arXiv subjects
Publications and source records attributed to Gunter Scharf.
We study CMB in the nonstandard background cosmology recently investigated. Using the previously calculated first order metric perturbations we discuss the Sachs-Wolfe and the integrated Sachs-Wolfe effects. We show how small-multipole CMB data can be used to determine the matter density of the Universe.
We study the ablation problem for the hyperbolic heat equation in an axisymmetrical geometry which can be conveniently realized in the lab. We determine an analytic solution which shows the approach to steady state. The thermal relaxation time $τ$ is best obtained from the small time behavior. The measurements give a surprisingly large $τ$ of about 7 minutes for 0.5 % NaCl in water. This shows that the hyperbolic equation must certainly be used instead of the parabolic heat equation in the ablation problem of electrocardiology.
We investigate the spherically symmetric 1D ablation problem. We show that the parabolic heat equation fails to describe the approach to steady state in infinite space. The hyperbolic equation shows an approach to steady state with a time constant given by the thermal relaxation time. However the infinite geometry is rather unphysical and gives rise to a so-called zero mode. Therefore we also consider the finite problem with a large boundary at constant temperature. Then both equations show approach to steady state, but only the hyperbolic equation seems to be physically correct for small times.
We discuss the forward and inverse problems between the potential V(x) measured in a heart chamber and its sources represented by a dipole density d(y) located on the heart wall. We show that the mapping from d(y) to V(x) is a compact integral operator. Its inverse is unbounded which makes the inverse problem ill-posed in the mathematical sense. We investigate methods to solve the inverse problem approximately in view of the mapping of complicated cardiac arrhythmias. We point out an analogy between phase mapping and 2-dimensional hydrodynamics.
Massive gravity previously constructed as the spin-2 quantum gauge theory leads in the mass zero limit to a modification of general relativity. As a relic from the massive theory a vector field v survives which couples to the metric only. However, the coupling does not involve covariant derivatives so that v must be considered as 4 scalar fields. We analyse the static, spherically symmetric solutions of this theory. From the corresponding geodesics we find the circular velocity profile. Interpreting this as coming from a dark density profile, the theory predicts a flat density core for r going to 0. But the dark density profile is not universal.
Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the perihelion precession and the light deflection in the post-Einsteinian approximation. The bounded orbits are computed in the post-Newtonian order. As a topical application we calculate the gravitational red shift for a star moving in the Schwarzschild field.
Based on the geodesic equation in a static spherically symmetric metric we discuss the rotation curve and gravitational lensing. The rotation curve determines one function in the metric without assuming Einstein's equations. Then lensing is considered in the weak field approximation of general relativity. From the null geodesics we derive the lensing equation and corrections to it.
The causal approach to perturbative quantum field theory is presented in detail, which goes back to a seminal work by Henri Epstein and Vladimir Jurko Glaser in 1973. Causal perturbation theory is a mathematically rigorous approach to renormalization theory, which makes it possible to put the theoretical setup of perturbative quantum field theory on a sound mathematical basis. Epstein and Glaser solved this problem for a special class of distributions, the time-ordered products, that fulfill a causality condition, which itself is a basic requirement in axiomatic quantum field theory. In their original work, Epstein and Glaser studied only theories involving scalar particles. In this review, the extension of the method to theories with higher spin, including gravity, is presented. Furthermore, specific examples are presented in order to highlight the technical differences between the causal method and other regularization methods, like, e.g. dimensional regularization.
The massive spin-2 quantum gauge theory previously developed is applied to calculate gravitational bremsstrahlung. It is shown that this theory is unique and free from defects. In particular, there is no strong coupling if the graviton mass becomes small. The cross sections go over smoothly into the ones of the massless theory in the limit of vanishing graviton mass. The massless cross sections are calculated for the full tensor theory.
We consider the massless supersymmetric vector multiplet in a purely quantum framework and propose a power counting formula. Then we prove that the interaction Lagrangian for a massless supersymmetric non-Abelian gauge theory (SUSY-QCD) is uniquely determined by some natural assumptions, as in the case of Yang-Mills models, however we do have anomalies in the second order of perturbation theory. The result can be easily generalized to the case when massive multiplets are present, but one finds out that the massive and the massless Bosons must be decoupled, in contradiction with the standard model. Going to the second order of perturbation theory produces an anomaly which cannot be eliminated. We make a thorough analysis of the model working only with the component fields.
We check whether the SU(5) model, originally suggested by Georgi and Glashow, is compatible with perturbative quantum gauge invariance in first and second order for massive asymptotic gauge fields. We see that this is not the case: the SU(5) grand unified model does not meet with our restrictions from second order gauge invariance.
Based on the photon-exciton Hamiltonian a microscopic theory of the Casimir problem for dielectrics is developed. Using well-known many-body techniques we derive a perturbation expansion for the energy which is free from divergences. In the continuum limit we turn off the interaction at a distance smaller than a cut-off distance $a$ to keep the energy finite. We will show that the macroscopic theory of the Casimir effect with hard boundary conditions is not well defined because it ignores the finite distance between the atoms, hence is including infinite self-energy contributions. Nevertheless for disconnected bodies the latter do not contribute to the force between the bodies. The Lorentz-Lorenz relation for the dielectric constant that enters the force is deduced in our microscopic theory without further assumptions. The photon Green's function can be calculated from a Dyson type integral equation. The geometry of the problem only enters in this equation through the region of integration which is equal to the region occupied by the dielectric. The integral equation can be solved exactly for various plain and spherical geometries without using boundary conditions. This clearly shows that the Casimir force for dielectrics is due to the forces between the atoms. Convergence of the perturbation expansion and the metallic limit are discussed. We conclude that for any dielectric function the transverse electric (TE) mode does not contribute to the zero-frequency term of the Casimir force.
We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one-dimensional physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang-Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.
We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space ${\cal F}^{+}({\sf H}_{\rm graviton})$ where the one-particle Hilbert space ${\sf H}_{graviton}$ carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass $m > 0$ and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type $Ker(Q)/Im(Q)$ where $Q$ is a gauge charge defined in an extension of the Hilbert space ${\cal H}_{\rm graviton}$ generated by the gravitational field $h_{μν}$ and some ghosts fields $u_μ, \tilde{u}_μ$ (which are vector Fermi fields) and $v_μ$ (which are vector field Bose fields.) Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theory.
We analyse some quantum multiplets associated with extended supersymmetries. We study in detail the general form of the causal (anti)commutation relations. The condition of positivity of the scalar product imposes severe restrictions on the (quantum) model. It is problematic if one can find out quantum extensions of the standard model with extended supersymmetries.
We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
We adress the problem of Fock space representations of (free) multiplet component fiels encountered in supersymmetric quantum field theory insisting on positivity and causality. We look in detail on the scalar and Majorana components of the chiral supersymmetric multiplet. Several Fock space representations are introduced. The last section contains a short application to the supersymmetric Epstein-Glaser method. The present paper is written in the vane of axiomatic quantum field theory with applications to the causal approach to supersymmetry.
We construct quantized free superfields and represent them as operator-valued distributions in Fock space starting with Majorana fields. The perturbative construction of the S-matrix for interacting theories is carried through by extending the causal method of Epstein and Glaser to superspace. We propose a scaling and singular order of distributions in superspace by a procedure which scales both commutative and non-commutative variables. Using this singular order the chiral (Wess-Zumino) model appears to be super-renormalizable.