共查询到20条相似文献,搜索用时 20 毫秒
1.
V. Jhangiani 《Foundations of Physics》1978,8(7-8):593-601
The formulas for the Lie covariant differentiation of spinors are deduced from an algebraic viewpoint. The Lie covariant derivative of the spinor connection is calculated, and is given a geometric meaning. A theorem about the Lie covariant derivative of an operator in spin space that was stated in Part I of this work is discussed. 相似文献
2.
3.
Granville A. Perkins 《Foundations of Physics》1978,8(9-10):745-757
In the early history of spinors it became evident that a single undotted covariant elementary spinor can represent a plane wave of light. Further study of that relation shows that plane electromagnetic waves satisfy the Weyl equation, in a way that indicates the correct spin angular momentum. On the subatomic scale the Weyl equation discloses more detail than the vector equations. The spinor and vector equations are equivalent when applied to plane waves, and more generally (in the absence of sources) on the large scale when the spinors are incoherent. 相似文献
4.
Christoph Bohle 《Journal of Geometry and Physics》2003,45(3-4):285-308
The aim of this paper is to describe some results concerning the geometry of Lorentzian manifolds admitting Killing spinors. We prove that there are imaginary Killing spinors on simply connected Lorentzian Einstein–Sasaki manifolds. In the Riemannian case, an odd-dimensional complete simply connected manifold (of dimension n≠7) is Einstein–Sasaki if and only if it admits a non-trivial Killing spinor to
. The analogous result does not hold in the Lorentzian case. We give an example of a non-Einstein Lorentzian manifold admitting an imaginary Killing spinor. A Lorentzian manifold admitting a real Killing spinor is at least locally a codimension one warped product with a special warping function. The fiber of the warped product is either a Riemannian manifold with a real or imaginary Killing spinor or with a parallel spinor, or it again is a Lorentzian manifold with a real Killing spinor. Conversely, all warped products of that form admit real Killing spinors. 相似文献
5.
Rabin Banerjee 《Annals of Physics》2004,311(1):245-264
6.
《Journal of Nonlinear Mathematical Physics》2013,20(1):27-34
It is known that the complex spin group Spin(n, ?) is the universal covering group of complex orthogonal group SO(n, ?). In this work we construct a new kind of spinors on some classes of Kahler–Norden manifolds. The structure group of such a Kahler–Norden manifold is SO(n, ?) and has a lifting to Spin(n, ?). We prove that the Levi-Civita connection on M is an SO(n, ?)-connection. By using the spinor representation of the group Spin(n, ?), we define the spinor bundle S on M. Then we define covariant derivative operator ? on S and study some properties of ?. Lastly we define Dirac operator on S. 相似文献
7.
Wei-Tong Shu 《Communications in Mathematical Physics》1991,140(3):449-480
In this paper I will first derive, based on energy estimations and geometric invariance, the asymptotic behavior of solutions of linear spin field equations in Minkowski space. It generalizes the result in [3] where it was proved for the spin-1 and spin-2 cases. The techniques are then applied to Yang-Mills equations, the result improves the previous one in [1] by allowing the initial data to have charge, dipole and quadrupole moments. The Lie derivative operator for spinors and some properties will be also discussed; they can be used to simplify some algebraic calculations of [4].This research is partially supported by a grant from NSF under DMS-8610730 相似文献
8.
Haishan Liu H. Lü Zhao-Long Wang 《The European Physical Journal C - Particles and Fields》2012,72(1):1853
The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy
effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only
scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part,
we demonstrate that Kaluza–Klein theory can be gauged so that the Killing spinors are charged under the Kaluza–Klein vector.
This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions
of these theories. 相似文献
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10.
V. Jhangiani 《Foundations of Physics》1977,7(1-2):111-120
The spinor covariant derivative through which the equations of quantum fields are generalized to include gravitational coupling has a direct and simple geometric significance. The formula for the difference of two spinor covariant derivatives taken in different order is derived geometrically; and the geometric proof of the covariant constancy of the spin-1/2 -matrices in curved space is given. 相似文献
11.
《Physics Reports》1986,137(1):35-47
If, following E. Cartan, the simplest spinors (pure) are conceived as equivalent to isotropic (or null or optical) polarized planes in complex spaces, then the most natural tensors generated (bilinearly) by the simplest spinors are isotropic vectors rather than ordinary linear ones. The conjecture that spinors are fundamental would then imply that non-linear geometry of isotropic elements should be more elementary in general than the linear one; and the relevance of optical geometry (optical flags, optical groups) on space-time manifolds for the explanation of optical phenomenology in the frame of general relativity [5] could already constitute a first confirmation of this conjecture.Only 2- and 4-component spinors build up linear spinor spaces while 8, 16, 32,...component pure spinors, instead, are subject to covariant (quadratic) constraint equations and build up non-linear sets isomorphic, up to a sign, to quadric Grassmanians and, for neutral and conformal spaces, to Lie groups.The possible relevance of such pure spinor properties for physics is conjectured and exemplified. 相似文献
12.
