scholarly journals THE REST-FRAME INSTANT FORM OF RELATIVISTIC PERFECT FLUIDS WITH EQUATION OF STATE ρ=ρ(n, s) AND OF NONDISSIPATIVE ELASTIC MATERIALS

2000 ◽  
Vol 15 (31) ◽  
pp. 4943-5015 ◽  
Author(s):  
LUCA LUSANNA ◽  
DOBROMILA NOWAK-SZCZEPANIAK
Keyword(s):  
Equation Of State ◽  
Rest Frame ◽  
Lagrangian Coordinates ◽  
Elastic Materials ◽  
Instant Form ◽  
Perfect Fluids ◽  
Minkowski Space Time ◽  
Spacelike Hypersurfaces ◽  
Photon Gas ◽  
Tetrad Gravity

For perfect fluids with equation of state ρ=ρ(n, s), Brown1 gave an action principle depending only on their Lagrange coordinates αi(x) without Clebsch potentials. After a reformulation on arbitrary spacelike hypersurfaces in Minkowski space–time, the Wigner-covariant rest-frame instant form of these perfect fluids is given. Their Hamiltonian invariant mass can be given in closed form for the dust and the photon gas. The action for the coupling to tetrad gravity is given. Dixon's multipoles for the perfect fluids are studied on the rest-frame Wigner hyperplane. It is also shown that the same formalism can be applied to nondissipative relativistic elastic materials described in terms of Lagrangian coordinates.

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

2015 ◽  
Vol 12 (07) ◽  
pp. 1550076 ◽  
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.

scholarly journals GENERALIZED EULERIAN COORDINATES FOR RELATIVISTIC FLUIDS: HAMILTONIAN REST-FRAME INSTANT FORM, RELATIVE VARIABLES, ROTATIONAL KINEMATICS

2004 ◽  
Vol 19 (17n18) ◽  
pp. 3025-3082 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Rest Frame ◽  
Deformable Body ◽  
Center Of Mass ◽  
Relativistic Fluids ◽  
Instant Form ◽  
Perfect Fluids ◽  
Rotational Kinematics ◽  
Eulerian Coordinates ◽  
New Formulation

We study the rest-frame instant form of a new formulation of relativistic perfect fluids in terms of new generalized Eulerian configuration coordinates. After the separation of the relativistic center of mass from the relative variables on the Wigner hyper-planes, we define orientational and shape variables for the fluid, viewed as a relativistic extended deformable body, by introducing dynamical body frames. Finally we define Dixon's multipoles for the fluid.

scholarly journals DIRAC FIELDS ON SPACELIKE HYPERSURFACES, THEIR REST-FRAME DESCRIPTION AND DIRAC OBSERVABLES

1999 ◽  
Vol 14 (12) ◽  
pp. 1877-1910 ◽  
Author(s):  
FRANCESCO BIGAZZI ◽  
LUCA LUSANNA
Keyword(s):  
Electromagnetic Field ◽  
Minkowski Space ◽  
Electric Current ◽  
Spin Structure ◽  
Rest Frame ◽  
Space Time ◽  
Spinning Particles ◽  
Dirac Fields ◽  
Minkowski Space Time ◽  
Spacelike Hypersurfaces

Grassmann-valued Dirac fields together with the electromagnetic field (the pseudo-classical basis of QED) are reformulated on spacelike hypersurfaces in Minkowski space–time and then restricted to Wigner hyperplanes to get their description in the rest-frame Wigner-covariant instant form of dynamics. The canonical reduction to the Wigner-covariant Coulomb gauge is done in the rest frame. It is shown, on the basis of a geometric inconsistency, that the description of fermions is incomplete, because there is no bosonic carrier of the spin structure describing the trajectory of the electric current in Minkowski space–time, as it was already emphasized in connection with the first quantization of spinning particles in a previous paper.

scholarly journals Review: Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge

2002 ◽  
Vol 34 (6) ◽  
pp. 877-1033 ◽  
Author(s):  
Roberto De Pietri ◽  
Luca Lusanna ◽  
Luca Martucci ◽  
Stefano Russo
Keyword(s):  
Rest Frame ◽  
Instant Form ◽  
Tetrad Gravity

scholarly journals A CANONICAL DECOMPOSITION IN COLLECTIVE AND RELATIVE VARIABLES OF A KLEIN–GORDON FIELD IN THE REST-FRAME WIGNER-COVARIANT INSTANT FORM

