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Z. Haba

Publications and source records attributed to Z. Haba.

At least 55 records · Page 3Linked to original sources
arXiv2009

Relativistic diffusion of elementary particles with spin

We obtain a generalization of the relativistic diffusion of Schay and Dudley for particles with spin. The diffusion equation is a classical version of an equation for the Wigner function of an elementary particle. The elementary particle is described by a unitary irreducible representation of the Poincare group realized in the Hilbert space of wave functions in the momentum space. The arbitrariness of the Wigner rotation appears as a gauge freedom of the diffusion equation. The spin is described as a connection of a fiber bundle over the momentum hyperbolic space (the mass-shell). Motion in an electromagnetic field, transport equations and equilibrium states are discussed.

hep-th↗
arXiv2009

Relativistic diffusion of massless particles

We obtain a limit when mass tends to zero of the relativistic diffusion of Schay and Dudley. The diffusion process has the log-normal distribution. We discuss Langevin stochastic differential equations leading to an equilibrium distribution.We show that for the Juttner equilibrium distribution the relativistic diffusion is a linear approximation to the Kompaneetz equation describing a photon diffusion in an electron gas.The stochastic equation corresponding to the Juttner distribution is explicitly soluble. We relate the relativistic diffusion to imaginary time quantum mechanics. Some astrophysical applications (including the Sunyaev-Zeldovich effect) are briefly discussed.

hep-th↗
arXiv2009

Euclidean scalar Green functions near the black hole and black brane horizons

We discuss approximations of the Riemannian geometry near the horizon. If a D+1 dimensional manifold N has a bifurcate Killing horizon then we approximate N by a product of the two-dimensional Rindler space and a D-1 dimensional Riemannian manifold M. We obtain approximate formulas for scalar Green functions. We study the behaviour of the Green functions near the horizon and their dimensional reduction. We show that if M is compact then the Green function near the horizon can be approximated by the Green function of a two-dimensional quantum field theory. The correction term is exponentially small away from the horizon. We extend the results to black brane solutions of supergravity in 10 and 11 dimensions. The near horizon geometry can be approximated by N=AdS_p x S_q. We discuss Euclidean Green functions on N and their behaviour near the horizon.

hep-th↗
arXiv2009

Relativistic diffusion

We discuss a relativistic diffusion in the proper time in an approach of Schay and Dudley. We derive (Langevin) stochastic differential equations in various coordinates.We show that in some coordinates the stochastic differential equations become linear. We obtain momentum probability distribution in an explicit form.We discuss a relativistic particle diffusing in an external electromagnetic field. We solve the Langevin equations in the case of parallel electric and magnetic fields. We derive a kinetic equation for the evolution of the probability distribution.We discuss drag terms leading to an equilibrium distribution.The relativistic analog of the Ornstein-Uhlenbeck process is not unique. We show that if the drag comes from a diffusion approximation to the master equation then its form is strongly restricted. The drag leading to the Tsallis equilibrium distribution satisfies this restriction whereas the one of the Juettner distribution does not. We show that any function of the relativistic energy can be the equilibrium distribution for a particle in a static electric field. A preliminary study of the time evolution with friction is presented. It is shown that the problem is equivalent to quantum mechanics of a particle moving on a hyperboloid with a potential determined by the drag. A relation to diffusions appearing in heavy ion collisions is briefly discussed.

hep-th↗
arXiv2008

Green functions and dimensional reduction of quantum fields on product manifolds

We discuss Euclidean Green functions on product manifolds P=NxM. We show that if M is compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this approximation. We show that for large distances on N the remainder is small. If P=R^{D-1}xS^{beta}, where S^{beta} is a circle of radius beta, then the result reduces to the well-known approximation of the D dimensional finite temperature quantum field theory to D-1 dimensional one in the high temperature limit. Analytic continuation of Euclidean fields is discussed briefly.

hep-th↗
arXiv2007

Green functions and Euclidean fields near the bifurcate Killing horizon

We approximate a Euclidean version of a D+1 dimensional manifold with a bifurcate Killing horizon by a product of a two-dimensional Rindler space and a D-1 dimensional manifold M. We obtain approximate formulas for the Green functions. We study the behaviour of Green functions near the horizon and their dimensional reduction. We show that if M is compact then the massless minimally coupled quantum field contains a zero mode which is a conformal invariant free field on R^2. Then, the Green function near the horizon can be approximated by the Green function of the two-dimensional quantum field theory. The correction term is exponentially small away from the horizon. If the volume of a geodesic ball is growing to infinity with its radius then the Green function cannot be approximated by a two-dimensional one.

hep-th↗
arXiv2007

A relationship between scalar Green functions on hyperbolic and Euclidean Rindler spaces

We derive a formula connecting in any dimension the Green function on the D+1 dimensional Euclidean Rindler space and the one for a minimally coupled scalar field with a mass m in the D dimensional hyperbolic space. The relation takes a simple form in the momentum space where the Green functions are equal at the momenta (p_0,\bf p) for Rindler and (m,\bf p) for hyperbolic space with a simple additive relation between the squares of the mass and the momenta. The formula has applications to finite temperature Green functions, Green functions on the cone and on the 9compactified) Milne space-time. Analytic continuations and interacting quantum fields are briefly discussed.

