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Luca Lusanna

Publications and source records attributed to Luca Lusanna.

At least 19 recordsLinked to original sources
arXiv2017

Dirac-Bergmann Constraints in Relativistic Physics: Non-Inertial Frames, Point Particles, Fields and Gravity

There is a review of the physical theories needing Dirac-Bergmann theory of constraints at the Hamiltonian level due to the existence of gauge symmetries. It contains: i) the treatment of systems of point particles in special relativity both in inertial and non-inertial frames with a Wigner-covariant way of eliminating relative times in relativistic bound states; ii) the description of the electro-magnetic field in relativistic atomic physics and of Yang-Mills fields in absence of Gribov ambiguity in particle physics; iii) the identification of the inertial gauge variables and of the physical variables in canonical ADM tetrad gravity in presence of the electro-magnetic field and of charged scalar point particles in asymptotically Minkowskian space-times without super-translations by means of a Shanmugadhasan canonical transformation to a York canonical basis adapted to ten of the 14 first-class constraints and the definition of the Hamiltonian Post-Minkowskian weak field limit. Review paper for a chapter of a future book

math-ph↗
arXiv2017

Dirac-Bergmann Constraints in Physics: Singular Lagrangians, Hamiltonian Constraints and the Second Noether Theorem

There is a review of the main mathematical properties of system described by singular Lagrangians and requiring Dirac-Bergmann theory of constraints at the Hamiltonian level. The following aspects are discussed: i) the connection of the rank and eigenvalues of the Hessian matrix in the Euler-Lagrange equations with the chains of first and second class constraints; ii) the connection of the Noether identities of the second Noether theorem with the Hamiltonian constraints; iii) the Shanmugadhasan canonical transformation for the identification of the gauge variables and for the search of the Dirac observables, i.e. the quantities invariant under Hamiltonian gauge transformations. Review paper for a chapter of a future book.

math-ph↗
arXiv2015

Killing Symmetries as Hamiltonian Constraints

The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time , while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive.

gr-qc↗
arXiv2014

Canonical ADM Tetrad Gravity: from Metrological Inertial Gauge Variables to Dynamical Tidal Dirac observables

Dirac constraint theory allows to identify the York canonical basis (diagonalizing the York-Lichnerowicz approach) in ADM tetrad gravity for asymptotically Minkowskian space-times without super-translations. This allows to identify the inertial (gauge) and tidal (physical) degrees of freedom of the gravitational field and to interpret Ashtekar variables in these space-times. The use of radar 4-coordinates centered on a time-like observer allows to connect the 3+1 splittings of space-time with the relativistic metrology used in atomic physics and astronomy. The asymptotic ADM Poincaré group replaces the Poincaré group of particle physics. The general relativistic remnant of the gauge freedom in clock synchronization is described by the inertial gauge variable ${}^3K$, the trace of the extrinsic curvature of the non-Euclidean 3-spaces. The theory can be linearized in a Post-Minkowskian way by using the asymptotic Minkowski metric as an asymptotic background at spatial infinity and the family of non-harmonic 3-orthogonal Schwinger time gauges allows to reproduce the known results on gravitational waves in harmonic gauges. It is shown that the main signatures for the existence of dark matter can be reinterpreted as an relativistic inertial effect induced by ${}^3K$: while in the space-time inertial and gravitational masses coincide (equivalence principle), this is not true in the non-Euclidean 3-spaces (breaking of Newton equivalence principle), where the inertial mass has extra ${}^3K$-dependent terms simulating dark matter. Therefore a Post-Minkowskian extension of the existing Post-Newtonian celestial reference frame is needed.

gr-qc↗
arXiv2014

Non-Inertial Frames in Minkowski Space-Time, Accelerated either Mathematical or Dynamical Observers and Comments on Non-Inertial Relativistic Quantum Mechanics

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and of how to define Unruh-DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.

gr-qc↗
arXiv2014

On Relativistic Entanglement and Localization of Particles and on their Comparison with the Non-Relativistic Theory

We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the relativistic center of mass, of the clock synchronization convention needed to define relativistic 3-spaces and of the elimination of the relative times in the relativistic bound states leads to a description with a decoupled non-local (non-measurable) relativistic center of mass and with only relative variables for the particles (single particle subsystems do not exist). We analyze the implications for entanglement of this relativistic spatial non-separability not existing in non-relativistic entanglement. Then we try to reconcile the two visions showing that also at the non-relativistic level in real experiments only relative variables are measured with their directions determined by the effective mean classical trajectories of particle beams present in the experiment. We discuss some of the existing problems with the observers and their reference frames, leaving to the future the discussion in non-inertial frames.

