Canonical ADM tetrad gravity: From metrological inertial gauge variables to dynamical tidal Dirac observables

In this updated review of canonical ADM tetrad gravity in a family of globally hyperbolic asymptotically Minkowskian space-times without super-translations I show which is the status-of-the-art in the search of a canonical basis adapted to the first-class Dirac constraints and of the Dirac observables of general relativity (GR) describing the tidal degrees of freedom of the gravitational field. In these space-times the asymptotic ADM Poincaré group replaces the Poincaré group of particle physics, there is a York canonical basis diagonalizing the York–Lichnerowicz approach and a post-Minkowskian linearization is possible with the associated description of gravitational waves in the family of non-harmonic 3-orthogonal Schwinger time gauges. Moreover I show that every fixation of the inertial gauge variables (i.e. the choice of a non-inertial frame) of every generally covariant formulation of GR is equivalent to a set of conventions for the metrology of the space-time (like the GPS ones near the Earth): for instance the freedom in clock synchronization is described by the inertial gauge variable York time (the trace of the extrinsic curvature of the instantaneous 3-spaces). This inertial gauge freedom and the non-Euclidean nature of the instantaneous 3-spaces required by the equivalence principle are connected with the dark side of the universe and could explain the presence of dark matter or at least part of it by means of the adoption of suitable metrical conventions for the ICRS celestial reference system. Also some comments on a canonical quantization of GR coherent with this viewpoint are done.

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The Einstein–Maxwell-particle system in the York canonical basis of ADM tetrad gravity. Part 3. The post-minkowskian N-body problem, its post-newtonian limit in nonharmonic 3-orthogonal gauges and dark matter as an inertial effect 1This paper is one of three companion papers published in the same issue of Can. J. Phys.

Canadian Journal of Physics ◽

10.1139/p11-102 ◽

2012 ◽

Vol 90 (11) ◽

pp. 1131-1178 ◽

Cited By ~ 11

Author(s):

David Alba ◽

Luca Lusanna

Keyword(s):

Dark Matter ◽

Particle System ◽

Clock Synchronization ◽

Dimensional Space ◽

Canonical Basis ◽

York Time ◽

Space Time ◽

Inertial Effect ◽

N Body Problem ◽

Tetrad Gravity

We conclude the study of the post-minkowskian (PM) linearization of ADM tetrad gravity in the York canonical basis for asymptotically minkowskian space–times in the family of nonharmonic 3-orthogonal gauges parametrized by the York time 3K(τ, s) (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 shape of the instantaneous 3-spaces as 3-submanifolds of space–time). As matter we consider only N scalar point particles with a Grassmann regularization of the self-energies and with an 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 3K(1) = (1/Δ)3K(1) (the nonlocal 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 antidamping) term depending only on 3K(1). This opens the possibility of explaining dark matter in Einstein theory as a relativistic inertial effect: the determination of 3K(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 used as an 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.

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Dust in the York canonical basis of ADM tetrad gravity: The problem of vorticity

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887815500760 ◽

2015 ◽

Vol 12 (07) ◽

pp. 1550076 ◽

Cited By ~ 4

Author(s):

David Alba ◽

Luca Lusanna

Keyword(s):

Clock Synchronization ◽

Canonical Basis ◽

York Time ◽

Back Reaction ◽

Hamiltonian Description ◽

Perfect Fluids ◽

Minkowski Space Time ◽

Hamilton Equations ◽

Inertial Frames ◽

Tetrad Gravity

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. This formalism is required when one wants to study the Hamiltonian version of cosmological models (for instance back-reaction as an alternative to dark energy) in the York canonical basis.

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SOME FIELD-THEORETICAL ASPECTS OF TWO TYPES OF THE POINCARÉ GROUP REPRESENTATIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x14500201 ◽

2014 ◽

Vol 29 (02) ◽

pp. 1450020

Author(s):

L. M. SLAD

Keyword(s):

Particle Physics ◽

Irreducible Representations ◽

Poincaré Group ◽

Group Representations ◽

Standard Type ◽

Poincare Group ◽

Relativistic Description ◽

Class Fields ◽

Infinite Component ◽

Hadronic States

The capabilities of some approaches to the relativistic description of hadronic states with any rest spin are analysed. The key feature in the Wigner's construction of irreducible representations of the Poincaré group, which makes this construction fruitless in particle physics, is picked out. A realization of unitary irreducible representations of the Poincaré group of the standard type, which has not yet been considered, is discussed. The viability of the description of hadrons by the Poincaré group representations of the standard type in the space of the infinite-component ISFIR-class fields is pointed out.

