arXiv subjects
Publications and source records attributed to K. J. M. Moriarty.
We use the quantum action to study quantum chaos at finite temperature. We present a numerical study of a classically chaotic 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling. We construct the quantum action non-perturbatively and find temperature dependent quantum corrections in the action parameters. We compare Poincaré sections of the quantum action at finite temperature with those of the classical action.
We suggest how to construct non-perturbatively a renormalized action in quantum mechanics. We discuss similarties and differences with the standard effective action. We propose that the new quantum action is suitable to define and compute quantum instantons and quantum chaos.
Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well potential.
We discuss $QCD$ in the Hamiltonian frame work. We treat finite density $QCD$ in the strong coupling regime. We present a parton-model inspired regularisation scheme to treat the spectrum ($θ$-angles) and distribution functions in $QED_{1+1}$. We suggest a Monte Carlo method to construct low-dimensionasl effective Hamiltonians. Finally, we discuss improvement in Hamiltonian $QCD$.
We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with renormalized parameters. We present numerical results for the $V \sim x^{4}$ potential. The renormalized action is relevant for quantum chaos and quantum instantons.
We suggest how to construct an effective low energy Hamiltonian via Monte Carlo starting from a given action. We test it by computing thermodynamical observables like average energy and specific heat for simple quantum systems.
We construct an effective Hamiltonian via Monte Carlo from a given action. This Hamiltonian describes physics in the low energy regime. We test it by computing spectrum, wave functions and thermodynamical observables (average energy and specific heat) for the free system and the harmonic oscillator. The method is shown to work also for other local potentials.
We present a non-perturbative study of the massive Schwinger model. We use a Hamiltonian approach, based on a momentum lattice corresponding to a fast moving reference frame, and equal time quantization.
We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving $d_{H}=2$ like the free motion. A velocity dependent action ($S \propto \int dt \mid \vec{v} \mid^α$) in the path integral (e.g. electrons moving in solids, or Brueckner's theory of nuclear matter) yields $d_{H}=\frac{α}{α- 1}$ if $α> 2$ and $d_{H}=2$ if $α\leq 2$. We discuss the relevance of fractal pathes in solid state physics and in $QFT$, in particular for the Wilson loop in $QCD$.
We study glueball and meson scattering in compact $QED_{2+1}$ gauge theory in a Hamiltonian formulation and on a momentum lattice. We compute ground state energy and mass, and introduce a compact lattice momentum operator for the computation of dispersion relations. Using a non-perturbative time-dependent method we compute scattering cross sections for glueballs and mesons. We compare our results with strong coupling perturbation theory.
We have studied the scalar $ϕ^4$-model in the symmetric phase and the non--compact $U(1)$ gauge theory on a momentum lattice using the Langevin equation for generating configurations. In the $ϕ^4$-model we have analyzed the renormalized mass and in the $U(1)$-model we have analyzed the Wilson loop operator. We used a second order algorithm for solving the Langevin equation, and we looked for the convergence rate of the method. We studied the stochastic time needed to generate equilibrium configurations and compared first and second order schemes for both models.