Related papers: A Wick Rotation for Spinor Fields: the Canonical A…
Adapting ideas of Daubechies and Klauder [J. Math. Phys. {\bf 26} (1985) 2239] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin-coherent vectors parametrized…
New conserved spin and orbital angular momentum operators of Dirac's theory on spatially flat FLRW spacetimes are proposed generalizing thus recent results concerning the role of Pryce's spin operator in the flat case [I. I. Cot\u aescu,…
We employ the polar decomposition of the Dirac field to describe it as an effective spinorial fluid. We then construct a $(1+1+2)$ covariant formalism for the Dirac field that avoids the introduction of tetrad fields and Clifford matrices.…
The Dirac equation is one of the most fundamental equations of modern physics. It is a spinor equation, but some tensor equivalents of the equation were proposed previously. Those equivalents were either nonlinear or involved several…
Grassmann-valued Dirac fields together with the electromagnetic field (the pseudoclassical basis of QED) are reformulated on spacelike hypersurfaces in Minkowski spacetime and then restricted to Wigner hyperplanes to get their description…
Representations of Dirac-Hestenes and Dirac spinor fields via coordinates of surfaces conformally immersed into 4-dimensional complex space are proposed. A relation between time evolution of spinor fields and integrable deformations of…
It is shown that, for spherically symmetric static backgrounds, a simple reduced Dirac equation can be obtained by using the Cartesian tetrad gauge in Cartesian holonomic coordinates. This equation is manifestly covariant under rotations so…
The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metrics leads to new contributions to the in-band energy operator in…
Chirality or handedness in condensed matter induces anomalous optical responses such as natural optical activity, rotation of the plane of light polarization, as a result of breaking of spatial-inversion symmetry. In this study, optical…
Using the fact that a spin connection is defined to an accuracy of a vector it is shown that the spin connection should be modified in such a manner that Dirac equation in a curve space would be compatible with Dirac equation in a flat…
The 2(2s+1)-component relativistic basis spinors for the arbitrary spin particles are established in position, momentum and four-dimensional spaces, where s=0,1 / 2,1, 3 / 2, 2, ... . These spinors for integral- and half-integral spins are…
We show that Clifford algebras are closely related to the study of isoclinic subspaces of spinor spaces and, consequently, to the Hurwitz-Radon matrix problem. Isocliny angles are introduced to parametrize gamma matrices, i.e., matrix…
The motion of circular WP for one electron in central Coulomb field with high Z is calculated. The WP is defined in terms of solutions of the Dirac equation in order to take into account all possible relevant effects in particular the…
Scalar fields on a two dimensional curved surface are considered and the canonical structure of this theory analyzed. Both the first and second order forms of the Einstein-Hilbert (EH) action for the metric are used (these being…
In this work, we have extended the factorization method of scalar shape-invariant Schr\"o\-din\-ger Hamiltonians to a class of Dirac-like matrix Hamiltonians. The intertwining operators of the Schr\"odinger equations have been implemented…
It is shown that new spin-orbit-like terms appear in the effective nonrelativistic weak Hamiltonian for nucleon provided that nuclear potential is taken into account. Arguments for their considerable enhancement, in particular, in…
Motivated by the quantization of linearized gravity, we consider gauge-fixed linearized Einstein equations and their Wick rotation near a Cauchy surface. We show that Calder\'on projectors for the Wick-rotated equations induce Hadamard…
We give a formula for the first eigenvalue of the Dirac operator acting on spinor fields of a spin compact irreducible symmetric space $G/K$.
We construct exact solutions of the Einstein-Dirac equation, which couples the gravitational field with an eigenspinor of the Dirac operator via the energy-momentum tensor. For this purpose we introduce a new field equation generalizing the…
The geometric aspect of Wick rotation in quantum field theory and its localization on manifolds are explored. After the explanation of the notion and its related geometric objects, we study the topology of the set of landing $W$ for Wick…