arXiv subjects

Hans A. Kastrup

Publications and source records attributed to Hans A. Kastrup.

4 recordsLinked to original sources

arXiv1995

Constructing solutions of Hamilton-Jacobi equations for 2 D fields with one component by means of Baecklund transformations

The Hamilton-Jacobi formalism generalized to 2-dimensional field theories according to Lepage's canonical framework is applied to several relativistic real scalar fields, e.g. massless and massive Klein-Gordon, Sinh and Sine-Gordon, Liouville and $ϕ^4$ theories. The relations between the Euler-Lagrange and the Hamilton-Jacobi equations are discussed in DeDonder and Weyl's and the corresponding wave fronts are calculated in Carathéodory's formulation. Unlike mechanics we have to impose certain integrability conditions on the velocity fields to guarantee the transversality relations and especially the dynamical equivalence between Hamilton-Jacobi wave fronts and families of extremals embedded therein. Bäcklund Transformations play a crucial role in solving the resulting system of coupled nonlinear PDEs.

hep-th↗

arXiv1995

Solutions of the Hamilton--Jacobi equation for one component two dimensional Field Theories

The Hamilton--Jacobi formalism generalized to 2--dimensional field theories according to Lepage's canonical framework is applied to several covariant real scalar fields, e.g. massless and massive Klein--Gordon, Sine--Gordon, Liouville and $ϕ^4$ theories. For simplicity we use the Hamilton--Jacobi equation of DeDonder and Weyl. Unlike mechanics we have to impose certain integrability conditions on the velocity fields to guarantee the transversality relations between Hamilton--Jacobi wave fronts and the corresponding families of extremals embedded therein. Bäcklund Transformations play a crucial role in solving the resulting system of coupled nonlinear PDEs.

hep-th↗

arXiv1992

Unstable particles in finite volume: The broken phase of the $4$-d $O(4)$ non-linear $σ$-model

According to a proposal of Lüscher it is possible to determine elastic scattering phases in infinite volume from the energy spectrum of two-particle states in a periodic box. We demonstrate the applicability of this method in the broken phase of the 4-dimensional $O(4)$ non-linear $σ$-model in a Monte-Carlo study on finite lattices. This non-perturbative approach also permits the study of unstable particles, the $\sg$-particle in our case. We observe the $\sg$-resonance and extract its mass and its width.

hep-lat↗

arXiv1992

Scaling analysis of the O(4)-symmetric $Φ^4$-theory in the broken phase

We study the $O(4)$-symmetric $ Φ^4 $-theory in the scaling region of the broken phase using the standard and a Symanzik improved action with infinite bare self-coupling $λ$. A high precision Monte Carlo simulation is performed by applying the reflection cluster algorithm. Employing the histogram method we analytically continue to a sequence of values of the hopping parameter $κ$ neighbouring the actually simulated ones. In the investigated vicinity of the critical point $κ_{c}$ finite volume effects affecting, e.g., the determination of the field expectation value $Σ$ and the mass $m_σ$ of the $σ$-particle are very well described by 1-loop renormalized perturbation theory. We carry out a detailed scaling analysis on a high level of precision. Finally we discuss the upper bound on the Higgs mass for both kinds of actions.

hep-lat↗