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 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.

scholarly journals CHARGED PARTICLES AND THE ELECTRO-MAGNETIC FIELD IN NONINERTIAL FRAMES OF MINKOWSKI SPACE-TIME I: ADMISSIBLE 3 + 1 SPLITTINGS OF MINKOWSKI SPACE-TIME AND THE NONINERTIAL REST FRAMES

2010 ◽  
Vol 07 (01) ◽  
pp. 33-93 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Magnetic Field ◽  
Minkowski Space ◽  
Maxwell Equations ◽  
Rest Frame ◽  
Center Of Mass ◽  
Space Time ◽  
Positive Energy ◽  
Electro Magnetic Field ◽  
Minkowski Space Time ◽  
Electro Magnetic

By using the 3 + 1 point of view and parametrized Minkowski theories we develop the theory of noninertial frames in Minkowski space-time. The transition from a noninertial frame to another one is a gauge transformation connecting the respective notions of instantaneous three-space (clock synchronization convention) and of the three-coordinates inside them. As a particular case we get the extension of the inertial rest-frame instant form of dynamics to the noninertial rest-frame one. We show that every isolated system can be described as an external decoupled noncovariant 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 three-center of mass inside the instantaneous three-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 noninertial frames. Then by means of a noncovariant decomposition we define the noninertial radiation gauge and we find the form of the noncovariant 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 noninertial 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.

On the dynamics of spinning particle in nonlinear relativity

2021 ◽  
Vol 36 (06) ◽  
pp. 2150048
Author(s):  
H. Guergouri ◽  
T. Foughali
Keyword(s):  
Minkowski Space ◽  
Equations Of Motion ◽  
Space Time ◽  
Conformally Flat ◽  
De Sitter ◽  
Spinning Particle ◽  
Spinning Particles ◽  
Minkowski Space Time ◽  
Conformally Flat Metric ◽  
Uniform Electromagnetic Field

In order to study the dynamics of spinning particles in R-Minkowski space–time, first we have used the Bhabha–Corben model to describe how a spinning particle behave in a uniform electromagnetic field. Then, to extend the Mathisson–Papapetrou equations to R-Minkowski space–time, that correspond to de Sitter space–time given by a conformally flat metric, it was necessary to determine the Killing vectors, which allowed us to find the equations of motion that describe the dynamics of spinning particles.

On generalized partially null Mannheim curves in Minkowski space-time

2016 ◽  
Vol 46 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Emilija Nešović ◽  
Milica Grbović
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time

scholarly journals A MAXWELL-LIKE FORMULATION OF GRAVITATIONAL THEORY IN MINKOWSKI SPACE–TIME

2007 ◽  
Vol 16 (06) ◽  
pp. 1027-1041 ◽  
Author(s):  
EDUARDO A. NOTTE-CUELLO ◽  
WALDYR A. RODRIGUES
Keyword(s):  
Gravitational Field ◽  
Minkowski Space ◽  
Gravitational Theory ◽  
Space Time ◽  
Lorentzian Geometry ◽  
Field Equations ◽  
Yang Mills ◽  
Minkowski Space Time ◽  
Clifford Bundle ◽  
Gauge Fixing

Using the Clifford bundle formalism, a Lagrangian theory of the Yang–Mills type (with a gauge fixing term and an auto interacting term) for the gravitational field in Minkowski space–time is presented. It is shown how two simple hypotheses permit the interpretation of the formalism in terms of effective Lorentzian or teleparallel geometries. In the case of a Lorentzian geometry interpretation of the theory, the field equations are shown to be equivalent to Einstein's equations.

scholarly journals CHARGED PARTICLES AND THE ELECTRO-MAGNETIC FIELD IN NONINERTIAL FRAMES OF MINKOWSKI SPACE–TIME II: "APPLICATIONS: ROTATING FRAMES, SAGNAC EFFECT, FARADAY ROTATION, WRAP-UP EFFECT"

2010 ◽  
Vol 07 (02) ◽  
pp. 185-213 ◽  
Author(s):  
DAVID ALBA ◽  
LUCA LUSANNA
Keyword(s):  
Minkowski Space ◽  
Faraday Rotation ◽  
Rotating Disk ◽  
Space Time ◽  
Sagnac Effect ◽  
Electro Magnetic Field ◽  
Minkowski Space Time ◽  
Relativistic Extension ◽  
Rotating Frames ◽  
Electro Magnetic

We apply the theory of noninertial 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 noninertial frames like the wrap-up effect and the Faraday rotation in astrophysics.

scholarly journals Nature itself in a mirror space–time

2015 ◽  
Vol 93 (10) ◽  
pp. 1005-1008 ◽  
Author(s):  
Rasulkhozha S. Sharafiddinov
Keyword(s):  
Dirac Equation ◽  
Minkowski Space ◽  
Space Time ◽  
Point Of View ◽  
Classical Solutions ◽  
Left Handed ◽  
Minkowski Space Time ◽  
Energy And Momentum ◽  
The Right ◽  
Structure Of Matter

The unity of the structure of matter fields with flavor symmetry laws involves that the left-handed neutrino in the field of emission can be converted into a right-handed one and vice versa. These transitions together with classical solutions of the Dirac equation testify in favor of the unidenticality of masses, energies, and momenta of neutrinos of the different components. If we recognize such a difference in masses, energies, and momenta, accepting its ideas about that the left-handed neutrino and the right-handed antineutrino refer to long-lived leptons, and the right-handed neutrino and the left-handed antineutrino are short-lived fermions, we would follow the mathematical logic of the Dirac equation in the presence of the flavor symmetrical mass, energy, and momentum matrices. From their point of view, nature itself separates Minkowski space into left and right spaces concerning a certain middle dynamical line. Thereby, it characterizes any Dirac particle both by left and by right space–time coordinates. It is not excluded therefore that whatever the main purposes each of earlier experiments about sterile neutrinos, namely, about right-handed short-lived neutrinos may serve as the source of facts confirming the existence of a mirror Minkowski space–time.

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