arXiv subjects

David Alba

Publications and source records attributed to David Alba.

At least 19 recordsLinked to original sources

arXiv2012

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 Poincar\'e 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↗

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 Poincar\'e 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↗

arXiv2010

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 ${}^3K(\tau, \vec \sigma)$ (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

Massless Particles plus Matter in the Rest-Frame Instant Form of Dynamics

After introducing the parametrized Minkowski theory describing a positive-energy scalar massless particle, we study the rest-frame instant form of dynamics of such a particle in presence of another massive one (to avoid the front form of dynamics). Then we describe massless particles with Grassmann-valued helicity and their quantization.

hep-th↗

arXiv2010

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↗

arXiv2009

Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: I. Admissible 3+1 Splittings of Minkowski Spacetime and the Non-Inertial Rest Frames

By using the 3+1 point of view and parametrized Minkowski theories we develop the theory of {\it non-inertial} frames in Minkowski space-time. The transition from a non-inertial frame to another one is a gauge transformation connecting the respective notions of instantaneous 3-space (clock synchronization convention) and of the 3-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the non-inertial rest-frame one. We show that every isolated system can be described as an external decoupled non-covariant canonical center of mass (described by frozen Jacobi data) carrying a pole-dipole structure: the invariant mass and an effective spin. Moreover we identify the constraints eliminating the internal 3-center of mass inside the instantaneous 3-spaces. In the case of the isolated system of positive-energy scalar particles with Grassmann-valued electric charges plus the electro-magnetic field we obtain both Maxwell equations and their Hamiltonian description in non-inertial frames. Then by means of a non-covariant decomposition we define the non-inertial radiation gauge and we find the form of the non-covariant Coulomb potential. We identify the coordinate-dependent relativistic inertial potentials and we show that they have the correct Newtonian limit. In the second paper we will study properties of Maxwell equations in non-inertial frames like the wrap-up effect and the Faraday rotation in astrophysics. Also the 3+1 description without coordinate-singularities of the rotating disk and the Sagnac effect will be given, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system.

gr-qc↗

arXiv2009

Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime: II. Applications: Rotating Frames, Sagnac Effect, Faraday Rotation, Wrap-up Effect

We apply the theory of non-inertial frames in Minkowski space-time, developed in the previous paper, to various relevant physical systems. We give the 3+1 description without coordinate-singularities of the rotating disk and the Sagnac effect, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system. Then we study properties of Maxwell equations in non-inertial frames like the wrap-up effect and the Faraday rotation in astrophysics.

gr-qc↗

arXiv2009

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↗

arXiv2009

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

A new formulation of relativistic quantum mechanics is proposed in the framework of the rest-frame instant form of dynamics with its instantaneous Wigner 3-spaces and with its description of the particle world-lines by means of derived non-canonical predictive coordinates. In it we quantize the frozen Jacobi data of the non-local 4-center of mass and the Wigner-covariant relative variables in an abstract (frame-independent) internal space whose existence is implied by Wigner-covariance. The formalism takes care of the properties of both relativistic bound states and scattering ones. There is a natural solution to the \textit{relativistic localization problem}. The non-relativistic limit leads to standard quantum mechanics but with a frozen Hamilton-Jacobi description of the center of mass. Due to the \textit{non-locality} of the Poincar\'e generators the resulting theory of relativistic entanglement is both \textit{kinematically non-local and spatially non-separable}: these properties, absent in the non-relativistic limit, throw a different light on the interpretation of the non-relativistic quantum non-locality and of its impact on foundational problems.

hep-th↗

arXiv2008

Charged Particles and the Electro-Magnetic Field in Non-Inertial Frames of Minkowski Spacetime

By using the 3+1 point of view and parametrized Minkowski theories we develop the theory of {\it non-inertial} frames in Minkowski space-time. The transition from a non-inertial frame to another one is a gauge transformation connecting the respective notions of instantaneous 3-space (clock synchronization convention) and of the 3-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the non-inertial rest-frame one. We show that every isolated system can be described as an external decoupled non-covariant canonical center of mass (described by frozen Jacobi data) carrying a pole-dipole structure: the invariant mass and an effective spin. Moreover we identify the constraints eliminating the internal 3-center of mass inside the instantaneous 3-spaces. In the case of the isolated system of positive-energy scalar particles with Grassmann-valued electric charges plus the electro-magnetic field we obtain both Maxwell equations and their Hamiltonian description in non-inertial frames. Then by means of a non-covariant decomposition we define the non-inertial radiation gauge and we find the form of the non-covariant Coulomb potential. We identify the coordinate-dependent relativistic inertial potentials and we show that they have the correct Newtonian limit. Then we study properties of Maxwell equations in non-inertial frames like the wrap-up effect and the Faraday rotation in astrophysics. Also the 3+1 description without coordinate-singularities of the rotating disk and the Sagnac effect are given, with added comments on pulsar magnetosphere and on a relativistic extension of the Earth-fixed coordinate system.