2000 ◽  
Vol 15 (18) ◽  
pp. 2821-2916 ◽  
Author(s):  
LUCA LUSANNA ◽  
MASSIMO MATERASSI
Keyword(s):  
Rest Frame ◽  
Center Of Mass ◽  
Momentum Tensor ◽  
Field Configuration ◽  
Canonical Decomposition ◽  
Electromagnetic Current ◽  
Instant Form ◽  
Spacelike Hypersurfaces ◽  
Klein Gordon ◽  
Relative Variable

The canonical decomposition of a real Klein–Gordon field in collective and relative variables proposed by Longhi and Materassi is reformulated on spacelike hypersurfaces. This allows us to obtain the complete canonical reduction of the system on Wigner hyperplanes, namely in the rest-frame Wigner-covariant instant form of dynamics. From the study of Dixon's multipoles for the energy–momentum tensor on the Wigner hyperplanes we derive the definition of the canonical center-of-mass variable for a Klein–Gordon field configuration: it turns out that the Longhi–Materassi global variable should be interpreted as a center of phase of the field configuration. A detailed study of the kinematical "external" and "internal" properties of the field configuration on the Wigner hyperplanes is done. The construction is then extended to charged Klein–Gordon fields: the centers of phase of the two real components can be combined to define a global center of phase and a collective relative variable describing the action–reaction between the two Feshbach–Villars components of the field with definite sign of energy and charge. The Dixon multipoles for both the energy–momentum and the electromagnetic current are given. Also the coupling of the Klein–Gordon field to scalar relativistic particles is studied and it is shown that in the reduced phase space, besides the particle and field relative variables, there is also a collective relative variable describing the relative motion of the particle subsystem with respect to the field one.

The motion of the particles volume corresponding to invariant solution of rank 2 submodel of hydrodynamic type

2016 ◽  
Vol 11 (2) ◽  
pp. 205-209
Author(s):  
D.T. Siraeva
Keyword(s):  
Equation Of State ◽  
Invariant Solution ◽  
Hydrodynamic Type ◽  
Lagrangian Coordinates ◽  
Hydrodynamic Equations ◽  
Rank 2 ◽  
Invariant Submodel ◽  
Entropy Functions

Invariant submodel of rank 2 on the subalgebra consisting of the sum of transfers for hydrodynamic equations with the equation of state in the form of pressure as the sum of density and entropy functions, is presented. In terms of the Lagrangian coordinates from condition of nonhyperbolic submodel solutions depending on the four essential constants are obtained. For simplicity, we consider the solution depending on two constants. The trajectory of particles motion, the motion of parallelepiped of the same particles are studied using the Maple.

scholarly journals SPINNING PARTICLES ON SPACELIKE HYPERSURFACES AND THEIR REST FRAME DESCRIPTION

1999 ◽  
Vol 14 (09) ◽  
pp. 1429-1484 ◽  
Author(s):  
FRANCESCO BIGAZZI ◽  
LUCA LUSANNA
Keyword(s):  
Spin Structure ◽  
Rest Frame ◽  
Negative Energy ◽  
Nonrelativistic Limit ◽  
Critical Discussion ◽  
Positive Energy ◽  
Spinning Particle ◽  
Spinning Particles ◽  
Spacelike Hypersurfaces ◽  
Energy Formula

A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. It is the pseudoclassical basis of the positive energy [Formula: see text] [or negative energy [Formula: see text]] part of the [Formula: see text] solutions of the Dirac equation. The study of the isolated system of N such spinning charged particles plus the electromagnetic field leads to their description in the rest frame Wigner-covariant instant form of dynamics on the Wigner hyperplanes orthogonal to the total four-momentum of the isolated system (when it is timelike). We find that on such hyperplanes these spinning particles have a nonminimal coupling only of the type "spin–magnetic field," like the nonrelativistic Pauli particles to which they tend in the nonrelativistic limit. The Lienard–Wiechert potentials associated with these charged spinning particles are found. Then, a comment is made on how to quantize the spinning particles respecting their fibered structure describing the spin structure.

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