Based on a unified quantum field theory of spinors assumed to describe all matter fields and their interactions we construct the space time structure of general relativity according to a general connection within the corresponding spinor space. The tetrad field and the corresponding metric field are composed from a space time dependent basis of spinors within the internal space of the fundamental matter field. Similar to twistor theory the Minkowski signature of the space time metric is related to this spinor nature of elementary matter, if we assume the spinor space to be endowed with a symplectic structure. The equivalence principle and the property of background independence arise from the fact that all elementary fields are composed from the fundamental spinor field. This means that the structure of space time according to general relativity seems to be a consequence of a fundamental theory of matter fields and not a presupposition as in the usual setting of relativistic quantum field theories.
In Hamiltonian GR, change has seemed to be missing, defined only asymptotically, or otherwise obscured at best. By construing change as essential time dependence, can one find change locally in Hamiltonian GR with spinors? This paper is motivated by tendencies in space-time philosophy to slight fermionic/spinorial matter, in Hamiltonian GR to misplace changes of time coordinate, and in treatments of the Einstein-Dirac equation to include a gratuitous local Lorentz gauge symmetry. Spatial dependence is dropped in most of the paper. To include all and only the coordinate freedom, the Einstein-Di…
Coupling spinor fields to the gravitational field, in the setting of general relativity, is standardly done via the introduction of a vierbein field and the (associated minimal) spin connection field. This makes three types of indices feature in the formalism: world/coordinate indices, Lorentz vector indices, and Lorentz spinor indices, respectively. This article will show, though, that it is possible to dispense altogther with the Lorentz indices, both tensorial ones and spinorial ones, obtaining a formalism featuring only world indices. This will be possible by having both the 'Dirac operato…
It is a commonplace attributed to Kretschmann that any local physical theory can be represented in arbitrary coordinates using tensor calculus. But the literature also claims that spinors _as such_ cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent, so what is general covariance for fermions? In fact both commonplaces are wrong. Ogievetsky and Polubarinov (OP) constructed spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn nonlinear group representations. Roughly and locally, OP spinors resemble the orthonormal basis…
The boundaries of quantum materials can host a variety of exotic effects such as topologically robust edge states or anyonic quasiparticles. Here, we show that fermionic systems such as graphene that admit a low energy Dirac description can exhibit counterintuitive relativistic effects at their boundaries. As an example, we consider carbon nanotubes and demonstrate that relativistic bulk spinor states can have non zero charge density on the boundaries, in contrast to the sinusoidal distribution of non-relativistic wave functions that are necessarily zero at the boundaries. This unusual propert…
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…
Lecture notes on Poincaré-invariant scattering amplitudes and tree-level recursion relations in spinor-helicity formalism. We illustrate the non-perturbative constraints imposed over on-shell amplitudes by the Lorentz Little Group, and review how they completely fix the three-point amplitude involving either massless or massive particles. Then we present an introduction to tree-level BCFW recursion relations, and some applications for massless scattering, where the derived three-point amplitudes are employed.
In this paper, we strictly establish classical concepts and relations according to a Dirac equation with scalar, vector and nonlinear potentials. To calculate classical parameters for moving spinor, the local Lorentz transformations for parameters are derived. The calculation shows that different kinds of potentials result in different energy-speed relations, and the energy-speed relations for these potentials are derived in detail. The usual mass-energy relation $E = mc^2$ holds only for the linear spinor. The energy-speed relations can be used as fingerprints to identify the interactive pote…
It was recently shown that the homogeneous and isotropic cosmology of a massless scalar field coupled to general relativity exhibits a new hidden conformal invariance under Mobius transformation of the proper time, additionally to the invariance under time-reparamterization. The resulting Noether charges form a $sl(2,\mathbb{R})$ Lie algebra, which encapsulates the whole kinematics and dynamics of the geometry. This allows to map FLRW cosmology onto conformal mechanics and formulate quantum cosmology in $\text{CFT}_1$ terms. Here, we show that this conformal structure is embedded in a larger $…
This present work is based on our previous publications, which all together trigger our "Killing spinor programme". Other significant spinor fields are injected into the scheme and the intricate relations between them and their bilinears are constructed here. The web of relations concerning these constructions are presented clearly in a Venn diagram. Particular attention is devoted to the construction of equations satisfied by the homogeneous bilinears induced from Dirac spinors. Contacts with various physics theories are made throughout the text and some of the future directions of the progra…
Transition probability calculations of strong field particle processes in the Furry picture, typically use fermion Volkov solutions. These solutions have a relatively complicated spinor due to the interaction of the electron spin with a strong external field, which in turn leads to unwieldy trace calculations. The simplification of these calculations would aid theoretical studies of strong field phenomena such as the predicted resonance behaviour of higher order Furry picture processes. Here, Fierz transformations of Volkov spinors are developed and applied to a 1st order and a 2nd order Furry…
We study the coupling of the non-minimal ghost fields of the pure spinor superstring in general curved backgrounds. The coupling is found solving the consistent relations from the nilpotency of the non-minimal BRST charge.