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A COVARIANT FORMULATION OF CLASSICAL SPINNING PARTICLE

Modern Physics Letters A ◽

10.1142/s0217732394000599 ◽

1994 ◽

Vol 09 (09) ◽

pp. 775-784 ◽

Cited By ~ 1

Author(s):

JIN-HO CHO ◽

JAE-KWAN KIM ◽

SEUNGJOON HYUN

Keyword(s):

Rest Frame ◽

Spin Component ◽

Covariant Formulation ◽

Poincaré Group ◽

Spinning Particle ◽

Poincare Group ◽

Fixed Frame

Covariantly we reformulate the description of a spinning particle in terms of the Poincaré group. We also construct a Lagrangian which entails all possible constraints explicitly; all constraints can be obtained just from the Lagrangian. Furthermore, in this covariant reformulation, the Lorentz element is to be considered to evolve the momentum or spin component from an arbitrary fixed frame and not just from the particle rest frame. Our system which is different from the usual formulation is directly comparable with the pseudoclassical formulation. We get a peculiar symmetry which resembles the supersymmetry of the pseudoclassical formulation.

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WIGNER THEORY OF THE NAMBU STRING: (I) THE OPEN STRING

International Journal of Modern Physics A ◽

10.1142/s0217751x92000740 ◽

1992 ◽

Vol 07 (08) ◽

pp. 1705-1754 ◽

Cited By ~ 4

Author(s):

F. COLOMO ◽

L. LUSANNA

Keyword(s):

Harmonic Analysis ◽

Center Of Mass ◽

Canonical Basis ◽

Virasoro Algebra ◽

Open String ◽

Poincaré Group ◽

Nonlinear Realization ◽

Poincare Group ◽

Gauge Sector ◽

Canonical Variables

A set of relative variables for the open string with P2>0 is found, which has Wigner covariance properties. It allows one to obtain global Lorentz-invariant abelianizations of the constraints, and then to find global Lorentz-invariant canonically conjugated gauge variables. By means of the multitemporal approach a noncanonical redundant set of Dirac observables is defined; these transform as spin-1 Wigner vectors and satisfy constraints of the type of σ models. The generalized Virasoro algebra, except for L0, lives entirely in the gauge sector of the theory. The original canonical variables are expressed by means of the resulting generalized harmonic analysis in terms of these observables, and of the noncovariant center-of-mass ones. Quantization is not done, because a canonical basis of observables is still lacking, but the program to find them is expounded: instead of making a reduction from O (D–1)(P) to O (D–2), which would give a nonlinear realization of the Poincaré group like in the noncovariant approach, one has to find a Thomas-spin-adapted basis of observables which are Lorentz-invariant (except for three of them).

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POINCARE INVARIANCE IN TEMPORAL GAUGE CANONICAL QUANTIZATION AND θ VACUA

International Journal of Modern Physics A ◽

10.1142/s0217751x94001114 ◽

1994 ◽

Vol 09 (16) ◽

pp. 2741-2753 ◽

Cited By ~ 2

Author(s):

HISASHI KIKUCHI

Keyword(s):

Hilbert Space ◽

Angular Momentum ◽

Unitary Transformation ◽

Canonical Quantization ◽

Momentum Tensor ◽

Poincaré Group ◽

Momentum Vector ◽

Poincare Group ◽

Temporal Gauge ◽

Poincaré Algebra

The Poincaré invariance in the temporal gauge canonical quantization of QCD is shown manifestly by verifying that the energy-momentum vector and angular momentum tensor satisfy the Poincaré algebra in the physical Hilbert space. Two different values of θ for the θ term in the QCD Lagrangian lead to different representations of the Poincaré group, which are, however, connected by a unitary transformation. Thus it is important to further restrict the physical Hilbert space to evaluate the θ dependence in temporal gauge canonical quantization.

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