gr-qc↗

arXiv2008

Towards Relativistic Atomic Physics. II. Collective and Relative Relativistic Variables for a System of Charged Particles plus the Electro-Magnetic Field

In this second paper we complete the classical description of an isolated system of "charged positive-energy particles, with Grassmann-valued electric charges and mutual Coulomb interaction, plus a transverse electro-magnetic field" in the rest-frame instant form of dynamics. In particular we show how to determine a collective variable associated with the internal 3-center of mass on the instantaneous 3-spaces, to be eliminated with the constraints ${\vec {\cal K}}_{(int)} \approx 0$. Here ${\vec {\cal K}}_{(int)}$ is the Lorentz boost generator in the unfaithful internal realization of the Poincare' group and its vanishing is the gauge fixing to the rest-frame conditions ${\vec {\cal P}}_{(int)} \approx 0$. We show how to find this collective variable for the following isolated systems: a) charged particles with a Coulomb plus Darwin mutual interaction; b) transverse radiation field; c) charged particles with a mutual Coulomb interaction plus a transverse electro-magnetic field. Then we define the Dixon multipolar expansion for the open particle subsystem. We also define the relativistic electric dipole approximation of atomic physics in the rest-frame instant form and we find the a possible relativistic generalization of the electric dipole representation.

hep-th↗

arXiv2008

Towards Relativistic Atomic Physics. I. The Rest-Frame Instant Form of Dynamics and a Canonical Transformation for a System of Charged Particles plus the Electro-Magnetic Field

A complete exposition of the rest-frame instant form of dynamics for arbitrary isolated systems (particles, fields, strings, fluids)admitting a Lagrangian description is given. The starting point is the parametrized Minkowski theory describing the system in arbitrary admissible non-inertial frames in Minkowski space-time, which allows one to define the energy-momentum tensor of the system and to show the independence of the description from the clock synchronization convention and from the choice of the 3-coordinates. In the inertial rest frame the isolated system is seen as a decoupled non-covariant canonical external center of mass carrying a pole-dipole structure (the invariant mass $M$ and the rest spin ${\vec {\bar S}}$ of the system) and an external realization of the Poincare' group. Then an isolated system of positive-energy charged scalar articles plus an arbitrary electro-magnetic field in the radiation gauge is investigated as a classical background for defining relativistic atomic physics. The electric charges of the particles are Grassmann-valued to regularize the self-energies. The rest-frame conditions and their gauge-fixings (needed for the elimination of the internal 3-center of mass) are explicitly given. It is shown that there is a canonical transformation which allows one to describe the isolated system as a set of Coulomb-dressed charged particles interacting through a Coulomb plus Darwin potential plus a free transverse radiation field: these two subsystems are not mutually interacting and are interconnected only by the rest-frame conditions and the elimination of the internal 3-center of mass. Therefore in this framework with a fixed number of particles there is a way out from the Haag theorem,at least at the classical level.

math-ph↗

arXiv2007

The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field

A new parametrization of the 3-metric allows to find explicitly a York map in canonical ADM tetrad gravity, the two pairs of physical tidal degrees of freedom and 14 gauge variables. These gauge quantities (generalized inertial effects) are all configurational except the trace ${}^3K(τ,\vec σ)$ of the extrinsic curvature of the instantaneous 3-spaces $Σ_τ$ (clock synchronization convention) of a non-inertial frame. The Dirac hamiltonian is the sum of the weak ADM energy $E_{ADM} = \int d^3σ{\cal E}_{ADM}(τ,\vec σ)$ (whose density is coordinate-dependent due to the inertial potentials) and of the first-class constraints. Then: i) The explicit form of the Hamilton equations for the two tidal degrees of freedom in an arbitrary gauge: a deterministic evolution can be defined only in a completely fixed gauge, i.e. in a non-inertial frame with its pattern of inertial forces. ii) A general solution of the super-momentum constraints, which shows the existence of a generalized Gribov ambiguity associated to the 3-diffeomorphism gauge group. It influences: a) the explicit form of the weak ADM energy and of the super-momentum constraint; b) the determination of the shift functions and then of the lapse one. iii) The dependence of the Hamilton equations for the two pairs of dynamical gravitational degrees of freedom (the generalized tidal effects) and for the matter, written in a completely fixed 3-orthogonal Schwinger time gauge, upon the gauge variable ${}^3K(τ,\vec σ)$, determining the convention of clock synchronization. Therefore it should be possible (for instance in the weak field limit but with relativistic motion) to try to check whether in Einstein's theory the {\it dark matter} is a gauge relativistic inertial effect induced by ${}^3K(τ,\vec σ)$.

