arXiv subjects
Publications and source records attributed to Z. Haba.
In the Brans-Dicke model we treat the scalar field exactly and expand the gravitational field in a power series. A comparison with 2D sigma models and ϕ^{4} perturbation theory in four dimensions suggests that the perturbation series in 4D Brans-Dicke model is renormalizable.
We discuss D-dimensional scalar and electromagnetic fields interacting with a quantized metric. The gravitons depend solely on twodimensional coordinates. We consider a conformal field theory model for the metric tensor. We show that an interaction with gravity improves the short distance behaviour. As a result there is no charge renormalization in the fourdimensional Higgs model.
We calculate the effective action in Yang-Mills and scalar ϕ^4 quantum field theory with quantized scale invariant metric treated non-perturbatively in d=4 dimensions. There is no charge renormalization in the one-loop order for matter fields. We show that the electromagnetic energy of point charges can be finite. The temperature dependence of the effective action in inflationary models is changed substantially as a result of an interaction with quantum gravity.
We assume that the fourdimensional quantum gravity is scale invariant at short distances. We show through a simple scaling argument that correlation functions of quantum fields interacting with gravity have a universal (more regular) short distance behavior.
The forward--backward path integral describing a charged particle moving in a thermal bath of photons is expressed in terms of the solution of a Langevin-type of equation. Approximate methods for solving this equation are discussed.
We present a two-dimensional classical stochastic differential equation for a displacement field of a point particle in two dimensions and show that its components define real and imaginary parts of a complex field satisfying the Schroedinger equation of a harmonic oscillator. In this way we derive the discrete oscillator spectrum from classical dynamics. The model is then generalized to an arbitrary potential. This opens up the possibility of efficiently simulating quantum computers with the help of classical systems.
From a forward--backward path integral, we derive a master equation for the emission and absorption of gravitons by a massive quantum object in a heat bath of gravitons. Such an equation could describe collapse phenomena of dense stars. We also present a useful approximate Langevin equation for such a system.
We set up a forward--backward path integral for a point particle in a bath of photons to derive a master equation for the density matrix which describes electromagnetic dissipation and decoherence. As an application, we recalculate the Weisskopf-Wigner formula for the natural line width of an atomic state at zero temperature and find, in addition, the temperature broadening caused by the decoherence term.
We consider second order differential operators with coefficients which are Gaussian random fields. When the covariance becomes singular at short distances then the propagators of the Schrödinger equation as well as of the wave equation behave in an anomalous way. In particular, the Feynman propagator for the wave equation is less singular than the one with deterministic coefficients. We suggest some applications to quantum gravity.
We consider a wave packet of a charged particle passing through a cavity filled with photons at temperature T and investigate its localization and interference properties. It is shown that the wave packet becomes localized and the interference disappears with an exponential speed after a sufficiently long path through the cavity.
Quantum mechanical interference of wave functions leads to some difficulties if a probability density is considered as a source of gravity. We show that an introduction of a quantum energy-momentum tensor as a source term in Einstein equations can be consistent with general relativity if the gravitational waves are quantized.
We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic wave function whose dynamics is determined by a non-linear Schrödinger-type evolution equation in an additional time parameter. The correct classical limit requires the proper time interpretation of the time parameter. An average over the proper time leads to the conventional quantum field theory of particles which are free at an infinite space separation. We consider models with scalar and vector fields on a pseudoriemannian manifold. A quantization of the Einstein gravity in this approach is briefly discussed.
We express the unitary time evolution in non-relativistic regularized quantum electrodynamics at zero and positive temperature by a Feynman integral defined in terms of a complex Brownian motion. An average over the quantum electromagnetic field determines the form of the quantum mechanics in an environment of a quantum black body radiation. In this non-perturbative formulation of quantum electrodynamics we prove the existence of the classical limit $\hbar \rightarrow 0$.We estimate an error to some approximations commonly applied in quantum radiation theory.
We consider a class of models describing a quantum oscillator in interaction with an environment. We show that models of continuous spontaneous localization based on a stochastic Schrödinger equation can be derived as an approximation to purely deterministic Hamiltonian systems. We show an exponential decay of off-diagonal matrix elements in the energy representation.
Quantum dynamics of integrable systems is discussed. Localized wave packets generalizing the conventional coherent states of minimal uncertainty are constructed. The wave packet moves along a certain trajectory and does not change its shape for times of order $\frac{1}{\hbar}$.