1,721,133 research outputs found
Classical characters of spinor fields in torsion gravity
No full textWe consider the problem of having relativistic quantum mechanics reformulated with hydrodynamic variables, and specifically the problem of deriving the Mathisson-Papapetrou-Dixon equations (describing the motion of a massive spinning body moving in a gravitational field) from the Dirac equation. The problem will be answered on a general manifold with torsion and gravity. We will demonstrate that when plane waves are considered the MPD equations describe the general relativistic wave-particle duality with torsion (Guedes and Pop & lstrok;awski 2024 Class. Quantum Grav. 41 065011), but we will also see that in such a form the MPD equations become trivial
On the Geometry of the Dirac Matter with the Fermionic Potentials and its Quantum Properties
No full textWe consider the torsional completion of gravity with electrodynamics for Dirac matter fields; we will see that these Dirac matter field equations will develop torsionally-induced non-linear interactions, which can be manipulated in order to be rearranged in the form of self-fermion potentials of a specific structure: we will see that this structure is formally equivalent to the one arising from quantum properties
Least-order torsion-gravity for fermion fields, and the nonlinear potentials in the standard models
No full textWe will consider the least-order torsional completion of gravity for a spacetime filled with fermionic Dirac matter fields, and we study the effects of the background-induced nonlinear potentials for the matter field themselves, in terms of their effects for both standard models of physics: from the one of cosmology to that of particles, we will discuss the mechanisms of generation of the cosmological constant and particles masses as well as the phenomenology of leptonic weak-like forces and neutrino oscillations, the problem of zero-point energy, how there can be neutral massive fields as candidates for dark matter, and the avoidance of gravitationally-induced singularity formation; we will show the way in which all these different effects can nevertheless be altogether described in terms of just a single model, which will be discussed in the beginning
Geometry of spinors: doubly-chiral plane-wave expansion
Full text linkWe employ the polar re-formulation of spinor fields to see in a new light
their classification into regular and singular spinors, these last also called
flag-dipoles, further splitting into the sub-classes of dipoles and flagpoles:
in particular, we will study the conditions under which flagpoles may be
solutions of the Dirac field equations. We argue for an enlargement of the
plane-wave expansion.Comment: 10 page
Torsionally-gravitating charged matter fields and quanta
No full textIn the present article we shall consider the torsional completion of a gravitational background that is filled with electrodynamically interacting material fields, taken to be of fermionic type, eventually deriving properties like the impossibility of singularities and the possibility of confinement, both necessary for a correct quantum description
Euler and Pontryagin currents of Dirac operator
Full text linkOn differential manifolds with spinor structure, it is possible to express
the Euler and Pontryagin currents in terms of tensors that also appear as
source in the Dirac equation. It is hence possible to tie concepts rooted in
geometry and topology to dynamical characters of quantum matter. Examples in
various low-dimensional systems are provided to ease visualization.Comment: 9 page
ON GEOMETRIC RELATIVISTIC FOUNDATIONS OF MATTER FIELD EQUATIONS AND PLANE WAVE SOLUTIONS
No full textIn this paper, we start from the geometric relativistic foundations to define the basis upon which matter field theories are built, and their wave solutions are investigated, finding that they display repulsive interactions able to reproduce the exclusion principle in terms of its effects in a dynamical way, then discussing possible consequences and problems
A Discussion on Dirac Field Theory, No-Go Theorems and Renormalizability
No full textWe study Dirac field equations coupled to electrodynamics with metric and torsion fields: we discuss how special spinorial solutions are incompatible with torsion; eventually these results will be used to sketch a discussion on the problem of renormalizability of point-like particles
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