gr-qc↗

arXiv2006

Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction

After a short review of the history and problems of relativistic Hamiltonian mechanics with action-at-a-distance inter-particle potentials, we study isolated two-body systems in the rest-frame instant form of dynamics. We give explicit expressions of the relevant relativistic notions of center of mass, we determine the generators of the Poincare' group in presence of interactions and we show how to do the reconstruction of particles' orbits from the relative motion and the canonical non-covariant center of mass. In the case of a simple Coulomb-like potential model, it is possible to integrate explicitly the relative motion and show the two dynamical trajectories.

hep-th↗

arXiv2006

Generalized Radar 4-Coordinates and Equal-Time Cauchy Surfaces for Arbitrary Accelerated Observers

All existing 4-coordinate systems centered on the world-line of an accelerated observer are only locally defined like it happens for Fermi coordinates both in special and general relativity. As a consequence, it is not known how non-inertial observers can build {\it equal-time surfaces} which a) correspond to a conventional observer-dependent definition of synchronization of distant clocks; b) are good Cauchy surfaces for Maxwell equations. Another type of coordinate singularities are those connected to the relativistic rotating coordinate systems (the rotating disk).We show that the use of Hamiltonian methods based on 3+1 splittings of space-time allows to define as many observer-dependent globally defined radar 4-coordinate systems as nice foliations of space-time with space-like hyper-surfaces admissible according to M$ø$ller (for instance only differentially rotating relativistic coordinate system are allowed). All these conventional notions of an {\it instantaneous 3-space} for an arbitrary observer can be empirically defined by introducing generalizations of Einstein ${1\over 2}$ convention for clock synchronization in inertial frames. Each admissible 3+1 splitting corresponds to a non-rigid non-inertial frame centered on the observer. When there is a Lagrangian description of an isolated relativistic system, its reformulation as a parametrized Minkowski theory allows to show that all the admissible synchronization conventions are {\it gauge equivalent}, as it also happens in canonical metric and tetrad gravity, where, however, the chrono-geometrical structure of space-time is dynamically determined.

gr-qc↗

arXiv2005

Quantum Mechanics in Non-Inertial Frames with a Multi-Temporal Quantization Scheme: II) Non-Relativistic Particles

The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid non-inertial frames, containing the standard rigidly linear accelereted and rotating ones, is given in the framework of parametrized Galilei theories. Then the multi-temporal quantization, in which the gauge variables, describing the non-inertial effects, are not quantized but considered as c-number generalized times, is applied to non relativistic particles. It is shown that with a suitable ordering there is unitary evolution in all times and that, after the separation of center of mass, it is still possible to identify the inertial bound states. The few existing results of quantization in rigid non-inertial frames are recovered as special cases.

hep-th↗

arXiv2005

Quantum Mechanics in Non'Inertial Frames with a Multi'Temporal Quantization Scheme: I) Relativistic Particles

We introduce a family of relativistic non-rigid non-inertial frames as a gauge fixing of the description of N positive energy particles in the framework of parametrized Minkowski theories. Then we define a multi-temporal quantization scheme in which the particles are quantized, but not the gauge variables describing the non-inertial frames: {\it they are considered as c-number generalized times}. We study the coupled Schroedinger-like equations produced by the first class constraints and we show that there is {\it a physical scalar product independent both from time and generalized times and a unitary evolution}. Since a path in the space of the generalized times defines a non-rigid non-inertial frame, we can find the associated self-adjoint effective Hamiltonian $\hat{H}_{ni}$ for the non-inertial evolution: it differs from the inertial energy operator for the presence of inertial potentials and turns out to be {\it frame-dependent} like the energy density in general relativity. After a separation of the relativistic center of mass from the relative variables by means of a recently developed relativistic kinematics, inside $\hat{H}_{ni}$ we can identify the self-adjoint relative energy operator (the invariant mass) ${\hat{\cal M}}$ corresponding to the inertial energy and producing the same levels for the spectra of atoms as in inertial frames. Instead the (in general time-dependent) effective Hamiltonian is responsible for the interferometric effects signalling the non-inertiality of the frame but is not interpretable as an energy like in the case of time-dependent c-number external electro-magnetic fields.

hep-th↗