Spinors & Space-Time: What Math Prereqs Are Needed?

In summary, the conversation discusses the use of spinors in modern theoretical physics and the recommended mathematical prerequisites for understanding Penrose's book "Spinors and space-time". The conversation also suggests starting with lighter materials, such as group theory books, before tackling more advanced texts on spinors. Specifically, "The Geometry of Minkowski Spacetime" by Gregory L. Naber is recommended as a good introduction to spinors.
  • #1
QuArK21343
47
0
Are spinors needed in modern theoretical physics as opposed to tensors? I have come across Penrose's book "Spinors and space-time". Does anybody know what mathematical prerequisites are needed to actually understand it? (at least volume 1) Can I manage to go through it with a good knowledge of real analysis and linear algebra and a very basic understanding of topology?
 
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  • #2
Penrose and Rindler is to me the ultimate level. You should start with something light, like a group theory book like Wu Ki Tung (1984), or Cromwell (vol.2) which have good chapters on spinorial representations of the restricted Lorentz group.
 
  • #3
Chapter 3 from The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity is a nice, readable introduction to spinors. Actually, the entire book is quite nice.
 
  • #4
George is speaking about

The Geometry of Minkowski Spacetime: An Introduction to the Mathematics of the Special Theory of Relativity (Applied Mathematical Sciences) by Gregory L. Naber.
 
  • #5
Ok, I have had a look at The Geometry of Minkowski Spacetime and seems really good. Thanks again for your advice!
 

1. What is a spinor?

A spinor is a mathematical object used to describe the quantum mechanical properties of particles. It is represented by a complex vector and can be used to describe the intrinsic angular momentum, or spin, of a particle.

2. What is the relationship between spinors and space-time?

Spinors are used in the mathematical framework of space-time to describe the behavior of particles with spin in a relativistic context. They are an essential part of the Dirac equation, which combines special relativity and quantum mechanics.

3. What are the prerequisites for understanding spinors and space-time?

A strong foundation in linear algebra and calculus is necessary for understanding spinors and space-time. Knowledge of abstract algebra, specifically group theory, is also helpful in understanding the mathematical properties of spinors.

4. Can spinors be visualized?

No, spinors cannot be visualized in the same way that vectors or matrices can be. They do not correspond to physical objects and are purely mathematical constructs used to describe the properties of particles.

5. How are spinors used in modern physics?

Spinors are used extensively in modern physics, particularly in the fields of particle physics and quantum field theory. They are also used in general relativity and cosmology to describe the behavior of particles in curved space-time. Spinors have also been used in the development of quantum computing and quantum information theory.

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