- #1
wphysics
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I am working on Chapter 5.6 of Weinberg QFT book vol1.
In page 231 and 232, he said (1,0) or (0,1) field corresponds to an antisymmetric tensor
[itex]
F^{\mu\nu}
[/itex]
that satisfies the further irreducibilitry 'duality' conditions
[itex]
F^{\mu\nu}= \pm {{i}\over{2}} \epsilon ^{\mu\nu\lambda\rho}F_{\lambda \rho}
[/itex]
for (1,0) and (0,1) fields, respectively.
I check that Self-dual antisymmetrc tensor has three independent components and so does Anti Self-dual antisymmetric tensor. So, I can guess that there might be correspondence between Self-dual(or Anti Self-dual) antisymmetric tensor and (1,0) field (or (0,1)field ).
But, I could not show how they are related to each other mathematically.
I would like you guys to show me that how we correspond Self-dual antisymmetric tensor with (1,0) field and
Anti Self-dual antisymmetric tensor with (0,1) field.
Thank you so much.
In page 231 and 232, he said (1,0) or (0,1) field corresponds to an antisymmetric tensor
[itex]
F^{\mu\nu}
[/itex]
that satisfies the further irreducibilitry 'duality' conditions
[itex]
F^{\mu\nu}= \pm {{i}\over{2}} \epsilon ^{\mu\nu\lambda\rho}F_{\lambda \rho}
[/itex]
for (1,0) and (0,1) fields, respectively.
I check that Self-dual antisymmetrc tensor has three independent components and so does Anti Self-dual antisymmetric tensor. So, I can guess that there might be correspondence between Self-dual(or Anti Self-dual) antisymmetric tensor and (1,0) field (or (0,1)field ).
But, I could not show how they are related to each other mathematically.
I would like you guys to show me that how we correspond Self-dual antisymmetric tensor with (1,0) field and
Anti Self-dual antisymmetric tensor with (0,1) field.
Thank you so much.