In this article a geometric process to compare spinors for different metrics is constructed. It makes possible the extension to spinor fields of a variant of the Lie derivative (called the metric Lie derivative), giving a geometric approach to a construction originally due to Yvette Kosmann. The comparison of spinor fields for two different Riemannian metrics makes the study of the variation of Dirac operators feasible. For this it is crucial to take into account the fact that the bundle in which the sections acted upon by the Dirac operators take their values is changing. We also give the formulas for the change in the eigenvalues of the Dirac operator. We conclude by giving a few cases in which an eigenvalue is stationary.
Recherche soutenue par le programme européen C.E.E. G.A.D.G.E.T. SC1-0105-C 相似文献
Recherche soutenue par le programme européen C.E.E. G.A.D.G.E.T. SC1-0105-C 相似文献
13.
Kenza Dighton 《International Journal of Theoretical Physics》1975,14(2):137-144
The equations of conformal Killing transport are discussed using tensor and spinor methods. It is shown that, in Minkowski space-time, the equations for a null conformal Killing vector ξ a are completely determined by the corresponding spinor ω A and its covariant derivative, which defines a spinor π A′ . In conformally flat space-time, the covariant derivative of π A′ is also involved. Some applications to twistor theory are briefly mentioned. 相似文献
14.
Davide Cassani Claudius Klare Dario Martelli Alessandro Tomasiello Alberto Zaffaroni 《Communications in Mathematical Physics》2014,327(2):577-602
We consider superconformal and supersymmetric field theories on four-dimensional Lorentzian curved space-times, and their five-dimensional holographic duals. As in the Euclidean signature case, preserved supersymmetry for a superconformal theory is equivalent to the existence of a charged conformal Killing spinor. Differently from the Euclidean case, we show that the existence of such spinors is equivalent to the existence of a null conformal Killing vector. For a supersymmetric field theory with an R-symmetry, this vector field is further restricted to be Killing. We demonstrate how these results agree with the existing classification of supersymmetric solutions of minimal gauged supergravity in five dimensions. 相似文献
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16.
The character of holomorphic functions on the space of pure spinors in 10, 11 and 12 dimensions is calculated. From this character
formula, we derive in a manifestly covariant way various central charges which appear in the pure spinor formalism for the
superstring. We also derive in a simple way the zero momentum cohomology of the pure spinor BRST operator for the D=10 and D=11 superparticle
Mathematics Subject Classifications (2000): 81T30, 83E30, 83E50 相似文献
17.
Using a link between Einstein-Sasakian structures and Killing spinors we prove a general construction principle of odd-dimensional Riemannian manifolds with real Killing spinors. In dimensionn=7 we classify all compact Riemannian manifolds with two or three Killing spinors. Finally we classify nonflat 7-dimensional Riemannian manifolds with parallel spinor fields. 相似文献
18.
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—flagpoles—spinors are considered, instead of the usual Dirac spinors. We also construct a mapping between spinors in the covariant framework and spinors in Lorentz symmetry breaking scenarios, showing how one may transliterate spinors of different classes between the two cases. Specific examples concerning the mapping of Dirac spinor fields in Lorentz violating scenarios into flagpole and flag-dipole spinors with full Lorentz invariance (including the cases of Weyl and Majorana spinors) are worked out. 相似文献
19.
V. L. Figueiredo E. Capelas de Oliveira W. A. Rodrigues Jr. 《International Journal of Theoretical Physics》1990,29(4):371-395
We deal with three different definitions for spinors: (I) thecovariant definition, where a particular kind ofcovariant spinor (c-spinor) is a set of complex variables defined by its transformations under a particular spin group; (II) theideal definition, where a particular kind of algebraic spinor (e-spinor) is defined as an element of a lateral ideal defined by the idempotente in an appropriated real Clifford algebra
p,q
(whene is primitive we writea-spinor instead ofe-spinor); (III) the operator definition where a particular kind of operator spinor (o-spinor) is a Clifford number in an appropriate Clifford algebra
p,q
determining a set of tensors by bilinear mappings. By introducing the concept of spinorial metric in the space of minimal ideals ofa-spinors, we prove that forp+q5 there exists an equivalence from the group-theoretic point of view among covariant and algebraic spinors. We also study in which senseo-spinors are equivalent toc-spinors. Our approach contain the following important physical cases: Pauli, Dirac, Majorana, dotted, and undotted two-component spinors (Weyl spinors). Moreover, the explicit representation of thesec-spinors asa-spinors permits us to obtain a new approach for the spinor structure of space-time and to represent Dirac and Maxwell equations in the Clifford and spin-Clifford bundles over space-time. 相似文献
20.
We derive, for spacetimes admitting a Spin(7) structure, the general local bosonic solution of the Killing spinor equation of 11-dimensional supergravity. The metric, four-form, and Killing spinors are determined explicitly, up to an arbitrary eight-manifold of Spin(7) holonomy. It is sufficient to impose the Bianchi identity and one particular component of the four-form field equation to ensure that the solution of the Killing spinor equation also satisfies all the field equations, and we give these conditions explicitly. 相似文献