Exploring Spinors: A Mathematical and Physical Perspective

In summary, the conversation is about a request for recommendations on readings about spinors in physics, specifically focusing on the mathematical formalism behind them. The person prefers a book that is not too in-depth but covers the boundary between math and physics. A recommendation is made for Van Proeyen's supergravity lectures.
  • #1
Silviu
624
11
Hello! Can someone recommend me some good readings about spinors in physics? I know some basics (i.e. how they work in Minkowski space for Dirac field), but I would like to understand more of the mathematical formalism behind them (how can you build them, in a general number of dimensions, how do you build the generators of their Lie Algebra etc.). I would honestly prefer a book that doesn't go too deep into the formalism (i.e. complete proofs of any small details, and extreme abstractisations), but something at the boundary between math and physics. Thank you!
 
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  • #2
Van Proeyen's supergravity lectures could be helpful.
 

1. What are spinors in higher dimensions?

Spinors in higher dimensions are mathematical objects that describe the behavior of spin particles in spaces with more than three dimensions. They are used in theoretical physics and mathematics to study symmetries and transformations in higher-dimensional spaces.

2. How are spinors different in higher dimensions compared to three dimensions?

In three dimensions, spinors are described by two-component objects, while in higher dimensions, they are described by objects with more components. This is due to the fact that in higher dimensions, there are more possible directions for spin to point in, resulting in a larger number of spin states.

3. What is the significance of spinors in physics and mathematics?

Spinors play an important role in both physics and mathematics, particularly in the fields of quantum mechanics, special and general relativity, and differential geometry. They are used to understand the symmetries and properties of these systems, and have applications in areas such as particle physics, cosmology, and string theory.

4. Can spinors be visualized in higher dimensions?

No, spinors cannot be visualized in the same way that we visualize objects in three dimensions. This is because spinors represent abstract mathematical objects that do not have a direct physical interpretation. However, their properties and behavior can be described and studied using mathematical equations and models.

5. Are spinors in higher dimensions related to spinors in three dimensions?

Yes, spinors in higher dimensions are mathematically related to spinors in three dimensions. This allows for the extension of concepts and techniques from three-dimensional spinors to higher dimensions, making it possible to study and understand the behavior of spin particles in these spaces.

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