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Domenico Giulini

Publications and source records attributed to Domenico Giulini.

At least 19 recordsLinked to original sources
arXiv2026

What if active and passive gravitational masses were not equal?

At first glance, combining Newton's laws of motion with his law of gravitation seems straightforward. Students learn to distinguish inertial from gravitational mass and that their empirical equality is a remarkable fact about nature that will later serve as the conceptual gateway to general relativity. However, a closer look reveals a further and often neglected distinction within Newtonian gravity: that between active and passive gravitational mass. A common textbook argument maintains that these must be equal, for otherwise Newton's third law would be violated. We review and critically re-examine this familiar reasoning and show that the supposed theoretical proof is not compelling. Our analysis highlights subtle structural assumptions within Newtonian mechanics and offers physics teachers and researchers a fresh opportunity to explore foundational questions with potentially interesting applications in observational astronomy. In addition, an extended appendix, which is not part of the published AJP paper, offers some mathematical background material on the Galilean group and its action as group of dynamical symmetries for the type of dynamical equations considered here.

physics.class-ph↗
arXiv2025

The trace-free Einstein tensor is not variational for the metric as field variable

It is well-known that the trace-free Einstein tensor of a pseudo-Riemannian metric cannot arise by variation of a local diffeomorphism-invariant action functional with the (inverse) metric as field variable. We show that this statement remains true even for general local actions, without the assumption of diffeomorphism invariance.

gr-qc↗
arXiv2025

Reconsidering Velocity Addition/Subtraction in Special Relativity

We reconsider velocity addition/subtraction in Special Relativity and re-derive its well-known non-commutative and non-associative algebraic properties in a self contained way, including various explicit expressions for the Thomas angle, the derivation of which will be seen to be not as challenging as often suggested. All this is based on the polar-decomposition theorem in the traditional component language, in which Lorentz transformations are ordinary matrices. In the second part of this paper we offer a less familiar alternative geometric view, that leads to an invariant definition of the concept of relative velocity between two states of motion, which is based on the boost-link-theorem, of which we also offer an elementary proof that does not seem to be widely known in the relativity literature. Finally we compare this to the corresponding geometric definitions in Galilei-Newton spacetime, emphasising similarities and differences.

math-ph↗
arXiv2024

Atom interferometers in weakly curved spacetimes using Bragg diffraction and Bloch oscillations

We present a systematic approach to determine all relativistic phases up to $\mathcal{O}(c^{-2})$ in light-pulse atom interferometers in weakly curved spacetime that are based on elastic scattering, namely Bragg diffraction and Bloch oscillations. Our analysis is derived from first principles using the parameterized post-Newtonian formalism. In the treatment developed here, we derive algebraic expressions for relativistic phases for arbitrary interferometer geometries in an automated manner. As case studies, we consider symmetric and antisymmetric Ramsey-Bordé interferometers, as well as a symmetric double diffraction interferometer with baseline lengths of 10 m and 100 m. We compare our results to previous calculations conducted for a Mach-Zehnder interferometer.

gr-qc↗
arXiv2023

Geometric post-Newtonian description of massive spin-half particles in curved spacetime

We consider the Dirac equation coupled to an external electromagnetic field in curved four-dimensional spacetime with a given timelike worldline $γ$ representing a classical clock. We use generalised Fermi normal coordinates in a tubular neighbourhood of $γ$ and expand the Dirac equation up to, and including, the second order in the dimensionless parameter given by the ratio of the geodesic distance to the radii defined by spacetime curvature, linear acceleration of $γ$, and angular velocity of rotation of the employed spatial reference frame along $γ$. With respect to the time measured by the clock $γ$, we compute the Dirac Hamiltonian to that order. On top of this `weak-gravity' expansion we then perform a post-Newtonian expansion up to, and including, the second order of $1/c$, corresponding to a `slow-velocity' expansion with respect to $γ$. As a result of these combined expansions we give the weak-gravity post-Newtonian expression for the Pauli Hamiltonian of a spin-half particle in an external electromagnetic field. This extends and partially corrects recent results from the literature, which we discuss and compare in some detail.

gr-qc↗
arXiv2023

Asymptotic Symmetries of SU(2) Yang-Mills-Higgs Theory in Hamiltonian Formulation

