Thorsten Prustel | Searcharxiv

arXiv2012

Note on an integral expression for the average lifetime of the bound state in 2D

Recently, an exact Green's function of the diffusion equation for a pair of spherical interacting particles in two dimensions subject to a backreaction boundary condition was used to derive an exact expression for the average lifetime of the bound state. Here, we show that the corresponding divergent integral may be considered as the formal limit of a Stieltjes transform. Upon analytically calculating the Stieltjes transform one can obtain an exact expression for the finite part of the divergent integral and hence for the average lifetime.

math-ph↗

arXiv2005

Generalized Gauge Theories with Nonunitary Parallel Transport: General Relativity with Cosmological Constant as an Example

In gauge theories parallel transporters (PTs) U(C) along paths C play an important role. Traditionally they are unitary or pseudoorthogonal maps between vector spaces. We propose to abandon unitarity of parallel transporters and with it the a priori assumption of metricity in general relativity. A *-operation on parallel transporters serves as a substitute for it, and this *-operation is proven to be unique on group theoretical grounds. The vierbein and the spin connection appear as distinguishable parts of a single de Sitter gauge field with field strength F. The action takes the form $\frac{3}{16πGΛ}\int tr(F \wedge F i γ_5)$ and both the Einstein field equations with arbitrarily small but nonvanishing cosmological constant $Λ$ and the condition of vanishing torsion are obtained from it. The equation of motion for classical massive bodies turns out to be de Sitter covariant.

hep-th↗