On the Dirac equation in a gravitation field

Dirac equation in a gravitation field and suggests starting with the arXiv link and then discussing the paper by Anthony Lasenby, Chris Doran, and Stephen Gull, which presents a superior formulation for gravitation and implementation of the Dirac equation. In summary, Carl suggests starting with the arXiv link and then discussing the paper by Lasenby et al. for a better understanding of the Dirac equation in a gravitation field.
  • #1
Ruslan_Sharipov
104
1
Let's discuss the Dirac equation in a gravitation field. I suggest to begin with the following article:

http://arxiv.org/abs/math.DG/0603367" [Broken]

It is rather simple. Your comments would be helpful for me.
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Your paper is beautiful. Have you seen this paper?

<b>Gravity, Gauge Theories and Geometric Algebra</b>
Anthony Lasenby, Chris Doran, Stephen Gull
http://www.arxiv.org/abs/gr-qc/0405033
[Phil. Trans. R. Soc. Lond. A 356, 487-582 (1998).]

I think the formulation they are using for gravitation is superior to all others, particularly in the ease with which the Dirac equation can be implemented in it.

Carl
 
  • #3


The Dirac equation in a gravitation field is an important topic in both physics and mathematics. The article you have suggested, "The Dirac Equation in a Gravitation Field" by H. Arodz and P. Kosiński, provides a clear and concise overview of this topic.

The Dirac equation is a fundamental equation in quantum mechanics that describes the behavior of spin-1/2 particles, such as electrons. It was originally formulated in the absence of a gravitational field, but it has been extended to include the effects of gravity. This is important because in the presence of a gravitational field, the behavior of particles can be significantly affected, and it is necessary to have a mathematical framework to describe this behavior.

The article discusses the mathematical formalism of the Dirac equation in a gravitational field, which involves the use of spinor fields and the coupling of the Dirac field to the gravitational field. The authors also provide a detailed derivation of the equation, which is helpful for those who are new to this topic.

One of the interesting aspects of the Dirac equation in a gravitational field is the inclusion of the spin-connection, which is a mathematical object that describes the curvature of space-time. This inclusion is necessary to ensure that the equation remains covariant under general coordinate transformations, which is a fundamental principle in general relativity.

Overall, I found this article to be a valuable resource for understanding the Dirac equation in a gravitational field. It presents the topic in a clear and concise manner, making it accessible to both physicists and mathematicians. The detailed derivation and inclusion of the spin-connection make it a comprehensive guide for those interested in this topic. Thank you for sharing this article.
 

1. What is the Dirac equation in a gravitation field?

The Dirac equation in a gravitation field is a mathematical equation that describes the behavior of spin-half particles, such as electrons, in the presence of a gravitational field. It was developed by physicist Paul Dirac in 1928 and combines elements of special relativity and quantum mechanics.

2. How does the Dirac equation differ from the Schrodinger equation?

The Dirac equation differs from the Schrodinger equation in that it takes into account the effects of special relativity, while the Schrodinger equation does not. This allows the Dirac equation to accurately describe the behavior of particles moving at high speeds, such as electrons.

3. What is the significance of the Dirac equation in physics?

The Dirac equation is significant in physics because it was the first equation to successfully combine quantum mechanics and special relativity. It also predicted the existence of antimatter, which was later experimentally confirmed. The equation has also been crucial in the development of quantum field theory and our understanding of the behavior of subatomic particles.

4. Can the Dirac equation be applied to other fields besides gravitation?

Yes, the Dirac equation can be applied to other fields besides gravitation, such as electromagnetism. In fact, it has been used to describe the behavior of particles in a variety of physical systems, including atoms, nuclei, and even the early universe.

5. What are some current research topics related to the Dirac equation in a gravitation field?

Current research topics related to the Dirac equation in a gravitation field include using the equation to study the behavior of particles in extreme gravitational environments, such as black holes, and developing new mathematical techniques to solve the equation in complex systems. There is also ongoing research into the possibility of unifying the Dirac equation with other fundamental equations, such as the general theory of relativity.

Similar threads

  • High Energy, Nuclear, Particle Physics
Replies
3
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
2
Views
1K
  • Quantum Interpretations and Foundations
Replies
0
Views
1K
  • Special and General Relativity
Replies
5
Views
999
Replies
4
Views
1K
  • Differential Geometry
Replies
1
Views
1K
Replies
26
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
1K
Replies
4
Views
939
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
Back
Top