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Domenico Giulini

Publications and source records attributed to Domenico Giulini.

At least 73 records · Page 4Linked to original sources
arXiv2000

Uniqueness of Simultaneity

We consider the problem of uniqueness of certain simultaneity structures in flat spacetime. Absolute simultaneity is specified to be a non-trivial equivalence relation which is invariant under the automorphism group Aut of spacetime. Aut is taken to be the identity-component of either the inhomogeneous Galilei group or the inhomogeneous Lorentz group. Uniqueness of standard simultaneity in the first, and absence of any absolute simultaneity in the second case are demonstrated and related to certain group theoretic properties. Relative simultaneity with respect to an additional structure X on spacetime is specified to be a non-trivial equivalence relation which is invariant under the subgroup in Aut that stabilises X. Uniqueness of standard Einstein simultaneity is proven in the Lorentzian case when X is an inertial frame. We end by discussing the relation to previous work of others.

gr-qc↗
arXiv2000

Decoherence: A dynamical approach to superselection rules?

It is well known that the dynamical mechanism of decoherence may cause apparent superselection rules, like that of molecular chirality. These `environment-induced' or `soft' superselection rules may be contrasted with `hard' superselection rules, like that of electric charge, whose existence is usually rigorously demonstrated by means of certain symmetry principles. We address the question of whether this distinction between `hard' and `soft' is well founded and argue that, despite first appearance, it might not be. For this we give a detailed and somewhat pedagogical exposition of the basic structural properties of the spaces of states and observables in order to establish a fairly precise notion of superselection rules. We then discuss two examples: the Bargmann superselection rule for overall mass in ordinary quantum mechanics, and the superselection rule for charge in quantum electrodynamics.

quant-ph↗
arXiv2000

".. I didn't reflect much on what I was doing.." How Planck discovered his radiation formula

On December 14. 1900, Max Planck communicated his derivation of his radiation formula, which he later called ``an act of desperation''. This date is widely recognized as birthday of quantum theory. For Planck it meant the end of his carefully planned and ambitious research project, in which he wanted to establish the second law of thermodynamics as strictly deterministic law for systems of matter and electromagnetic radiation in interaction. He knew he could not succeed within classical mechanics, but had the somewhat strange hope that the inclusion of Maxwell's electrodynamics would change the situation. Later he always disagreed with Einstein's light-quantum hypothesis, because it implied a renunciation from Maxwell's theory, which in Germany gained full recognition and acceptance as late as the 1890's, mainly through the theoretical and experimental work of Heinrich Hertz.

quant-ph↗
arXiv2000

The mystery of cosmological vacuum energy density and the accelerated expansion of the universe

The principles of General Relativity allow for a non-vanishing cosmological constant, which can possibly be interpreted at least partially in terms of quantum-fluctuations of matter fields. Depending on sign and magnitude it can cause accelerated or decelerated expansion at certain stages of cosmic evolution. Recent observations in cosmology seem to indicate that we presently live in an accelerated phase. We recall the history and fundamental issues connected with the cosmological constant and then discuss present evidences for a positive value, which causes the accelerated expansion.

astro-ph↗
arXiv2000

Group Averaging and Refined Algebraic Quantization

We review the framework of Refined Algebraic Quantization and the method of Group Averaging for quantizing systems with first-class constraints. Aspects and results concerning the generality, limitations, and uniqueness of these methods are discussed.

gr-qc↗
arXiv1999

States, Symmetries and Superselection

The process of dynamical decoherence may cause apparent superselection rules, which are sometimes called `environmentally induced' or `soft'. A natural question is whether such dynamical processes are eventually also responsible for at least some of the superselection rules which are usually presented as fundamentally rooted in the kinematical structure of the theory (so called `hard' superselection rules). With this question in mind, I re-investigate two well known examples where superselection rules are usually argued to rigorously exist within the given mathematical framework. These are (1) the Bargmann superselection rule for the total mass in Galilei invariant quantum mechanics and (2) the charge superselection rule in quantum electrodynamics. I argue that, for various reasons, the kinematical arguments usually given are not physically convincing unless they are based on an underlying dynamical process.

quant-ph↗
arXiv1999

A Uniqueness Theorem for Constraint Quantization

This work addresses certain ambiguities in the Dirac approach to constrained systems. Specifically, we investigate the space of so-called ``rigging maps'' associated with Refined Algebraic Quantization, a particular realization of the Dirac scheme. Our main result is to provide a condition under which the rigging map is unique, in which case we also show that it is given by group averaging techniques. Our results comprise all cases where the gauge group is a finite-dimensional Lie group.

gr-qc↗
arXiv1999

On the Generality of Refined Algebraic Quantization

The Dirac quantization `procedure' for constrained systems is well known to have many subtleties and ambiguities. Within this ill-defined framework, we explore the generality of a particular interpretation of the Dirac procedure known as refined algebraic quantization. We find technical conditions under which refined algebraic quantization can reproduce the general implementation of the Dirac scheme for systems whose constraints form a Lie algebra with structure constants. The main result is that, under appropriate conditions, the choice of an inner product on the physical states is equivalent to the choice of a ``rigging map'' in refined algebraic quantization.

gr-qc↗
arXiv1998

Is There a General Area Theorem for Black Holes?

