Question

In: Physics

Derive the Dirac gamma matrices for 2-space dimensions and 1-time dimension.

Expert Solution

Gamma matrices satisfy clifford algebra

And these matrices have dimension n .ie. matrices with

where d is the dimension you want to find it

Here d=2+1=3

But d/2 is not an integer hence taking a number higher i.e 4

===4

Hence these matrices will be

Hence we can use the same gamma matrices and just ignoring

Hence then the gamma matrices are

But we usually look for gamma matrices in lower dimensions

SO we can look for matrices also

But the above matrices satisfy clifford algebra

REMEMBER GAMMA MATRICES DO NOT HAVE UNIQUE REPRESENTATION

Hence if you find matrices as gamma matrices for 2+1 just make sure they satisfy clifford algebra, then those can also be considered as gamma matrices

Usually you will see pauli matrices as gamma matrices in 2+1 which are given as

genius_generous answered 2 years ago

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