Dirac equation in curved spacetime

In mathematical physics, the Dirac equation in curved spacetime generalizes the original Dirac equation to curved space.

It can be written by using vierbein fields and the gravitational spin connection. The vierbein defines a local rest frame, allowing the constant Dirac matrices to act at each spacetime point. In this way, Dirac's equation takes the following form in curved spacetime:

Here  is the vierbein and  is the covariant derivative for fermionic fields, defined as follows

where  is the commutator of Dirac matrices:

and  are the spin connection components.

Note that here Latin indices denote the "Lorentzian" vierbein labels while Greek indices denote manifold coordinate indices.

See also

 Dirac equation in the algebra of physical space
 Dirac spinor
 Maxwell's equations in curved spacetime
 Two-body Dirac equations

References

Category:Quantum field theory
Category:Spinors
Category:Partial differential equations
Category:Fermions
Curved spacetime