Tagged Questions
6
votes
2answers
266 views
Dirac equation in curved space-time
I have seen the Dirac equation in curved space-time written as $$[i\bar{\gamma}^{\mu}\frac{\partial}{\partial x^{\mu}}-i\bar{\gamma}^{\mu}\Gamma_{\mu}-m]\psi=0 $$
This ...
1
vote
2answers
205 views
Geometrical interpretation of the Dirac equation
Is there a geometrical intuitive picture behind the Dirac equation, and the gamma matrices that it uses? I know the geometric algebra is a Clifford algebra. Can the properties of geometric algebra, be ...
2
votes
1answer
142 views
Geometric interpretation of perturbation theory in quantum field theory
I am studying GR right now, and one interesting thing I learned about vectors is that they are defined to have the same properties as derivatives.
With this in mind, can I make a differential ...
1
vote
0answers
102 views
Extending General Relativity with Kahler Manifolds?
Standard general relativity is based on Riemannian manifolds.
However, the simplest extension of Riemannian manifolds seems to be Kahler manifolds, which have a complex (hermitian) structure, a ...
2
votes
1answer
186 views
Killing vectors for SO(3) (rotational) symmetry
I am reading a paper$^1$ by Manton and Gibbons on the dynamics of BPS monopoles. In this, they write the Atiyah-Hitchin metric for a two-monopole system. The first part is for the one monopole moduli ...
9
votes
1answer
191 views
Can Fermionic symmetries be fully integrated into geometric deformation complexes or symplectic reduction?
How should a geometer think about quotienting out by a Fermionic symmetry? Is this a formal concept? A strictly linear concept? A sheaf theoretic concept?
How does symplectic reduction work with odd ...
