arXiv subjects
Publications and source records attributed to H. A. Kastrup.
We discuss the possibility of extracting phase shifts from finite volume energies for meson-meson scattering, where the mesons are fermion-antifermion bound states of the massive Schwinger model with SU(2) flavour symmetry. The existence of analytical strong coupling predictions for the mass spectrum and for the scattering phases makes it possible to test the reliability of numerical results.
Many authors - beginning with Bekenstein - have suggested that the energy levels E_n of a quantized isolated Schwarzschild black hole have the form E_n = sigma sqrt{n} E_P, n=1,2,..., sigma =O(1), with degeneracies g^n. In the present paper properties of a system with such a spectrum, considered as a quantum canonical ensemble, are discussed: Its canonical partition function Z(g,beta=1/kT), defined as a series for g<1, obeys the 1-dimensional heat equation. It may be extended to values g>1 by means of an integral representation which reveals a cut of Z(g,beta) in the complex g-plane from g=1 to infinity. Approaching the cut from above yields a real and an imaginary part of Z. Very surprisingly, it is the (explicitly known) imaginary part which gives the expected thermodynamical properties of Schwarzschild black holes: Identifying the internal energy U with the rest energy Mc^2 requires beta to have the value (in natural units) beta = 2M(lng/sigma^2)[1+O(1/M^2)], (4pi sigma^2=lng gives Hawking's beta_H), and yields the entropy S=[lng/(4pi sigma^2)] A/4 + O(lnA), where A is the area of the horizon.
Bianchi -I, -III, and FRW type models minimally coupled to a massive spatially homogeneous scalar field (i.e. a particle) are studied in the framework of semiclassical quantum gravity. In a first step we discuss the solutions of the corresponding equation for a Schrödinger particle propagating on a classical background. The back reaction of the Schrödinger particle on the classical metric is calculated by means of the Wigner function and by means of the expectation value of the energy-momentum-tensor of the field as a source. Both methods in general lead to different results.
The known canonical quantum theory of a spherically symmetric pure (Schwarzschild) gravitational system describes isolated black holes by plane waves exp(-iMc^2τ/\hbar) with respect to their continuous masses M and the proper time τof obsevers at spatial infinity. On the other hand Bekenstein and Mukhanov postulated discrete mass levels for such black holes in the spirit of the Bohr-Sommerfeld quantisation in atomic physics. The two approaches can be related by postulating periodic boundary conditions in time for the plane waves and by identifying the period Δin real time with the period Δ_H= 8πGM/c^3 in Euclidean time. This yields the mass spectrum M_n=(1/2)\sqrt{n}m_P, n=1,2,... .
We extract scattering phases for fermion-fermion scattering from Monte Carlo simulations of the two-dimensional Gross-Neveu model. This is done by means of Lüscher's method, which exploits the volume dependence of the energies of two-particle states. The results are compared with the analytical predictions.
Encouraged by the successful applications of Lüscher's method to boson--boson scattering we discuss the possibility of extracting scattering phase shifts from finite--volume energies for fermion--fermion scattering in the Gross--Neveu model.
According to a proposal of Luescher 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 four-dimensional O(4) non-linear sigma-model in a Monte Carlo study on finite lattices. This non-perturbative approach also permits the study of unstable particles, the sigma-particle in our case. We observe the sigma-resonance and extract its mass and width. In all scattering channels investigated the results are completely consistent with perturbative calculations.
It is shown - in Ashtekar's canonical framework of General Relativity - that spherically symmetric (Schwarzschild) gravity in 4 dimensional space-time constitutes a finite dimensional completely integrable system. Canonically conjugate observables for asymptotically flat space-times are masses as action variables and - surprisingly - time variables as angle variables, each of which is associated with an asymptotic "end" of the Cauchy surfaces. The emergence of the time observable is a consequence of the Hamiltonian formulation and its subtleties concerning the slicing of space and time and is not in contradiction to Birkhoff's theorem. The results are of interest as to the concept of time in General Relativity. They can be formulated within the ADM formalism, too. Quantization of the system and the associated Schrödinger equation depend on the allowed spectrum of the masses.
Using Luescher's method we determine the elastic scattering phases in the broken phase of the 4-dimensional O(4) non-linear sigma-model from the two-particle energy spectrum in a Monte-Carlo study on finite lattices. In the isospin-0-channel we observe the sigma-resonance and extract its mass and its width. In all scattering channels investigated the results are consistent with perturbative calculations.
We show that the quantization of spherically symmetric pure gravity can be carried out completely in the framework of Ashtekar's self-dual representation. Consistent operator orderings can be given for the constraint functionals yielding two kinds of solutions for the constraint equations, corresponding classically to globally nondegenerate or degenerate metrics. The physical state functionals can be determined by quadratures and the reduced Hamiltonian system possesses 2 degrees of freedom, one of them corresponding to the classical Schwarzschild mass squared and the canonically conjugate one representing a measure for the deviation of the nonstatic field configurations from the static Schwarzschild one. There is a natural choice for the scalar product making the 2 fundamental observables self-adjoint. Finally, a unitary transformation is performed in order to calculate the triad-representation of the physical state functionals and to provide for a solution of the appropriately regularized Wheeler-DeWitt equation.