arXiv subjects
Publications and source records attributed to Domenico Giulini.
Wheeler's Superspace is the arena in which Geometrodynamics takes place. I review some aspects of its geometrical and topological structure that Wheeler urged us to take seriously in the context of canonical quantum gravity.
On his way to General Relativity (GR) Einstein gave several arguments as to why a special relativistic theory of gravity based on a massless scalar field could be ruled out merely on grounds of theoretical considerations. We re-investigate his two main arguments, which relate to energy conservation and some form of the principle of the universality of free fall. We find that such a theory-based a priori abandonment not to be justified. Rather, the theory seems formally perfectly viable, though in clear contradiction with (later) experiments. This may be of interest to those who teach GR and/or have an active interest in its history.
Minkowski Space is the simplest four-dimensional Lorentzian Manifold, being topologically trivial and globally flat, and hence the simplest model of spacetime--from a General-Relativistic point of view. But this does not mean that it is altogether structurally trivial. In fact, it has a very rich structure, parts of which will be spelled out in detail in this contribution. This will contain elementary aspects of affine spaces, various paths to the Poincare group, the lattices of causally and chronologically complete regions, and last but not least, the Noether-Herglotz theorem.
"Symmetry" was one of the most important methodological themes in 20th-century physics and is probably going to play no lesser role in physics of the 21st century. As used today, there are a variety of interpretations of this term, which differ in meaning as well as their mathematical consequences. Symmetries of crystals, for example, generally express a different kind of invariance than gauge symmetries, though in specific situations the distinctions may become quite subtle. I will review some of the various notions of "symmetry" and highlight some of their uses in specific examples taken from Pauli's scientific oevre.
In December 1924 Wolfgang Pauli proposed the idea of an inner degree of freedom of the electron, which he insisted should be thought of as genuinely quantum mechanical in nature. Shortly thereafter Ralph Kronig and, independently, Samuel Goudsmit and George Uhlenbeck took up a less radical stance by suggesting that this degree of freedom somehow corresponded to an inner rotational motion, though it was unclear from the very beginning how literal one was actually supposed to take this picture, since it was immediately recognised (already by Goudsmit and Uhlenbeck) that it would very likely lead to serious problems with Special Relativity if the model were to reproduce the electron's values for mass, charge, angular momentum, and magnetic moment. However, probably due to the then overwhelming impression that classical concepts were generally insufficient for the proper description of microscopic phenomena, a more detailed reasoning was never given. In this contribution I shall investigate in some detail what the restrictions on the physical quantities just mentioned are, if they are to be reproduced by rather simple classical models of the electron within the framework of Special Relativity. It turns out that surface stresses play a decisive role and that the question of whether a classical model for the electron does indeed contradict Special Relativity can only be answered on the basis of an \emph{exact} solution, which has hitherto not been given.
We give an introduction to the canonical formalism of Einstein's theory of general relativity. This then serves as the starting point for one approach to quantum gravity called quantum geometrodynamics. The main features and applications of this approach are briefly summarized.
We give a rigorous derivation of the general-relativistic formula for the two-way Doppler tracking of a spacecraft in Friedmann-Lemaitre-Robertson-Walker and in McVittie spacetimes. The leading order corrections of the so-determined acceleration to the Newtonian acceleration are due to special-relativistic effects and cosmological expansion. The latter, although linear in the Hubble constant, is negligible in typical applications within the Solar System.
Mapping-class groups of 3-manifolds feature as symmetry groups in canonical quantum gravity. They are an obvious source through which topological information could be transmitted into the quantum theory. If treated as gauge symmetries, their inequivalent unitary irreducible representations should give rise to a complex superselection structure. This highlights certain aspects of spatial diffeomorphism invariance that to some degree seem physically meaningful and which persist in all approaches based on smooth 3-manifolds, like geometrodynamics and loop quantum gravity. We also attempt to give a flavor of the mathematical ideas involved.
I review, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie algebra, comparison with the Galilei group, Einstein synchronization, the lattice of causally and chronologically complete regions in Minkowski space, rigid motion (the Noether-Herglotz theorem), and the geometry of rotating reference frames. Representation-theoretic aspects of the Lorentz group are not included. A series of appendices present some related mathematical material.
In the first part of this paper I review some of the difficulties that seem to obstruct generally valid definitions of "general covariance" and/or "background independence" The second and more historical part deals with a rather strange argument that Einstein put forward in his 1913 "Entwurf paper" with M. Grossmann to discredit scalar theories of gravity in order to promote general covariance.
In this expository paper we address the question of whether, and to what extent, the cosmological expansion influences the dynamics on small scales (as compared to cosmological ones), particularly in our Solar System. We distinguish between dynamical and kinematical effects and critically review the status of both as presented in the current literature.
Starting with Einstein's famous papers of 1905, we review some of the ensuing developments and their impact on present-day physics. We attempt to cover topics that are of interest to historians and philosophers of science as well as to physicists. This paper will appear in ``2005: The Centenary of Einstein's Annus Mirabilis'', the special March 2006 issue of Studies in History and Philosophy of Modern Physics.
Retrospectively, in 1905, Special Relativity seemed palpably close; it was "in the air". But apparently it needed the fresh approach of an unprejudiced newcomer, Einstein, to take the final step. I report, in a pedagogical fashion, on the scientific background that triggered the formulation of Special Relativity and also on the role of Lorentz and Poincare.
From its very beginning, Quantum Theory developed contrary to the intentions of its creators. For Max Planck it marks the failure of a long-term research program, in which he tried to understand the 2nd law of thermodynamics deterministically in terms of mechanics and electrodynamics. For Albert Einstein it meant a refutation of his scientific credo. I describe parts of the early stages of this most remarkable development, up to Einstein's light-quantum hypotheis and its unfavourable reception by most other physicists.
For two-black-hole time-symmetric initial data we consider the Corvino construction of gluing an exact Schwarzschild end. We propose to do this by using Brill waves. We address the question of whether this method can be used to reduce the overall energy, which seems to relate to the question of whether it can reduce the amount of `spurious' gravitational radiation. We find a positive answer at first order in the inverse gluing radius.
This is a pedagogical and (almost) self-contained introduction into the theorem of Groenewold and van Howe, which states that a naive transcription of Dirac's quantisation rules cannot work. Some related issues in quantisation theory are also discussed. First-class constrained systems are briefly described in a slightly more `global' fashion.
This is an introduction into the problem of how to set up black hole initial-data for the matter-free field equations of General Relativity. The approach is semi-pedagogical and addresses a more general audience of astrophysicists and students with no specialized training in General Relativity beyond that of an introductory lecture.
We consider the classical theory of a gravitational field with spin 2 and non-vanishing (Pauli-Fierz) mass in flat spacetime, coupled to electromagnetism and point particles. We establish the law of light propagation and calculate the amount of deflection in the background of a spherically symmetric gravitational field. As the mass tends to zero, the deflection is shown to converge to 3/4 of the value predicted by the massless theory (linearized General Relativity), even though the spherically symmetric solution of the gravitational field equations has no regular limit. This confirms an old argument of van Dam and Veltman on a purely classical level, but also shows its subtle nature.