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Felix Finster

Publications and source records attributed to Felix Finster.

At least 145 records · Page 8Linked to original sources
arXiv2008

Light-Cone Expansion of the Dirac Sea to First Order in the External Potential

The perturbation of the Dirac sea to first order in the external potential is calculated in an expansion around the light cone. It is shown that the perturbation consists of a causal contribution, which describes the singular behavior of the Dirac sea on the light cone and contains bounded line integrals over the potential and its partial derivatives, and a non-causal contribution, which is a smooth function. As a preparatory step, we construct a formal solution of the inhomogeneous Klein-Gordon equation in terms of an infinite series of line integrals. More generally, the method presented can be used for an explicit analysis of Feynman diagrams of the Dirac, Klein-Gordon, and wave equations in position space.

hep-th↗
arXiv2008

A Time Independent Energy Estimate for Outgoing Scalar Waves in the Kerr Geometry

The Cauchy problem for the scalar wave equation in the Kerr geometry is considered, with initial data which is smooth and compactly supported outside the event horizon. A time-independent energy estimate for the outgoing wave is obtained. As an application we estimate the outgoing energy for wave-packet initial data, uniformly as the support of the initial data is shifted to infinity. The main mathematical tool is our previously derived integral representation of the wave propagator.

math-ph↗
arXiv2008

From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives

This survey article reviews recent results on fermion system in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a lattice model for a static and isotropic space-time, outline the analysis of regularization tails of vacuum Dirac sea configurations, and introduce a Lorentz invariant action for the masses of the Dirac seas. We mention the method of the continuum limit, which allows to analyze interacting systems. Open problems are discussed.

math-ph↗
arXiv2008

Non-Existence of Black Hole Solutions for a Spherically Symmetric, Static Einstein-Dirac-Maxwell System

We consider for j=1/2, 3/2,... a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein-Dirac-Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner-Nordstrom solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a "cloud" of spin-1/2-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon.

gr-qc↗
arXiv2007

The Principle of the Fermionic Projector: An Approach for Quantum Gravity?

In this short article we introduce the mathematical framework of the principle of the fermionic projector and set up a variational principle in discrete space-time. The underlying physical principles are discussed. We outline the connection to the continuum theory and state recent results. In the last two sections, we speculate on how it might be possible to describe quantum gravity within this framework.

gr-qc↗
arXiv2007

Fermion Systems in Discrete Space-Time

Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.

hep-th↗
arXiv2007

Fermion Systems in Discrete Space-Time - Outer Symmetries and Spontaneous Symmetry Breaking

A systematic procedure is developed for constructing fermion systems in discrete space-time which have a given outer symmetry. The construction is illustrated by simple examples. For the symmetric group, we derive constraints for the number of particles. In the physically interesting case of many particles and even more space-time points, this result shows that the permutation symmetry of discrete space-time is always spontaneously broken by the fermionic projector.

math-ph↗
arXiv2007

Local U(2,2) Symmetry in Relativistic Quantum Mechanics

Local gauge freedom in relativistic quantum mechanics is derived from a measurement principle for space and time. For the Dirac equation, one obtains local U(2,2) gauge transformations acting on the spinor index of the wave functions. This local U(2,2) symmetry allows a unified description of electrodynamics and general relativity as a classical gauge theory.

hep-th↗
arXiv2006

Spectral Estimates and Non-Selfadjoint Perturbations of Spheroidal Wave Operators

We derive a spectral representation for the oblate spheroidal wave operator which is holomorphic in the aspherical parameter $Ω$ in a neighborhood of the real line. For real $Ω$, estimates are derived for all eigenvalue gaps uniformly in $Ω$. The proof of the gap estimates is based on detailed estimates for complex solutions of the Riccati equation. The spectral representation for complex $Ω$ is derived using the theory of slightly non-selfadjoint perturbations.

math-ph↗
arXiv2003

The Long-Time Dynamics of Dirac Particles in the Kerr-Newman Black Hole Geometry

We consider the Cauchy problem for the massive Dirac equation in the non-extreme Kerr-Newman geometry outside the event horizon. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. It is proved that for initial data in L^\infty_loc near the event horizon with L^2 decay at infinity, the probability of the Dirac particle to be in any compact region of space tends to zero as t goes to infinity. This means that the Dirac particle must either disappear in the black hole or escape to infinity.

gr-qc↗
arXiv2003

Curvature Estimates in Asymptotically Flat Lorentzian Manifolds

We consider an asymptotically flat Lorentzian manifold of dimension (1,3). An inequality is derived which bounds the Riemannian curvature tensor in terms of the ADM energy in the general case with second fundamental form. The inequality quantifies in which sense the Lorentzian manifold becomes flat in the limit when the ADM energy tends to zero.

math.DG↗
arXiv2002

Decay Rates and Probability Estimates for Massive Dirac Particles in the Kerr-Newman Black Hole Geometry

The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr-Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in L^\infty_loc at least at the rate t^{-5/6}. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p=0,1 or 0<p<1. The proofs are based on a refined analysis of the Dirac propagator constructed in gr-qc/0005088.

gr-qc↗
arXiv2000

The Interaction of Dirac Particles with Non-Abelian Gauge Fields and Gravity - Bound States

We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang/Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

gr-qc↗