Related papers: A Judgement on Sinors
We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to…
We define spinors for pairs of tangent disks in the Euclidean plane and prove a number of theorems, one of which may be interpreted as a "square root of Descartes Theorem". In any Apollonian disk packing, spinors form a network. In the…
We study spinful non-interacting electrons moving in two-dimensional materials which exhibit a spectral gap about the Fermi energy as well as time-reversal invariance. Using Fredholm theory we revisit the (known) bulk topological invariant,…
Spinor fields depending on tensor fields and other spinor fields are considered. The concept of extended spinor fields is introduced and the theory of differentiation for such fields is developed.
A nice paper by Morrison demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay…
A unified description of all interactions could be based on a higher-dimensional theory involving only spinor fields. The metric arises as a composite object and the gravitational field equations contain torsion-corrections as compared to…
This paper explains why spacetime singularities do not constitute a breakdown of physical laws, and points out that the difference between the metrics at singularities and those outside of singularities is factual, rather than nomological.
We prove the existence of singular harmonic ${\bf Z}_2$ spinors on $3$-manifolds with $b_1 > 1$. The proof relies on a wall-crossing formula for solutions to the Seiberg-Witten equation with two spinors. The existence of singular harmonic…
Contemporary research programs in fundamental physics appear to suggest that there could be two (physical) times---or none at all. This essay articulates these possibilities in the context of quantum gravity, and in particular of…
In this note we discuss the possibility to get a time rather than space in the scenario of (de)construction of new dimension.
Within the scope of isotropic FRW cosmological model the role of nonlinear spinor field in the evolution of the Universe is studied. It is found that unlike in anisotropic cosmological models in the present case the spinor field does not…
At first we introduce the space-time manifold and we compare some aspects of Riemannian and Lorentzian geometry such as the distance function and the relations between topology and curvature. We then define spinor structures in general…
By exploring a spinor space whose elements carry a spin 1/2 representation of the Lorentz group and satisfy the the Fierz-Pauli-Kofink identities we show that certain symmetries operations form a Lie group. Moreover, we discuss the reflex…
Alternative approaches to the study of the quantum-gravity problem are handling the role of spacetime very differently. Some are focusing on the analysis of one or another novel formulation of "empty spacetime", postponing to later stages…
This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…
This paper does not contain any new results, it is just an attempt to present, in a systematic way, one construction which establishes an interesting relationship between some ideas and notions well-known in the theory of integrable systems…
We introduce spinors, at a level appropriate for an undergraduate or first year graduate course on relativity, astrophysics or particle physics. The treatment assumes very little mathematical knowledge (mainly just vector analysis and some…
The relationship between spinors and Clifford (or geometric) algebra has long been studied, but little consistency may be found between the various approaches. However, when spinors are defined to be elements of the even subalgebra of some…
Some notes and questions about the concept of time are exposed. Particular reference is given to the problem in quantum mechanics, in connection with the indeterminacy principle.
The bundles suitable for a description of higher-spin fields can be built in terms of a 2-spinor bundle as the basic `building block'. This allows a clear, direct view of geometric constructions aimed at a theory of such fields on a curved…