Walter Thirring

Dynamical Entropy of C* Algebras and von Neumann Algebras

The definition of the dynamical entropy is extended for automorphism groups ofC* algebras. As an example, the dynamical entropy of the shift of a lattice algebra is studied, and it is shown that in some cases it coincides with the entropy density.

An alternative approach to the theory of gravitation

In constructing a theory of gravitation using a massless tensor field and observing all axioms of field theory one meets many similarities to electrodynamics. The field equations require a conserved source and admit a gauge-group. However, the equations of motion of particles are gauge invariant only if the gauge transformation of the field is supplemented by a linear coordinate transformation. As a consequence the original pseudo-Euclidean metric is gauge-variant and therefore unobservable. One can define a gauge-invariant uring rods and clocks. This “renormalized” metric which is directly defined by observable quantities agrees with the Riemannian metric of Einsteins general relativity. Selecting a certain gauge by boundary conditions one obtains Newtons theory in first approximation. In this “unrenormalized” picture the effect of a gravitational potential is to change the effective charge and mass of particles, rather than the metric. The presence of other masses decreases the charge and increases the mass in agreement with Machs principle. The three observable effects of general relativity can be easily understood in both the renormalized and the unrenormalized pictures provided they are carefully kept apart.

Bound for the Kinetic Energy of Fermions Which Proves the Stability of Matter

We first prove that Σ |e (V)|, the sum of the negative energies of a single particle in a potential V, is bounded above by (4/15 π )∫|V|5/2. This in turn, implies a lower bound for the kinetic energy of N fermions of the form 3/5 (3π/4)2/3 ∫ρ 5/3, where ρ (x) is the one-particle density. From this, using the no-binding theorem of Thomas-Fermi theory, we present a short proof of the stability of matter with a reasonable constant for the bound.

Introduction to Kaluza-Klein-Theories

In 1919 TH. KALZUA [1] made a remarkable observation. If one considers Einstein’s theory in 5 dimensions and calculates with the ansatz

Classical dynamical systems

g = {g^{\mu \nu }}{d_\mu }d{x_\nu } + {\left( {{A^\mu }d{x_\mu }} \right)^2},\mu = 1, \ldots 4,

QUASIPARTICLES AT FINITE TEMPERATURES

(1.1) and gμν ,5 = Aμ ,5 = 0 the curvature scalar R(5) in 5 dimensions one finds

Thermodynamic functions for fermions with gravostatic and electrostatic interactions

{R^{\left( 5 \right)}} = {R^{\left( 4 \right)}} - \frac{1}{4}\left( {{A_\mu }{,_\nu } - {A_{\nu ,\mu }}} \right)\left( {{A^\mu }^{,\nu } - {A^{\nu ,\mu }}} \right).