter equation decouples in the so-called (r,a) basis. The general result is applied to scalar field theory with pure lambda*phi**4 and mixed g*phi**3+lambda*phi**4 interactions. In both cases our calculation confirms the leading order expression for the shear viscosity previously obtained in the imaginary time formalism.Comment: Expanded introduction and conclusions. Several references and a footnote added. Fig.5 and its discussion in the text modified to avoid double counting. Signs in Eqs. (45) and (53) correcte

Finite Temperature Effective Potential for the Abelian Higgs Model to the Order e4,λ2e^4,\lambda^2

A complete calculation of the finite temperature effective potential for the abelian Higgs model to the order $e^4,\lambda^2$ is presented and the result is expressed in terms of physical parameters defined at zero temperature. The absence of a linear term is verified explicitly to the given order and proven to survive to all orders. The first order phase transition has weakened in comparison with lower order calculation, which shows up in a considerable decrease of the surface tension. The only difference from the original version is the splitting of some overlong lines causing problems with certain mailers.Comment: 13 pages LaTex ( figures not included , hardcopy available on request : [email protected] or t00heb@dhhdesy3 ) , DESY 93-08

A Gauge field Induced by the Global Gauge Invariance of Action Integral

As a general rule, it is considered that the global gauge invariance of an action integral does not cause the occurrence of gauge field. However, in this paper we demonstrate that when the so-called localized assumption is excluded, the gauge field will be induced by the global gauge invariance of the action integral. An example is given to support this conclusion.Comment: 13 pages. Some typing errors are corrected and the format is update

High-Q2Q^2 Elastic eded-scattering and QCD predictions

In the framework of pertubative QCD it is argued that in the elastic $ed$-scattering at $Q^{2}\sim$ few $(GeV/c)^{2}$ the light-cone-frame helicity-flip amplitudes could not be omitted. The obtained $\frac{B}{A}$ ratio of Rosenbluth structure functions is shown to be in a good agreement with experimental data. The high $Q^2$ behavior of tensor analysing power $T_{20}$ is discussed.Comment: 6 pages + 2 ps figures not included, LaTeX, ITP-93-33

Resummation Methods at Finite Temperature: The Tadpole Way

We examine several resummation methods for computing higher order corrections to the finite temperature effective potential, in the context of a scalar $\phi^4$ theory. We show by explicit calculation to four loops that dressing the propagator, not the vertex, of the one-loop tadpole correctly counts ``daisy'' and ``super-daisy'' diagrams.Comment: 18 pages, LaTeX, CALT-68-1858, HUTP-93-A011, EFI-93-2

A Diagrammatic Interpretation of the Boltzmann Equation

We study nonlinear response in weakly coupled nonequilibrium $\phi^4$ theory in the context of both classical transport theory and real time quantum field theory, based on a generalized Kubo formula which we derive. A novel connection between these two approaches is established which provides a diagrammatic interpretation of the Boltzmann equation.Comment: 5 pages in RevTex with 4 Postscript figure

Electroweak phase diagram at finite lepton number density

We study the thermodynamics of the electroweak theory at a finite lepton number density. The phase diagram of the theory is calculated by relating the full 4-dimensional theory to a 3-dimensional effective theory which has been previously solved using nonperturbative methods. It is seen that the critical temperature increases and the value of the Higgs boson mass at which the first order phase transition line ends decreases with increasing leptonic chemical potential.Comment: 16 pages, 14 figures, RevTex4, v2: references added, minor corrections, v3: small changes, references added, published in Phys. Rev.