The general validity of the area law for black holes is still an open problem. We first show in detail how to complete the usually incompletely stated text-book proofs under the assumption of piecewise $C^2$-smoothness for the surface of the black hole. Then we prove that a black hole surface necessarily contains points where it is not $C^1$ (called ``cusps'') at any time before caustics of the horizon generators show up, like e.g. in merging processes. This implies that caustics never disappear in the past and that black holes without initial cusps will never develop such. Hence black holes which will undergo any non-trivial processes anywhere in the future will always show cusps. Although this does not yet imply a strict incompatibility with piecewise $C^2$ structures, it indicates that the latter are likely to be physically unnatural. We conclude by calling for a purely measure-theoretic proof of the area theorem.

gr-qc↗
arXiv1998

The Generalized Thin-Sandwich Problem and its Local Solvability

We consider Einstein Gravity coupled to dynamical matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate the conditions under which a free specification of a spatial field configuration for the total system and its derivative with respect to coordinate-time determines a solution to the field equations (generalized thin-sandwich problem). Sufficient conditions for local solvability (in the space of fields) are established.

gr-qc↗
arXiv1998

On the Construction of Time-Symmetric Black Hole Initial Data

We review in a pedagogical fashion the 3+1-split which serves to put Einstein's equations into the form of a dynamical system with constraints. We then discuss the constraint equations under the simplifying assumption of time-symmetry. Multi-Black-Hole data are presented and more explicitly described in the case of two holes. The effect of different topologies is emphasized.

gr-qc↗
arXiv1996

Consistently Implementing the Fields Self-Energy in Newtonian Gravity

We consider in a pedagogical fashion alterations to Newtonian gravity due to the postulate that all energy corresponds to active gravitational mass when applied to the self-energy of the gravitational field. We show why a simple addition of ${1\over c^2}$ times the gravitational field energy to the matter density in Newton's field equation is inconsistent. A consistent prescription is shown and discussed. The connection to general relativity is pointed out.

gr-qc↗
arXiv1995

The Group of Large Diffeomorphisms in General Relativity

We investigate the group of large diffeomorphisms fixing a frame at a point for general closed 3-manifolds. We derive some general structural properties of these groups which relate to the picture of the manifold as being composed of extended `objects' (geons).

gr-qc↗
arXiv1995

Quantum Mechanics On Spaces With Finite Fundamental Group

We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that arise from the non-simply connectedness of the classical configuration space. We define the quantum theory on the universal cover but restrict the algebra of observables $Ø$ to the commutant of the algebra generated by deck-transformations. We apply standard superselection principles and construct the corresponding sectors. We emphasize the relevance of all sectors and not just the abelian ones.

quant-ph↗
arXiv1995

A Euclidean Bianchi Model Based On $S^3/D_8^*$

We explain how the round four-sphere can be sliced along homogeneous 3~-~manifolds of topology $S^3/D_8^*$. This defines a Euclidean Bianchi type IX model for Einstein's equations with cosmological constant. The geometric properties of this model are investigated.

gr-qc↗
arXiv1995

On Galilei Invariance in Quantum Mechanics and the Bargmann Superselection Rule

We reinvestigate Bargmann's superselection rule for the overall mass of $n$ particles in ordinary quantum mechanics with Galilei invariant interaction potential. We point out that in order for mass to define a superselection rule it should be considered as a dynamical variable. We present a minimal extension of the original dynamics in which mass it treated as dynamical variable. Here the classical symmetry group turns out to be given by an $\reals$-extension of the Galilei group which formerly appeared only at the quantum level. There is now no obstruction to implement an action of the classical symmetry group on Hilbert space. We include some critical comments of a general nature on formal derivations of superselection rules without dynamical context.

quant-ph↗
arXiv1995

Diffeomorphism invariant subspaces in Witten's 2+1 quantum gravity on ${\bf R} \times T^2$

We address the role of large diffeomorphisms in Witten's 2+1 gravity on the manifold ${\bf R} \times T^2$. In a ``spacelike sector" quantum theory that treats the large diffeomorphisms as a symmetry, rather than as gauge, the Hilbert space is shown to contain no nontrivial finite dimensional subspaces that are invariant under the large diffeomorphisms. Infinite dimensional closed invariant subspaces are explicitly constructed, and the representation of the large diffeomorphisms is thus shown to be reducible. Comparison is made to Witten's theory on ${\bf R} \times Σ$, where $Σ$ is a higher genus surface.

gr-qc↗