Grasmann Lagrangian - literature

In summary, the conversation was about the request for suggestions on articles and books related to Lagrangian and Hamiltonian systems with Grasmann variables. One person suggested Henneaux's book on quantization of gauge systems and the references therein, while the other person asked for additional suggestions. The first person then recommended the book, "Constrained Dynamics With Applications to Yang Mills Theory" by Sundermayer, as a good addition to Henneaux's book.
  • #1
Omega137
22
0
Hello!

Can anybody suggest me some articles and books on Lagrangian and Hamiltonian
systems with Grasmann variables?

Thank you for your help!

O
 
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  • #2
Try Henneaux's book on quantization of gauge systems and the references therein.
 
  • #3
Thank you! Any other idea?

bigubau said:
Try Henneaux's book on quantization of gauge systems and the references therein.
 
  • #4
Omega137 said:
Thank you! Any other idea?
No, the Henneaux book is the most complete source available on this issue.
 
  • #5
The following book can be a good addition to Henneaux's book: Sundermayer - Constrained Dynamics With Applications to Yang Mills Theory, General Relativity Classical Spin Dual String Model Lecture Notes in Physics, with the mentioned examples.
 

1. What is the Grasmann Lagrangian?

The Grasmann Lagrangian is a mathematical expression used in the field of theoretical physics to describe the dynamics of particles and fields. It is a function of a set of generalized coordinates and their time derivatives, and is used to calculate the equations of motion for a physical system.

2. Who first proposed the Grasmann Lagrangian?

The Grasmann Lagrangian was first proposed by Hermann Grasmann, a German mathematician and physicist, in the 19th century. He developed the concept of Grassmann algebra, which is the basis for the Lagrangian formalism used in modern physics.

3. What is the significance of the Grasmann Lagrangian in theoretical physics?

The Grasmann Lagrangian is a fundamental tool in theoretical physics as it allows for the formulation of the equations of motion for a physical system in a concise and elegant manner. It is used in various fields such as classical mechanics, quantum mechanics, and field theory to describe the behavior of particles and fields.

4. How does the Grasmann Lagrangian differ from the Hamiltonian?

The Grasmann Lagrangian and the Hamiltonian are two different mathematical approaches to describe the dynamics of a physical system. While the Lagrangian is a function of the coordinates and their time derivatives, the Hamiltonian is a function of the coordinates and their momenta. The equations of motion obtained from the Lagrangian are equivalent to those obtained from the Hamiltonian, but each approach has its advantages in different situations.

5. Are there any real-world applications of the Grasmann Lagrangian?

Yes, the Grasmann Lagrangian has numerous real-world applications in physics, engineering, and other fields. It has been used to model the behavior of particles in particle accelerators, describe the motion of celestial bodies in astronomy, and even in the development of control systems for robots and other mechanical systems.

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