We investigate the asymptotic symmetry group of a SU(2)-Yang-Mills theory coupled to a Higgs field in the Hamiltonian formulation. This extends previous work on the asymptotic structure of pure electromagnetism by Henneaux and Troessaert, and on electromagnetism coupled to scalar fields and pure Yang-Mills fields by Tanzi and Giulini. We find that there are no obstructions to global electric and magnetic charges, though that is rather subtle in the magnetic case. Again it is the Hamiltionian implementation of boost symmetries that need a careful and technically subtle discussion of fall-off and parity conditions of all fields involved.

hep-th↗
arXiv2022

Coupling Quantum Matter and Gravity

In this contribution we deal with several issues one encounters when trying to couple quantum matter to classical gravitational fields. We start with a general background discussion and then move on to two more technical sections. In the first technical part we consider the question how the Hamiltonian of a composite two-particle system in an external gravitational field can be computed in a systematic post-Newtonian setting without backreaction. This enables us to reliably estimate the consistency and completeness of less systematic and more intuitive approaches that attempt to solve this problem by adding `relativistic effects' by hand. In the second technical part we consider the question of how quantum matter may act as source for classical gravitational fields via the semiclassical Einstein equations. Statements to the effect that this approach is fundamentally inconsistent are critically reviewed.

gr-qc↗
arXiv2021

Asymptotic symmetries of scalar electrodynamics and of the abelian Higgs model in Hamiltonian formulation

We investigate the asymptotic symmetry group of a scalar field minimally-coupled to an abelian gauge field using the Hamiltonian formulation. This extends previous work by Henneaux and Troessaert on the pure electromagnetic case. We deal with minimally coupled massive and massless scalar fields and find that they behave differently insofar as the latter do not allow for canonically implemented asymptotic boost symmetries. We also consider the abelian Higgs model and show that its asymptotic canonical symmetries reduce to the Poincaré group in an unproblematic fashion.

hep-th↗
arXiv2021

A group-theoretic characterisation of Taub-Nut spacetime

We prove that any $G=SU(2)\times U(1)$ symmetric spacetime that is Ricci flat (i.e. solves the matter-free $Λ=0$ Einstein equations) with non-null $G$-orbits is locally isometric to some maximally extended generalised Taub-NUT spacetime.

math-ph↗
arXiv2020

Asymptotic symmetries of Yang-Mills fields in Hamiltonian formulation

We investigate the asymptotic symmetry group of the free SU(N)-Yang-Mills theory using the Hamiltonian formalism. We closely follow the strategy of Henneaux and Troessaert who successfully applied the Hamiltonian formalism to the case of gravity and electrodynamics, thereby deriving the respective asymptotic symmetry groups of these theories from clear-cut first principles. These principles include the minimal assumptions that are necessary to ensure the existence of Hamiltonian structures (phase space, symplectic form, differentiable Hamiltonian) and, in case of Poincaré invariant theories, a canonical action of the Poincaré group. In the first part of the paper we show how these requirements can be met in the non-abelian SU(N)-Yang-Mills case by imposing suitable fall-off and parity conditions on the fields. We observe that these conditions admit neither non-trivial asymptotic symmetries nor non-zero global charges. In the second part of the paper we discuss possible gradual relaxations of these conditions by following the same strategy that Henneaux and Troessaert had employed to remedy a similar situation in the electromagnetic case. Contrary to our expectation and the findings of Henneaux and Troessaert for the abelian case, there seems to be no relaxation that meets the requirements of a Hamiltonian formalism and allows for non-trivial asymptotic symmetries and charges. Non-trivial asymptotic symmetries and charges are only possible if either the Poincaré group fails to act canonically or if the formal expression for the symplectic form diverges, i.e. the form does not exist. This seems to hint at a kind of colour-confinement built into the classical Hamiltonian formulation of non-abelian gauge theories.

hep-th↗
arXiv2020

Classical perspectives on the Newton--Wigner position observable

This paper deals with the Newton--Wigner position observable for Poincaré-invariant classical systems. We prove an existence and uniqueness theorem for elementary systems that parallels the well-known Newton--Wigner theorem in the quantum context. We also discuss and justify the geometric interpretation of the Newton--Wigner position as `centre of spin', already proposed by Fleming in 1965 again in the quantum context.

