arXiv subjects

Peter Ullrich

Publications and source records attributed to Peter Ullrich.

2 recordsLinked to original sources

arXiv2004

Uniqueness in the Characteristic Cauchy Problem of the Klein-Gordon Equation and Tame Restrictions of Generalized Functions

We show that every tempered distribution, which is a solution of the (homogenous) Klein-Gordon equation, admits a ``tame'' restriction to the characteristic (hyper)surface $\{x^0+x^n=0\}$ in $(1+n)$-dimensional Minkowski space and is uniquely determined by this restriction. The restriction belongs to the space $\cS'_{\partial_-}(\R^n)$ which we have introduced in \cite{PullJMP}. Moreover, we show that every element of $\cS'_{\partial_-}(\R^n)$ appears as the ``tame'' restriction of a solution of the (homogeneous) Klein-Gordon equation.

math-ph↗

arXiv1997

The Continuum Version of ϕ^4_{1+1}-theory in Light-Front Quantization

A genuine continuum treatment of the massive ϕ^4_{1+1}-theory in light-cone quantization is proposed. Fields are treated as operator valued distributions thereby leading to a mathematically well defined handling of ultraviolet and light cone induced infrared divergences and of their renormalization. Although non-perturbative the continuum light cone approach is no more complex than usual perturbation theory in lowest order. Relative to discretized light cone quantization, the critical coupling increases by 30% to a value r = 1.5. Conventional perturbation theory at the corresponding order yields r_1=1, whereas the RG improved fourth order result is r_4 = 1.8 +-0.05.

hep-th↗