arXiv subjects
Publications and source records attributed to M. G. Schmidt.
The corelation masses of the 3-dimensional SU(2)-Higgs-model are calculated from the bound state Green's function. For a heavy-light and a light-light system the results are reported. We compare with lattice data and find good agreement.
Higher order coefficients of the inverse mass expansion of one-loop effective actions are obtained from a one-dimensional path integral representation. For the case of a massive scalar loop in the background of both a scalar potential and a (non Abelian) gauge field explicit results to $O(T^5)$ in the proper time parameter are presented.
The effective action describing the long range fluctuations in the high temperature phase of the electroweak standard theory is a strongly coupled SU(2)-Higgs-model in three dimensions. We outline in detail a model in which the spatial correlation scales in this phase are calculated as inverse relativistic bound state masses. Selection rules for these states are derived. The correlation masses are calculated by evaluating the bound state Green's function. The scalar-scalar-potential and its influence on the masses is investigated. The predictions for the correlation masses agree very well with the lattice data available now.
We calculate the finite temperature 2-loop effective potential in the MSSM with stop condensation, using a 3-dimensional effective theory. We find that in a part of the parameter space, a two-stage electroweak phase transition appears possible. The first stage would be the formation of a stop condensate, and the second stage is the transition to the standard electroweak minimum. The two-stage transition could significantly relax the baryon erasure bounds, but the parameter space allowing it (m_H \lsim 100 GeV, m_tR \sim 155-160 GeV) is not very large. We estimate the reliability of our results using renormalization scale and gauge dependence. Finally we discuss some real-time aspects relevant for the viability of the two-stage scenario.
The main perturbative contribution to the free energy of an electroweak interface is due to the effective potential and the tree level kinetic term. The derivative corrections are investigated with one-loop perturbation theory. The action is treated in derivative, in heat kernel, and in a multi local expansion. The massive contributions turn out to be well described by the Z-factor. The massless mode, plagued by infrared problems, is numerically less important. Its perturbatively reliable part can by calculated in derivative expansion as well. A self consistent way to include the Z-factor in the formula for the interface tension is presented.
The high temperature phase of the electroweak standard theory is described by a strongly coupled SU(2)-Higgs-model in three dimensions. As in the Abbott-Farhi-model Higgs and W-boson are low lying bound states. Using a method by Simonov based on the Feynman-Schwinger representation of correlators we calculate the masses of these states. Our results are compared with lattice masses.
The worldline path integral approach to the Bern-Kosower formalism is reviewed, which offers an alternative to Feynman diagram calculations in quantum field theory. Recent progress in constructing a multiloop generalization of this formalism is reported.
We calculate the high-temperature two-loop effective potential using a general 't~Hooft background gauge. The dependence on the gauge-fixing parameter $ξ$ is investigated. The effective coupling constant at the critical temperature $g_3(T_c)^2$ is decreased considerably compared to the one-loop result, independent of $ξ$.
The one--loop effective action for the case of a massive scalar loop in the background of both a scalar potential and an abelian or non--abelian gauge field is written in a one--dimensional path integral representation. From this the inverse mass expansion is obtained by Wick contractions using a suitable Green function, which allows the computation of higher order coefficients. For the scalar case, explicit results are presented up to order O(T**8) in the proper time expansion. The relation to previous work is clarified.
We use the worldline path integral approach to the Bern-Kosower formalism for extending this formalism to the calculation of higher order corrections to N - photon scattering. The case of the two-loop QED beta-function is considered in detail. (Talk given by C. S. at the Workshop QCD 94, Montpellier, France, 7 - 13 July, 1994)
We discuss the critical bubbles of the electroweak phase transition using an effective high-temperature 3-dimensional action for the Higgs field $φ$. The separate integration of gauge and Goldstone boson degrees of freedom is conveniently described in the 't Hooft-Feynman covariant background gauge. The effective dimensionless gauge coupling $g_3(T)^2$ in the broken phase is well behaved throughout the phase transition. However, the behavior of the one-loop $Z(φ)$ factors of the Higgs and gauge kinetic terms signalizes the breakdown of the derivative expansion and of the perturbative expansion for a range of small $φ$ values increasing with the Higgs mass $m_H$. Taking a functional $S_z[φ]$ with constant $Z(φ)=z$ instead of the full non-local effective action in some neighborhood of the saddlepoint we are calculating the critical bubbles for several temperatures. The fluctuation determinant is calculated to high accuracy using a variant of the heat kernel method. It gives a strong suppression of the transition rate compared to previous estimates.
We investigate an extension of the standard model with a second Higgs doublet, showing a two stage phase transition. Wash-out of a baryon asymmetry after the phase transition can be easily avoided in this class of models. B+L transitions are more strongly suppressed in the intermediate phase than in the high temperature symmetric phase,however. Therefore, it becomes more difficult if not impossible to generate a sufficient baryon asymmetry during the phase transition.
We investigate the structure of the configuration space of gauge theories and its description in terms of the set of absolute minima of certain Morse functions on the gauge orbits. The set of absolute minima that is obtained when the background connection is a pure gauge is shown to be isomorphic to the orbit space of the pointed gauge group. We also show that the stratum of irreducible orbits is geodesically convex, i.e. there are no geometrical obstructions to the classical motion within the main stratum. An explicit description of the singularities of the configuration space of SU(2) theories on a topologically simple space-time and on the lattice is obtained; in the continuum case we find that the singularities are conical and that the singular stratum is isomorphic to a Z_2 orbifold of the configuration space of electrodynamics.
We propose a multiloop generalization of the Bern-Kosower formalism, based on Strassler's approach of evaluating worldline path integrals by worldline Green functions. Those Green functions are explicitly constructed for the basic two-loop graph, and for a loop with an arbitrary number of propagator insertions. For scalar and abelian gauge theories, the resulting integral representations allow to combine whole classes of Feynman diagrams into compact expressions.
The higher derivative expansion of the one-loop effective action for an external scalar potential is calculated to order O(T**7), using the string-inspired Bern-Kosower method in the first quantized path integral formulation. Comparisons are made with standard heat kernel calculations and with the corresponding Feynman diagrammatic calculation in order to show the efficiency of the present method.
Strassler's formulation of the string-derived Bern-Kosower formalism is reconsidered with particular emphasis on effective actions and form factors. Two- and three point form factors in the nonabelian effective action are calculated and compared with those obtained in the heat kernel approach of Barvinsky, Vilkovisky et al. We discuss the Fock-Schwinger gauge and propose a manifestly covariant calculational scheme for one-loop effective actions in gauge theory.