Related papers: Hestenes' Tetrad and Spin Connections

The Finslerian curvature is introduced in the three-dimensional isospin space, suggesting that the isospin-pion field transforms according to non-linear Finslerian invariance transformations. The fundamental non-linear realization is…

We study the initial value problem of the Einstein-Dirac system, and show the stability of the Minkowski solution in the massless case with the use of generalized wave coordinates. This requires the understanding of the Dirac equation in…

The supersymmetric analysis of spinning cosmic string spacetime, involving an electron in magnetic fields, has been conducted. We examined the Dirac system within extended special functions known as exceptional orthogonal polynomials.…

It is shown, in the context of a recent formulation of elementary particles in terms of, what may be called, a Quantum Mechanical Kerr-Newman metric, that spin is a consequence of a space-time cut off at the Compton wavelength and Compton…

We study the Dirac-Yang-Mills equations on closed spin manifolds with a focus on uncoupled solutions, i.e. solutions for which the connection form satisfies the Yang-Mills equation. Such solutions require the Dirac current, a quadratic form…

We define and study the probability current and the Hamiltonian operator for a fully general set of Dirac matrices in a flat spacetime with affine coordinates, by using the Bargmann-Pauli hermitizing matrix. We find that with some weak…

Based on the Arnowitt-Deser-Misner (ADM) canonical formulation of general relativity, a canonical formulation of gravitationally interacting classical spinning-object systems is given to linear order in spin. The constructed position,…

Using the language of the Geometric Algebra, we recast the massive Dirac bispinor as a set of Lorentz scalar, vector, bivector, pseudovector, and pseudoscalar fields that obey a generalized form of Maxwell's equations of electromagnetism.…

It is shown that the non-relativistic `Dirac' equation of L\'evy-Leblond, we used recently to describe a spin $1/2$ field interacting non-relativistically with a Chern-Simons gauge field, can be obtained by lightlike reduction from $3+1$…

Relativistic spin-1/2 particles in curved spacetime are naturally described by Dirac theory, which is a dynamical and Lorentz-invariant field theory. In this work, we propose a non-dynamical fermion theory in 3+1 dimensions dubbed spinor…

Fermionic continuous spin field propagating in (A)dS space-time is studied. Gauge invariant Lagrangian formulation for such fermionic field is developed. Lagrangian of the fermionic continuous spin field is constructed in terms of triple…

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar…

We formulate the Migdal-Eliashberg theory of electron-phonon interactions in terms of classical spins by mapping the free energy to a Heisenberg spin chain in a Zeeman magnetic field. Spin components are energy-integrated normal and…

We apply a recently presented BRST procedure to construct the Largangian cubic vertex of higher-spin gauge field triplets interacting with massive free scalars. In flat space, the spin-s triplet propagates the series of irreducible spin-s,…

We introduce a spin field approach, that is compatible with the Cartan moving frame method, to describe the submanifold in a flat space. In fact, we consider a kind of spin field $\psi$, that satisfies a Killing spin field equation…

It is shown how spin one vector matter fields can be coupled to a Yang-Mills theory. Such matter fields are defined as belonging to a representation $R$ of this Yang-Mills gauge algebra $\mathfrak{g}$. It is also required that these fields…

A common view is that generalization of a wave equation on Riemannian space-time is substantially determined by what a particle is - boson or fermion. As a rule, they say that tensor equations for bosons are extended in a simpler way then…

We consider on a spin manifold with boundary a Dirac operator $D_A$ with chiral boundary conditions, twisted by a unitary connection $A$. When $m$ is not in the chiral spectrum of $D_A$, we define an analogue of the Dirichlet-to-Neumann map…

Using the Clifford and the Spin-Clifford formalisms we prove that the classical relativistic Hamilton Jacobi equation for a charged massive (and spinning) particle interacting with an external electromagnetic field is equivalent to a…

The Mashhoon rotation-spin coupling is studied by means of the parallelism description of general relativity. The relativistic rotational tetrad is exploited, which results in the Minkowski metric, and the torsion axial-vector and Dirac…