hep-th↗
arXiv2006

Bounds on the heat kernel of the Schroedinger operator in a random electromagnetic field

We obtain lower and upper bounds on the heat kernel and Green functions of the Schroedinger operator in a random Gaussian magnetic field and a fixed scalar potential. We apply stochastic Feynman-Kac representation, diamagnetic upper bounds and the Jensen inequality for the lower bound. We show that if the covariance of the electromagnetic (vector) potential is increasing at large distances then the lower bound is decreasing exponentially fast for large distances and a large time.

quant-ph↗
arXiv2006

Heat equilibrium distribution in a turbulent flow

We consider a shear flow of a scale invariant homogeneous Gaussian random velocity field which does not depend on coordinates in the direction of the flow. We investigate a heat advection coming from a Gaussian random homogeneous source. We discuss a relaxation at large time of a temperature distribution determined by the forced advection-diffusion equation. We represent the temperature correlation functions by means of the Feynman-Kac formula. Jensen inequalities are applied for lower and upper bounds on the correlation functions. We show that at finite time there is no velocity dependence of long range temperature correlations (low momentum asymptotics) in the direction of the flow but the equilibrium heat distribution has large distance correlations (low momentum behaviour) with an index depending on the scaling index of the random flow and of the index of the random forcing. If the velocity has correlations growing with the distance (a turbulent flow) then the large distance correlations depend in a crucial way on the scaling index of the turbulent flow. In such a case the correlations increase in the direction of the flow and decrease in the direction perpendicular to the flow making the stream of heat more coherent.

physics.flu-dyn↗
arXiv2006

Quantum field theory with an interaction on the boundary

We consider quantum theory of fields ϕdefined on a D dimensional manifold (bulk) with an interaction V(ϕ) concentrated on a d<D dimensional surface (brane). Such a quantum field theory can be less singular than the one in d dimensions with the interaction $V(ϕ)$. It is shown that scaling properties of fields on the brane are different from the ones in the bulk.

hep-th↗
arXiv2005

Quantum field theory on manifolds with a boundary

We discuss quantum theory of fields ϕdefined on (d+1)-dimensional manifold {\cal M} with a boundary {\cal B}. The free action W_{0}(ϕ) which is a bilinear form in ϕdefines the Gaussian measure with a covariance (Green function) {\cal G}. We discuss a relation between the quantum field theory with a fixed boundary condition Φand the theory defined by the Green function {\cal G}. It is shown that the latter results by an average over Φof the first. The QFT in (anti)de Sitter space is treated as an example. It is shown that quantum fields on the boundary are more regular than the ones on (anti) de Sitter space.

hep-th↗
arXiv2005

Estimates on Green functions of second order differential operators with singular coefficients

We investigate the Green functions G(x,x^{\prime}) of some second order differential operators on R^{d+1} with singular coefficients depending only on one coordinate x_{0}. We express the Green functions by means of the Brownian motion. Applying probabilistic methods we prove that when x=(0,{\bf x}) and x^{\prime}=(0,{\bf x}^{\prime}) (here x_{0}=0) lie on the singular hyperplanes then G(0,{\bf x};0,{\bf x}^{\prime}) is more regular than the Green function of operators with regular coefficients.

math-ph↗
arXiv2004

Green functions and propagation of waves in strongly inhomogeneous media

We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of Green functions of operators with bounded coefficients. We discuss some consequences of such an anomalous short or long distance behaviour for a diffusion and wave propagation in an inhomogeneous medium.

hep-th↗
arXiv2004

Dimensional reduction of quantum fields on a brane

If we restrict a quantum field defined on a regular D dimensional curved manifold to a d dimensional submanifold then the resulting field will still have the singularity of the original D dimensional model. We show that a singular background metric can force the restricted field to behave as a d dimensional quantum field.

hep-th↗
arXiv2003

Quantization of the scalar field in a static quantum metric

We investigate the Hamiltonian formulation of quantum scalar fields in a static quantum metric. We derive a functional integral formula for the propagator. We show that the quantum metric substantially changes the behaviour of the scalar propagator and the effective Yukawa potential.

hep-th↗
arXiv2002

The Φ^4 quantum field in a scale invariant random metric

We discuss a D-dimensional Euclidean scalar field interacting with a scale invariant quantized metric. We assume that the metric depends on d-dimensional coordinates where d<D. We show that the interacting quantum fields have more regular short distance behaviour than the free fields. A model of a Gaussian metric is discussed in detail. In particular, in the Φ^4 theory in four dimensions we obtain explicit lower and upper bounds for each term of the perturbation series. It turns out that there is no coupling constant renormalization in the Φ^4 model in four dimensions. We show that in a particular range of the scale dimension there are models in D=4 without any divergencies.

hep-th↗
arXiv2002

Scale invariant Euclidean field theory in any dimension

We discuss D-dimensional scalar field interacting with a scale invariant random metric which is either a Gaussian field or a square of a Gaussian field. The metric depends on d-dimensional coordinates (where d is less than D). By a projection to a lower dimensional subspace we obtain a scale invariant non-Gaussian model of Euclidean quantum field theory in D-d or d dimensions.

hep-th↗