quant-ph↗
arXiv2013

On the Relativistic Micro-Canonical Ensemble and Relativistic Kinetic Theory for N Relativistic Particles in Inertial and Non-Inertial Rest Frames

A new formulation of relativistic classical mechanics allows a revisiting of old unsolved problems in relativistic kinetic theory and in relativistic statistical mechanics. In particular a definition of the relativistic micro-canonical partition function is given strictly in terms of the Poincaré generators of an interacting N-particle system both in the inertial and non-inertial rest frames. The non-relativistic limit allows a definition of both the inertial and non-inertial micro-canonical ensemble strictly in terms of the Galilei generators. Also the one-particle relativistic distribution function is defined and a new approach to the relativistic Boltzmann equation is delineated. Finally there are some comments on relativistic dissipative fluids.

math-ph↗
arXiv2012

On the Transition from the Quantum to the Classical Regime for Massive Scalar Particles: A Spatiotemporal Approach

(abridged)If the space-time is presupposed, the coordinate representation of the solutions $ψ(\vec x, t)$ of the Schroedinger equation of a quantum system containing one massive scalar particle has a {\it preferred status}. It is then possible to perform a multipolar expansion of the density matrix $ρ(\vec x, t) = |ψ(\vec x, t)|^2$ (and more generally of the Wigner function) around a space-time trajectory ${\vec x}_c(t)$ to be properly selected. A special set of solutions $ψ_{EMWF}(\vec x, t)$, named {\it Ehrenfest monopole wave functions}(EMWF), is characterized by the conditions that: (i) the quantum expectation value of the position operator coincides at any time with the searched classical trajectory, $< ψ_{EMWF} | {\hat {\vec x}} | ψ_{EMWF}> = {\vec x}_c(t)$: this is possible only when the dipole vanishes; (ii) Ehrenfest's theorem holds for the expectation values of the position and momentum operator: its application to EMWF leads then to a {\it closed Newton equation of motion for the classical trajectory, where the effective force is the Newton force plus non-Newtonian terms (of order $\hbar^2$ or higher) depending on the higher multipoles of the probability distribution $ρ$.} These results can be extended to N particle systems and to relativistic quantum mechanics. There is substantial agreement with Bohr's viewpoint: the macroscopic description of the preparation, certain intermediate steps and the detection of the final outcome of experiments involving massive particles are dominated by these 'classical {\it effective} trajectories'. In the framework of decoherence, one gets a transition from an {\it improper quantum} mixture to a {\it classical statistical} one, when both the particle and the pointer wave functions appearing in the reduced density matrix are EMWF.

quant-ph↗
arXiv2012

From Clock Synchronization to Dark Matter as a Relativistic Inertial Effect

Lecture at BOSS2011 on relativistic metrology, on clock synchronization, relativistic dynamics and non-inertial frames in Minkowski spacetime, on relativistic atomic physics, on ADM canonical tetrad gravity in asymptotically Minkowskian spacetimes, on the York canonical basis identifying the inertial (gauge) and tidal degrees of freedom of the gravitational field, on the Post-Minkowskian linearization in 3-orthogonal gauges, on the Post-Newtonian limit of matter Hamilton equations, on the possibility to interpret dark matter as a relativistic inertial effect connected with relativistic metrology (i.e. clock synchronization) in Einstein GR.

gr-qc↗
arXiv2011

A Relativistic Version of the Two-Level Atom in the Rest-Frame Instant Form of Dynamics

We define a relativistic version of the two-level atom, in which an extended atom is replaced by a point particle carrying suitable Grassmann variables for the description of the two-level structure and of the electric dipole. After studying the isolated system "atom plus the electro-magnetic field" in the electric-dipole representation as a parametrized Minkowski theory, we give its restriction to the inertial rest frame and the explicit form of the Poincaré generators. After quantization we get a two-level atom with a spin 1/2 electric dipole and the relativistic generalization of the Hamiltonians of the Rabi and Jaynes-Cummings models.

