Corses on vector and principale bundles and spinorielle geometry

In summary, you might want to look into courses at universities in your homeland, Europe, or North America.
  • #1
Feynman
159
0
Good morning,
Can you help me to find a corses on vector and principale bundles and spinorielle geometry :rolleyes:
thanks
 
Physics news on Phys.org
  • #2
Google on "Holonomy groups in differential geometry" or "spinor geometry" and you will find a lot of information.

Course titles may or may include "holonomy" or "spinor" depending on how specific the topic.

Which country did you have in mind? In the US, try math departments at Harvard, Princenton, Caltech, to name a few.

Also, check the International Journal of Mathematics and Mathematical Sciences for references and who is doing what in the field.
 
  • #3
I'm from Lebanon
 
  • #4
Courses in vector or principal bundles and spinor geometry

Here are some ideas - but you will have to contact each institution - from Lebanon, Europe might be your best option. There is also the American University in Beirut or German Institute in Cairo.

http://edge.imada.sdu.dk/ - European Differential Geometry Endeavor

http://www.maths.cam.ac.uk/faculty.html - Mathematics at Cambridge

http://www.maths.ox.ac.uk/ - Mathematics at Oxford

http://www.leiden.edu/index.php3?m=3&c=357 - University of Leiden
Geometry and Topology

http://wwwlb.aub.edu.lb/~webfas/academic_units/departments.html - American University in Beirut

http://wwwlb.aub.edu.lb/~webfas/academic_units/departments.html - Universtität Stuttgart, Institut für Geometrie und Topologie

http://www.science.ankara.edu.tr/mathemathics/eng.htm - University of Ankara (Turkey) Mathematics Department-

I would suggest that you read some mathematics journals to see who is publishing in the areas of interest and then contact the author or university for a recommendation.

Many US, European and Asian universities with Science (and Mathematics) departments will probably have a course in geometry and/or topology - which these days may include spinor geometry.
 
Last edited by a moderator:

1. What is a vector bundle?

A vector bundle is a mathematical construction that describes a space where each point has an associated vector space. It is a generalization of the concept of a tangent space, which describes the space of all possible directions at a point on a manifold. In a vector bundle, the vector spaces are allowed to vary smoothly from point to point on the base manifold.

2. What is a principal bundle?

A principal bundle is a type of fiber bundle where the fibers are modeled on a Lie group. It is used to describe the symmetry properties of a space, where the group acts on the base manifold in a natural way. Examples of principal bundles include the frame bundle of a Riemannian manifold and the gauge group bundle in gauge theory.

3. What is spinorial geometry?

Spinorial geometry is a branch of mathematics that studies the geometric properties of spinors, which are mathematical objects that encode both the geometric and algebraic properties of a space. It is used in theoretical physics, particularly in the study of quantum mechanics and general relativity, to describe the behavior of particles with half-integer spin.

4. How are vector bundles and principal bundles related?

Vector bundles can be seen as special cases of principal bundles, where the group action is the general linear group. In other words, a vector bundle is a principal bundle with a specific type of fiber. This relationship allows for the use of techniques from principal bundle theory in the study of vector bundles.

5. What is the significance of spinorial geometry?

Spinorial geometry has many applications in physics, including in the study of particle physics, quantum field theory, and general relativity. It provides a powerful framework for understanding the behavior of particles with spin, and has led to important discoveries in theoretical physics, such as the Dirac equation and the spin-statistics theorem.

Similar threads

  • Differential Geometry
Replies
15
Views
3K
Replies
8
Views
2K
  • Differential Geometry
Replies
7
Views
2K
Replies
3
Views
2K
  • Differential Geometry
Replies
18
Views
2K
  • Differential Geometry
Replies
6
Views
2K
  • Special and General Relativity
Replies
29
Views
1K
Replies
4
Views
2K
  • Differential Geometry
Replies
2
Views
2K
  • Differential Geometry
2
Replies
55
Views
7K
Back
Top