Where ? denotes the Hermitian adjoint of the spinor ? and ? 0 is the time-like gamma matrix.
2.
In 5 spacetime dimensions, the 4 gammas above together with the fifth gamma matrix to be presented below generate the Clifford algebra.
3.
The formula defining the fifth gamma matrix shows that it is the " of a four-dimensional geometric algebra of the gamma matrices.
4.
A tilde symbol is used over the two sets of potentials to indicate that they may have additional gamma matrix dependencies not present in the one-body Dirac equation.
5.
Where " C " is the charge conjugation matrix, which is defined by the property that when it conjugates a gamma matrix, the gamma matrix is negated and transposed.
6.
Where " C " is the charge conjugation matrix, which is defined by the property that when it conjugates a gamma matrix, the gamma matrix is negated and transposed.
7.
If a pure spinor that determines a particular complex structure is closed, or more generally if its exterior derivative is equal to the action of a gamma matrix on itself, then the almost complex structure is integrable and so such pure spinors correspond to generalized complex structures.
8.
However, when instead expanding this expression around a value of " p " ? where one or more of the components are at the corners of the Brillouin zone ( i . e . equal to / " a " ), one finds the same continuum form again, although the sign in front of the gamma matrix can change.
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