We make an explicit link between the cubic interactions of off-shell fields and the on-shell three-point amplitudes in four dimensions. Both the cubic interactions and the on-shell three-point amplitudes had been independently classified in the literature, but their relation has not been made explicit. The aim of this note is to provide such a relation and discuss similarities and differences of their constructions. For the completeness of our analysis, we also derive the covariant form of all parity-odd massless vertices.
This is an overview of the method of pure spinor superfields, written for "Handbook of Quantum Gravity", eds. C. Bambi, L. Modesto and I. Shapiro. The main focus is on the use of the formalism in maximal supergravity on a flat background. The basics of pure spinor superfields, and their relation to standard superspace, is reviewed. The pure spinor superstring model of Berkovits is briefly discussed. Consequences for divergence properties of loop diagrams in maximal supergravity are restated. Some final remarks are made concerning desirable development of the theoretical framework.
In the work, the recurrent differential relations that connecting the polarization spin-tensor of the wave function of a free massive particle of an arbitrary spin for $D=4$ and new formula of the $D$-dimensional Behrends-Fronsdal spin projection operator are found.
Twistors, special relativity, conformal symmetry and minimal coupling - a review
本文提出了一种用旋量和扭量语言研究狭义相对论动力学的方法。利用扭量空间的自然共形不变辛结构，构建了一个模型，它描述了一个相对论性的大质量，自旋和带电粒子，最低限度地耦合到外部的电-磁场。在双扭量相空间上，相对论性哈密顿动力学由Poincare标量函数产生，该函数由经典极限（由我们适当定义）的二阶函数和外部电-磁场的最小耦合Dirac算子得到.在这样定义的相对论经典极限中，没有格拉斯曼变量。此外，描述相对论自旋动力学的产生方程与所谓的Thomas Bergman Michel Telegdi方程有很大的不同。
Spinor structure is understood as a totality of tensor products of biquaternion algebras, and the each tensor product is associated with an irreducible representation of the Lorentz group. A so-defined algebraic structure allows one to apply modulo 8 periodicity of Clifford algebras on the system of real and quaternionic representations of the Lorentz group. It is shown that modulo 8 periodic action of the Brauer-Wall group generates modulo 2 periodic relations on the system of representations, and all the totality of representations under this action forms a self-similar fractal structure. So…
In this paper we advance into a generalized spinor classification, based on the so-called Lounesto's classification. The program developed here is based on an existing freedom on the spinorial dual structures definition, which, in a certain simple physical and mathematical limit, allows us to recover the usual Lounesto's classification. The protocol to be accomplished here gives full consideration in the understanding of the underlying mathematical structure, in order to satisfy the quadratic algebraic relations known as Fierz-Pauli-Kofink identities, and also to provide physical observables. …
In this paper we discuss fundamental aspects related to the helicity and dynamics of the spin-$1/2$ fermions encompassed within the very well-known Lounesto's classification. More specifically, we investigate how the bi-spinorial structures behave under discrete symmetries, as well as analyse some consequences on the spinors dynamics. In addition, we find an interesting relation between the spinor helicity and the Lounesto spinor classification.
For internal gauge forces, the result of locally gauging, i.e., of performing the substitution $\partial \rightarrow D$, is physically the same whether performed on the action or on the corresponding Euler-Lagrange equations of motion. Rather unsettling, though, such commutativity fails for the standard way of coupling a Dirac fermion to the gravitational field in the setting of a local Lorentz gauge theory of general relativity in the vierbein formalism, the equivalence principle thus seemingly being here violated. This paper will present a formalism in which commutativity holds for the gravi…