math-ph↗
arXiv2011

Dust in the York Canonical Basis of ADM Tetrad Gravity: the Problem of Vorticity

Brown's formulation of dynamical perfect fluids in Minkowski space-time is extended to ADM tetrad gravity in globally hyperbolic, asymptotically Minkowskian space-times. For the dust we get the Hamiltonian description in closed form in the York canonical basis, where we can separate the inertial gauge variables of the gravitational field in the non-Euclidean 3-spaces of global non-inertial frames from the physical tidal ones. After writing the Hamilton equations of the dust, we identify the sector of irrotational motions and the gauge fixings forcing the dust 3-spaces to coincide with the 3-spaces of the non-inertial frame. The role of the inertial gauge variable York time (the remnant of the clock synchronization gauge freedom) is emphasized. Finally the Hamiltonian Post-Minkowskian linearization is studied. The future application of this formalism will be the study of cosmological back-reaction (as an alternative to dark energy) in the York canonical basis.

gr-qc↗
arXiv2011

The Einstein-Maxwell-Particle System in the York Canonical Basis of ADM Tetrad Gravity: I) The Equations of Motion in Arbitrary Schwinger Time Gauges

We study the coupling of N charged scalar particles plus the electro-magnetic field to ADM tetrad gravity and its canonical formulation in asymptotically Minkowskian space-times without super-translations. We make the canonical transformation to the York canonical basis, where there is a separation between the {\it inertial} (gauge) variables and the {\it tidal} ones inside the gravitational field and a special role of the Eulerian observers associated to the 3+1 splitting of space-time. The Dirac Hamiltonian is weakly equal to the weak ADM energy. The Hamilton equations in Schwinger time gauges are given explicitly. In the York basis they are naturally divided in four sets: a) the contracted Bianchi identities; b) the equations for the inertial gauge variables; c) the equations for the tidal ones; d) the equations for matter. Finally we give the restriction of the Hamilton equations and of the constraints to the family of {\it non-harmonic 3-orthogonal} gauges, in which the instantaneous Riemannian 3-spaces have a diagonal 3-metric. The non-fixed inertial gauge variable ${}^3K$ (the freedom in the clock synchronization convention) gives rise to a negative kinetic term in the weak ADM energy vanishing only in the gauges with ${}^3K = 0$: is it relevant for dark energy and back-reaction? In the second paper there will be the linearization of the theory to obtain Hamiltonian post-Minkowskian gravity with asymptotic Minkowski background, non-flat instantaneous 3-spaces and no post-Newtonian expansion. This will allow to explore the inertial effects induced by the York time ${}^3K$ in non-flat 3-spaces and to check how much dark matter can be explained as an inertial aspect of Einstein's general relativity.

gr-qc↗
arXiv2011

The Einstein-Maxwell-Particle System: II) The Weak Field Approximation in the Non-Harmonic 3-Orthogonal Gauges and Hamiltonian Post-Minkowskian Gravity: the N-Body Problem and Gravitational Waves with Asymptotic Background

In this second paper we define a Post-Minkowskian (PM) weak field approximation leading to a linearization of the Hamilton equations of ADM tetrad gravity in the York canonical basis in a family of non-harmonic 3-orthogonal Schwinger time gauges. The York time ${}^3K$ (the relativistic inertial gauge variable, not existing in Newtonian gravity, parametrizing the family and connected to the freedom in clock synchronization, i.e. to the definition of the instantaneous 3-spaces) is put equal to an arbitrary numerical function. A ultraviolet cutoff on the matter allows a consistent linearization, which is shown to be the lowest order of a Hamiltonian Post-Minkowskian (HPM) expansion. We solve the constraints and the Hamilton equations for the tidal variables and we find Post-Minkowskian gravitational waves with asymptotic background (and the correct quadrupole emission formula and energy balance) propagating on dynamically determined non-Euclidean 3-spaces in these non-harmonic gauges. In conclusion we get a PM solution for the gravitational field and we identify a class of PM Einstein space-times, which will be studied in more detail in a third paper together with the PM equations of motion for the particles and their Post-Newtonian expansion (but in absence of the electro-magnetic field). Finally we make a discussion on the {\it gauge problem in general relativity} to understand which type of experimental observations may lead to a preferred choice for the inertial gauge variable ${}^3K$ in the PM space-times. In the third paper we will show that this choice is connected with the problem of dark matter.

