In this paper, we present a theory for gravity coupled with scalar, SU$(n)$ and spinor fields on manifolds with null-boundary. We perform the symplectic reduction of the space of boundary fields and give the constraints of the theory in terms of local functionals of boundary vielbein and connection. For the three different couplings, the analysis of the constraint algebra shows that the set of constraints does not form a first class system.
We present a necessary and sufficient condition for a spinor $ω$ to be of nullity zero, i.e. such that for any null vector $v$, $v ω\ne 0$. This dives deeply in the subtle relations between a spinor $ω$ and $ω_c$, the (complex) conjugate of $ω$ belonging to the same spinor space.
We explore the three separate isomorphisms that link together simple spinors, null vectors and the orthogonal group O(n) and exploit them to look back at these arguments from a unified viewpoint.
In this work, we consider a generalization of quantum electrodynamics including Lorentz violation and torsional-gravity, in the context of general spinor fields as classified in the Lounesto scheme. Singular spinor fields will be shown to be less sensitive to the Lorentz violation, as far as couplings between the spinor bilinear covariants and torsion are regarded. In addition, we prove that flagpole spinor fields do not admit minimal coupling to the torsion. In general, mass dimension four couplings are deeply affected when singular flagpole spinors are considered, instead of the usual Dirac …
We describe a novel twistorial construction of the asymptotic BMS symmetries at null infinity for asymptotically flat spacetimes. We define BMS twistors as spinor solutions to some set of components of the usual spacetime twistor equation restricted to null infinity. The space of BMS twistors is infinite-dimensional. We show that given two BMS twistors their symmetric tensor product can be used to generate (complex) vector fields which are the infinitesimal BMS symmetries of null infinity. In this sense BMS twistors are "square roots" of BMS symmetries. We also show that these BMS twistor equa…
Holonomy algebras of Lorentzian Weyl spin manifolds with weighted parallel spinors are found. For Lorentzian Weyl manifolds admitting recurrent null vector fields are introduced special local coordinates similar to Kundt and Walker ones. Using that, the local form of all Lorentzian Weyl spin manifolds with weighted parallel spinors is given. The Einstein-Weyl equation for the obtained Weyl structures is analyzed and examples of Einstein-Weyl spaces with weighted parallel spinors are given.
The Lounesto classification splits spinors in six classes: I, II, III are those for which at least one among scalar and pseudo-scalar bi-linear spinor quantities is non-zero, its spinors are called regular, and among them we find the usual Dirac spinor. IV, V, VI are those for which the scalar and pseudo-scalar bi-linear spinor quantities are identically zero, its spinors are called singular, and they are split in further sub-classes: IV has no further restrictions, its spinors are called flag-dipole; V is the one for which the spin axial-vector vanishes, its spinors are called flagpole, and a…
We study the geometric properties of a $(2m+1)$-dimensional complex manifold $\mathcal{M}$ admitting a holomorphic reduction of the frame bundle to the structure group $P \subset \mathrm{Spin}(2m+1,\mathbb{C})$, the stabiliser of the line spanned by a pure spinor at a point. Geometrically, $\mathcal{M}$ is endowed with a holomorphic metric $g$, a holomorphic volume form, a spin structure compatible with $g$, and a holomorphic pure spinor field $ξ$ up to scale. The defining property of $ξ$ is that it determines an almost null structure, i.e.\ an $m$-plane distribution $\mathcal{N}_ξ$ along whic…
In the 2-spinor formalism, the gravity can be dealt with curvature spinors with four spinor indices. Here we show a new effective method to express the components of curvature spinors in the rank-2 $4 \times 4$ tensor representation for the gravity in a locally inertial frame. In the process we have developed a few manipulating techniques, through which the roles of each component of Riemann curvature tensor are revealed. We define a new algebra `sedon', whose structure is almost the same as sedenion except the basis multiplication rule. Finally we also show that curvature spinors can be repre…
We present a tetrad-affine approach to $f(\mathcal{Q})$ gravity coupled to spinor fields of spin-1/2. After deriving the field equations, we derive the conservation law of the spin density, showing that the latter ensures the vanishing of the antisymmetric part of the Einstein-like equations, just as it happens in theories with torsion and metricity. We then focus on Bianchi type-I cosmological models proposing a general procedure to solve the corresponding field equations and providing analytical solutions in the case of gravitational Lagrangian functions of the kind $f(\mathcal{Q})=α\mathcal…
By using the matrix-model representation, we show that correlation numbers of boundary changing operators (BCO) in $(2,2p+1)$ minimal Liouville gravity satisfy some identities, which we call the null identities. These identities enable us to express the correlation numbers of BCO in terms of those of boundary preserving operators. We also discuss a physical implication of the null identities as the manifestation of the boundary interaction.
The Lounesto spinor classification is an important tool in fundamental physics, because it makes explicit the pleiade of spinors types, beyond the used in quantum field theory (QFT). In this work, we show how the classification emerges in two topics: first we show that the bilinear covariants arise naturally in the equation of motion for a fermionic field in a Riemann-Cartan background (with gravitational dynamics f(R)) and we identify a singular spinor field (a flag-dipole one) as a solution of the presented model. This is the first solution flag-dipole founded in the literature. We investiga…