math-ph↗
arXiv2019

Post-Newtonian corrections to Schrödinger equations in gravitational fields

In this paper we extend the WKB-like `non-relativistic' expansion of the minimally coupled Klein--Gordon equation after Kiefer and Singh [1], Lämmerzahl [2] and Giulini and Großardt [3] to arbitrary order in $c^{-1}$, leading to Schrödinger equations describing a quantum particle in a general gravitational field, and compare the results with canonical quantisation of a free particle in curved spacetime, following Wajima et al. [4]. Furthermore, using a more operator-algebraic approach, the Klein--Gordon equation and the canonical quantisation method are shown to lead to the same results for some special terms in the Hamiltonian describing a single particle in a general stationary spacetime, without any `non-relativistic' expansion.

gr-qc↗
arXiv2019

Post-Newtonian Hamiltonian description of an atom in a weak gravitational field

We extend the systematic calculation of an approximately relativistic Hamiltonian for centre of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [1] to the case including a weak post-Newtonian gravitational background field, described by the Eddington--Robertson parametrised post-Newtonian metric. Starting from a proper relativistic description of the situation, this approach allows to systematically derive the coupling of the model system to gravity, instead of `guessing' it by means of classical notions of relativistic effects. We embed this technical result into a critical discussion concerning the problem of implementing and interpreting general couplings to the gravitational field and the connected problem of how to properly address the question concerning the validity of the Equivalence Principle in Quantum Mechanics.

quant-ph↗
arXiv2019

Lie sphere-geometry in lattice cosmology

In this paper we propose to use Lie sphere-geometry as a new tool to systematically construct time-symmetric initial data for a wide variety of generalised black-hole configurations in lattice cosmology. These configurations are iteratively constructed analytically and may have any degree of geometric irregularity. We show that for negligible amounts of dust these solutions are similar (in a sense made precise) to the swiss-cheese models at the moment of maximal expansion. As Lie sphere-geometry has so far not received much attention in cosmology, we will devote a large part of this paper to explain its geometric background in a language familiar to general relativists.

gr-qc↗
arXiv2018

Numerical Approach for Corvino-Type Gluing of Brill-Lindquist Initial Data

Building on the work of Giulini and Holzegel (2005), a new numerical approach is developed for computing Cauchy data for Einstein's equations by gluing a Schwarzschild end to a Brill-Lindquist metric via a Corvino-type construction. In contrast to, and in extension of, the numerical strategy of Doulis and Rinne (2016), the overdetermined Poisson problem resulting from the Brill wave ansatz is decomposed to obtain two uniquely solvable problems. A pseudospectral method and Newton-Krylov root finder are utilized to perform the gluing. The convergence analysis strongly indicates that the numerical strategy developed here is able to produce highly accurate results. It is observed that Schwarzschild ends of various ADM masses can be glued to the same interior configuration using the same gluing radius.

gr-qc↗
arXiv2018

Laue's Theorem Revisited: Energy-Momentum Tensors, Symmetries, and the Habitat of Globally Conserved Quantities

The energy-momentum tensor for a particular matter component summarises its local energy-momentum distribution in terms of densities and current densities. We re-investigate under what conditions these local distributions can be integrated to meaningful global quantities. This leads us directly to a classic theorem by Max von Laue concerning integrals of components of the energy-momentum tensor, whose statement and proof we recall. In the first half of this paper we do this within the realm of Special Relativity and in the traditional mathematical language using components with respect to affine charts, thereby focusing on the intended physical content and interpretation. In the second half we show how to do all this in a proper differential-geometric fashion and on arbitrary space-time manifolds, this time focusing on the group-theoretic and geometric hypotheses underlying these results. Based on this we give a proper geometric statement and proof of Laue's theorem, which is shown to generalise from Minkowski space (which has the maximal number of isometries) to space-times with significantly less symmetries. This result, which seems to be new, not only generalises but also clarifies the geometric content and hypotheses of Laue's theorem. A series of three appendices lists our conventions and notation and summarises some of the conceptual and mathematical background needed in the main text.

math-ph↗
arXiv2015

Dynamical and Hamiltonian formulation of General Relativity

This is a substantially expanded version of a chapter-contribution to "The Springer Handbook of Spacetime", edited by Abhay Ashtekar and Vesselin Petkov, published by Springer Verlag in 2014. This contribution introduces the reader to the reformulation of Einstein's field equations of General Relativity as a constrained evolutionary system of Hamiltonian type and discusses some of its uses, together with some technical and conceptual aspects. Attempts were made to keep the presentation self contained and accessible to first-year graduate students. This implies a certain degree of explicitness and occasional reviews of background material.

gr-qc↗