Institut für Theoretische Physik

The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wavefunction Ψ and its spatial derivative ∂_x Ψ, both restricted to the boundary of the detector's spacetime volume, is derived for the general case, where the probability current at the detector's boundary may vary its sign.

We study products of distributions in serveral variables, having in mind applications to quantum electrodynamics. We introduce a new product, the parameter product, and relate it to known ones. It allows us to rigorously interpret and evaluate products arising in the computations of the one-loop vacuum polarization of zero-mass QED₂ , thereby avoiding the occurrence of renormalization ambiguities from the very beginning.

The Fourier transform of the (indefinite metric) Wightman two-point function - (1/4π) ln( - x² + i ε x⁰ ) |_{ε↓0} of a free massless scalar quantum field in two-dimensional spacetime has been inconsistently reported by various authors. We compute the correct one from the definition of the Fourier transform of tempered distributions.

Previous studies have indicated that the cell membrane of Madin Darby Canine Kidney (MDCK) cells is hyperpolarized by a number of hormones and trace elements, in parallel with an enhancement of potassium selectivity. Without knowledge of the cell membrane resistance (R_m), however, any translation of potassium selectivity into potassium conductance remains equivocal. The present study was performed to determine the R_m of MDCK cells by cellular cable analysis. To this end, three microelectrodes were impaled into three different cells of a cell cluster; current was injected via one microelectrode and the corresponding voltage deflections measured by the other two microelectrodes. In order to extract the required specific resistances, the experimental data were analysed mathematically in terms of an electrodynamical model derived from Maxwell's equations. As a result, a mean R_m of 2.0±0.2 kΩcm² and an intercellular coupling resistance (R_c) of 6.1±0.8 MΩ were obtained at a mean potential difference across the cell membrane of -47.0±0.6 mV. An increase of the extracellular K⁺ concentration from 5.4 to 20 mmol/l depolarized the cell membrane by 16.2±0.5 mV and decreased R_m by 30.6±3.0%; 1 mmol/l barium depolarized the cell membrane by 20.1±1.1 mV and increased R_m by 75.9±14.3%. Omission of extracellular bicarbonate and carbon dioxide at constant extracellular pH caused a transient hyperpolarization (up to –60.4±1.4 mV), a decrease of R_m (by 75±4.5%) and a decrease of R_c (by 23.1±8.4%). The changes in R_m and R_c were probably the result of intracellular alkalosis. Cadmium ions (1 μmol/l) led to a sustained, reversible hyperpolarization (to –64.8±1.3 mV) and to a decrease of R_m (by 77.0±2.7%); mercury ions (1 μmol/l) cause a sustained hyperpolarization (to –60.1±1.2 mV) and a decrease of R_m (by 76.3±3.9%). Neither manoeuvre significantly altered R_c. We have previously shown that both cadmium and mercury hyperpolarize the cell membrane potential and increase its potassium selectivity; the decrease of the R_m observed in the present study indicates that these effects are due to an increase of the potassium-selective conductance of the cell membrane.

We compute the vacuum expectation value (Ω, j^μ(x) j^ν(y) Ω) ≡ J^μν(x-y) for a relativistic, Hermitian, not necessarily local vector field in two-dimensional space-time when ∂_μ J^μν = ∂_μ J^νμ = ∂_μ ε_α^μ J^αν = ∂_μ ε_α^μ J^να = 0 holds in S’(R²), the space of tempered distributions. As the space-time symmetry group of the model we take the inhomogeneous proper orthochronous Lorentz group P₊^↑. (Ω, Tj^μ (x) j^ν (y) Ω) is verified to have anomalous (axial-)vector Ward identities due to nonvanishing equal-time current-current commutators. Additional conditions on j^μ are specified which imply that j^μ is a free zero-mass Wightman field with ∂_μ j^μ = ∂_μ ε_ν^μ j^ν = 0.

We study the half-integer charged-soliton sector of the (φ)⁴ Higgs-type scalar field model with Yukawa coupling to a massless Dirac field in 2-dimensional space-time in its bozonized version: we find the one-soliton solution to the coupled nonlinear field equations of the model which represents the quantum soliton with fermion number 1/2 and compute its mass. A comparison with the corresponding c-number solution of the fermionic model is included.

For massive QED with a gauge-fixing term a candidate for the energy-momentum tensor is presented. Both cases of scalar and spinor matter fields are treated. The energy-momentum tensor is invariant under the restricted gauge transformations which exist in that model. This property guarantees that the unphysical scalar photons do not contribute to the energy-momentum densities. The difference between the translational generators and the energy-momentum observables is pointed out.