What do you mean by Spinors?
In geometry and physics, spinors /spɪnər/ are elements of a complex vector space that can be associated with Euclidean space. Unlike vectors and tensors, a spinor transforms to its negative when the space is continuously rotated through a complete turn from 0° to 360° (see picture).
What is the difference between a spinor and a vector?
Spinors transform in a single-sided way. Geometrically, vectors are the oriented lines that you’re used to, with a weight equal to the vector’s magnitude. Spinors represent linear combinations of scalars and bivectors, oriented planes.
What does the Dirac equation say?
In particle physics, the Dirac equation is a relativistic wave equation formulated by British physicist Paul Dirac in 1928. It describes fields corresponding to elementary spin-½ particles as a vector of four complex numbers, in contrast to the Schrödinger equation which described a field of only one complex value.
Is a spinor a tensor?
You can think of a spinor as a complex version of a tensor: it acts on complex vector spaces linearly.
Is a spinor a vector?
Spinor is a vector in the basis of not space-time, but its spin states; in on sense, spinor is not a vector, since it will not transform as you transform the space (rotation, etc) .
Are Spinors vectors?
What did Paul Dirac do?
Career. Dirac established the most general theory of quantum mechanics and discovered the relativistic equation for the electron, which now bears his name. The remarkable notion of an antiparticle to each fermion particle – e.g. the positron as antiparticle to the electron – stems from his equation.
Why is the Dirac equation beautiful?
The Dirac equation By finding the equation explaining how electrons spin when they approach light speed, Dirac made the first steps in what we now know as quantum field theory and predicted the existence of antimatter. Apparently when Dirac himself was asked about his equation, he answered, “I found it beautiful.”
What are spinners physics?
Fidget spinners are essentially pocket gyroscopes. Gyroscopes are spinning devices mounted on an axis used to provide stability to a body through the resistance of motion due to rotational momentum.
Is a scalar a tensor?
In fact tensors are merely a generalisation of scalars and vectors; a scalar is a zero rank tensor, and a vector is a first rank tensor. The rank (or order) of a tensor is defined by the number of directions (and hence the dimensionality of the array) required to describe it.
How do you rotate a spinor?
A distinguishing feature of spinors is their behavior under rotation. Whereas a vector boson, with spin 1, will return to its initial state after a rotation by , a spinor requires two full rotations, with the angle advancing by to recover its initial state….
| helicity | +1/2 -1/2 |
|---|---|
| rotation angle ϕ/π | 4. |
| animate |
What is a spinor in physics?
Definition of spinor. : a vector whose components are complex numbers in a two-dimensional or four-dimensional space and which is used especially in the mathematics of the theory of relativity.
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. Only after a rotation by 720° a spinor is again the same. In contrast a vector is completely unchanged if you rotate it by 360°. This crazy property can be illustrated as shown, for example, here:
What do you think about the book spinors?
Going through the material on spinors though, I’m pretty happy with how that part of the book turned out, think it provides a clear explanation of a beautiful and important story, one that is not readily available elsewhere. One aspect of this that I emphasize is the remarkable parallel between
What are the applications of spinors in math?
Spinors in representation theory. One major mathematical application of the construction of spinors is to make possible the explicit construction of linear representations of the Lie algebras of the special orthogonal groups, and consequently spinor representations of the groups themselves.