WebSep 7, 2024 · FAQ. A spinor is a mathematical object similar to a vector. However, while a vector points in some spatial direction, like, for example, in the direction of the north pole, a spinor points in a direction in an internal space. A curious property of a spinor is that if you rotate it by 360° it isn't the same but get's a minus sign. WebNov 13, 2011 · Abstract. The concept of a “spinor” emerged from the work of E. Cartan on the representations of simple Lie algebras. However, it was not until Dirac employed a special case in the construction of his relativistically invariant equation for the electron with “spin” that the notion acquired its present name or its current stature in ...
A spinor representation of Maxwell equations and Dirac equation
In geometry and physics, spinors /spɪnər/ are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight (infinitesimal) rotation. Unlike vectors and tensors, a … See more What characterizes spinors and distinguishes them from geometric vectors and other tensors is subtle. Consider applying a rotation to the coordinates of a system. No object in the system itself has moved, only the … See more The most general mathematical form of spinors was discovered by Élie Cartan in 1913. The word "spinor" was coined by Paul Ehrenfest in his work on quantum physics. Spinors were first applied to mathematical physics See more A space of spinors can be constructed explicitly with concrete and abstract constructions. The equivalence of these constructions is a consequence of the uniqueness of the spinor representation of the complex Clifford algebra. For a complete example … See more • In 1 dimension (a trivial example), the single spinor representation is formally Majorana, a real 1-dimensional representation that does not transform. • In 2 Euclidean dimensions, the left-handed and the right-handed Weyl spinor are 1-component See more The space of spinors is formally defined as the fundamental representation of the Clifford algebra. (This may or may not decompose into irreducible representations.) … See more Some simple examples of spinors in low dimensions arise from considering the even-graded subalgebras of the Clifford algebra Cℓp, q( See more A number of Clebsch–Gordan decompositions are possible on the tensor product of one spin representation with another. These decompositions express the tensor product in terms of the alternating representations of the orthogonal group. See more WebJan 4, 2005 · Greetings--I have a few questions from An Introduction to Quantum Field Theory by Peskin and Schroeder. First of all, I'm a little skeptical about the product where because the order seems backward. The product is ok because it is the "conventional" matrix multiplication of a row vector with a column vector to yield a scalar (with a gamma ... fromage sicilien au herbe
(PDF) Theory of Spinors in Curved Space-Time - ResearchGate
WebMar 7, 2011 · A spinor is described by a complex phasor in addition to a helicity. This is represented in the graphic by rotation in a circle normal to its spin direction, with the complex phase color coded. A rotation in space by an angle is accompanied by a phase change of . Thus after rotation by , the spin direction of the particle is recovered but the ... WebJun 1, 2024 · The spinor theory can also describe the forces acting on the rigid body. The forces on the rigid body . include the rotating component and the moving component, so it can be expressed by six ... WebMay 23, 2024 · $\begingroup$ Seeking a spinor analog of "tensors as multilinear maps" might not be the path that leads most physicists to become comfortable with spinors. The path might be more like this: Quantum physics is expressed in terms of observables. If we only require the pattern of observables to be Poincaré-symmetric, without requiring that … fromager strasbourg