gr-qc↗
arXiv2011

The Einstein-Maxwell-Particle System in the York Canonical Basis of ADM Tetrad Gravity: III) The Post-Minkowskian N-Body Problem, its Post-Newtonian Limit in Non-Harmonic 3-Orthogonal Gauges and Dark Matter as an Inertial Effect

We conclude the study of the Post-Minkowskian linearization of ADM tetrad gravity in the York canonical basis for asymptotically Minkowskian space-times in the family of non-harmonic 3-orthogonal gauges parametrized by the York time ${}^3K(τ, \vec σ)$ (the inertial gauge variable, not existing in Newton gravity, describing the general relativistic remnant of the freedom in clock synchronization in the definition of the instantaneous 3-spaces). As matter we consider only N scalar point particles with a Grassmann regularization of the self-energies and with a ultraviolet cutoff making possible the PM linearization and the evaluation of the PM solution for the gravitational field. We study in detail all the properties of these PM space-times emphasizing their dependence on the gauge variable ${}^3{\cal K}_{(1)} = {1\over {\triangle}}\, {}^3K_{(1)}$ (the non-local York time): Riemann and Weyl tensors, 3-spaces, time-like and null geodesics, red-shift and luminosity distance. Then we study the Post-Newtonian (PN) expansion of the PM equations of motion of the particles. We find that in the two-body case at the 0.5PN order there is a damping (or anti-damping) term depending only on ${}^3{\cal K}_{(1)}$. This open the possibility to explain dark matter in Einstein theory as a relativistic inertial effect: the determination of ${}^3{\cal K}_{(1)}$ from the masses and rotation curves of galaxies would give information on how to find a PM extension of the existing PN Celestial frame (ICRS) used as observational convention in the 4-dimensional description of stars and galaxies. Dark matter would describe the difference between the inertial and gravitational masses seen in the non-Euclidean 3-spaces, without a violation of their equality in the 4-dimensional space-time as required by the equivalence principle.

gr-qc↗
arXiv2010

Relativistic Entanglement from Relativistic Quantum Mechanics in the Rest-Frame Instant Form of Dynamics

After a review of the problems induced by the Lorentz signature of Minkowski space-time, like the need of a clock synchronization convention for the definition of 3-space and the complexity of the notion of relativistic center of mass, there is the introduction of a new formulation of relativistic quantum mechanics compatible with the theory of relativistic bound states. In it the zeroth postulate of non-relativistic quantum mechanics is not valid and the physics is described in the rest frame by a Hilbert space containing only relative variables. The non-locality of the Poincare' generators imply a kinematical non-locality and non-separability influencing the theory of relativistic entanglement and not connected with the standard quantum non-locality.

quant-ph↗
arXiv2010

Dark Matter as a Relativistic Inertial Effect in Einstein Canonical Gravity?

After the study of non-inertial frames in special relativity with emphasis on the problem of clock synchronization (i.e. of how to define 3-space), an overview is given of Einstein canonical gravity in the York canonical basis and of its Hamiltonian Post-Minkowskian (PM) linearization in 3-orthogonal gauges. It is shown that the York time (the trace of the extrinsic curvature of 3-spaces) is the inertial gauge variable describing the general relativistic remnant of the clock synchronization gauge freedom. The dark matter implied by the rotation curves of galaxies can be explained with a choice of the York time implying a PM extension of the Newtonian celestial frame ICRS.

gr-qc↗
arXiv2010

Hamiltonian ADM Gravity in Non-Harmonic Gauges with Well Defined Non-Euclidean 3-Spaces: How Much Darkness can be Explained as a Relativistic Inertial Effect?

In special and general relativity the synchronization convention of distant clocks may be simulated with a mathematical definition of global non-inertial frames (the only ones existing in general relativity due to the equivalence principle) with well-defined instantaneous 3-spaces. For asymptotically Minkowskian Einstein space-times this procedure can be used at the Hamiltonian level in the York canonical basis, where it is possible for the first time to disentangle tidal gravitational degrees of freedom from gauge inertial ones. The most important inertial effect connected with clock synchronization is the York time {}^3K(τ, σ^r), not existing in Newton gravity. This fact opens the possibility to describe some aspects of {\it darkness} as a relativistic inertial effect in Einstein gravity by means of a Post-Minkowskian reformulation of the Celestial Reference System ICRS.

gr-qc↗