- Feynman slash notation
-
In the study of Dirac fields in quantum field theory, Richard Feynman invented the convenient Feynman slash notation (less commonly known as the Dirac slash notation[1]). If A is a covariant vector (i.e., a 1-form),
using the Einstein summation notation where γ are the gamma matrices.
Contents
Identities
Using the anticommutators of the gamma matrices, one can show that for any aμ and bμ,
.
In particular,
Further identities can be read off directly from the gamma matrix identities by replacing the metric tensor with inner products. For example,
-
.
- where
is the Levi-Civita symbol.
With four-momentum
Often, when using the Dirac equation and solving for cross sections, one finds the slash notation used on four-momentum:
using the Dirac basis for the
's,
as well as the definition of four momentum
We see explicitly that
See also
- Gamma matrices
- Trace theorems
References
- ^ Steven Weinberg (1964), The quantum theory of fields, Volume 2, Cambridge University Press, 1995, pp. 358, ISBN 0521550017, http://books.google.com/books?id=3ws6RJzqisQC&lpg=PA358&dq=%22Dirac%20Slash%22&pg=PA358#v=onepage&q&f=false
- Halzen, Francis; Martin, Alan (1984). Quarks & Leptons: An Introductory Course in Modern Particle Physics. John Wiley & Sons. ISBN 0-471-88741-2.
Categories:- Quantum field theory
- Spinors
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