Anticommuting sets of Dirac $gamma$-matrices Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)a problem about the equivament of two vector groups $(I)$ and $(II)$Clifford algebra - Gamma matricesProve two sets span the same subspaceFind a basis for $U+W$ and $Ucap W$Dirac Gamma Matrices identities..Anticommuting matrices and their eigenvalues$dimoperatornamenullT>2$ is not a subspace of $mathcalL(mathbfR^5,mathbfR^4)$Characterizing families of $p^2$ orthogonal $p times p$ unitaries?Gamma matrices and special relativityMatrix anticommuting with four or five Dirac $Gamma$-matrices
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Anticommuting sets of Dirac $gamma$-matrices
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)a problem about the equivament of two vector groups $(I)$ and $(II)$Clifford algebra - Gamma matricesProve two sets span the same subspaceFind a basis for $U+W$ and $Ucap W$Dirac Gamma Matrices identities..Anticommuting matrices and their eigenvalues$dimoperatornamenullT>2$ is not a subspace of $mathcalL(mathbfR^5,mathbfR^4)$Characterizing families of $p^2$ orthogonal $p times p$ unitaries?Gamma matrices and special relativityMatrix anticommuting with four or five Dirac $Gamma$-matrices
$begingroup$
At the end of this webpage, it is said that there exist 6 maximal anticommuting sets each consisting of 5 Dirac $gamma$-matrices. I couldn't find anything more in the book cited there, either.
But what is the relation between these 6 sets? Are they related by unitary transformations or else?
For example, we can think of the following to sets.
$$alpha_0=sigma_zotimestau_z,alpha_1=sigma_xotimestau_0,alpha_2=sigma_yotimestau_0,alpha_3=sigma_zotimestau_x,alpha_4=sigma_zotimestau_y$$
$$beta_0=sigma_zotimestau_0,beta_1=sigma_xotimestau_z,beta_2=sigma_yotimestau_0,beta_3=sigma_xotimestau_x,beta_4=sigma_xotimestau_y$$
linear-algebra matrices clifford-algebras
asked Apr 8 at 19:55
xiaohuamaoxiaohuamao
319111
$endgroup$
add a comment |
$begingroup$
At the end of this webpage, it is said that there exist 6 maximal anticommuting sets each consisting of 5 Dirac $gamma$-matrices. I couldn't find anything more in the book cited there, either.
But what is the relation between these 6 sets? Are they related by unitary transformations or else?
For example, we can think of the following to sets.
$$alpha_0=sigma_zotimestau_z,alpha_1=sigma_xotimestau_0,alpha_2=sigma_yotimestau_0,alpha_3=sigma_zotimestau_x,alpha_4=sigma_zotimestau_y$$
$$beta_0=sigma_zotimestau_0,beta_1=sigma_xotimestau_z,beta_2=sigma_yotimestau_0,beta_3=sigma_xotimestau_x,beta_4=sigma_xotimestau_y$$
linear-algebra matrices clifford-algebras
asked Apr 8 at 19:55
xiaohuamaoxiaohuamao
319111
$endgroup$
add a comment |
$begingroup$
At the end of this webpage, it is said that there exist 6 maximal anticommuting sets each consisting of 5 Dirac $gamma$-matrices. I couldn't find anything more in the book cited there, either.
But what is the relation between these 6 sets? Are they related by unitary transformations or else?
For example, we can think of the following to sets.
$$alpha_0=sigma_zotimestau_z,alpha_1=sigma_xotimestau_0,alpha_2=sigma_yotimestau_0,alpha_3=sigma_zotimestau_x,alpha_4=sigma_zotimestau_y$$
$$beta_0=sigma_zotimestau_0,beta_1=sigma_xotimestau_z,beta_2=sigma_yotimestau_0,beta_3=sigma_xotimestau_x,beta_4=sigma_xotimestau_y$$
linear-algebra matrices clifford-algebras
asked Apr 8 at 19:55
xiaohuamaoxiaohuamao
319111
$endgroup$
At the end of this webpage, it is said that there exist 6 maximal anticommuting sets each consisting of 5 Dirac $gamma$-matrices. I couldn't find anything more in the book cited there, either.
But what is the relation between these 6 sets? Are they related by unitary transformations or else?
For example, we can think of the following to sets.
$$alpha_0=sigma_zotimestau_z,alpha_1=sigma_xotimestau_0,alpha_2=sigma_yotimestau_0,alpha_3=sigma_zotimestau_x,alpha_4=sigma_zotimestau_y$$
$$beta_0=sigma_zotimestau_0,beta_1=sigma_xotimestau_z,beta_2=sigma_yotimestau_0,beta_3=sigma_xotimestau_x,beta_4=sigma_xotimestau_y$$
linear-algebra matrices clifford-algebras
linear-algebra matrices clifford-algebras
asked Apr 8 at 19:55
xiaohuamaoxiaohuamao
319111
asked Apr 8 at 19:55
xiaohuamaoxiaohuamao
319111
edited Apr 9 at 4:09
xiaohuamao
asked Apr 8 at 19:55
xiaohuamaoxiaohuamao
319111
asked Apr 8 at 19:55
xiaohuamaoxiaohuamao
319111
asked Apr 8 at 19:55
xiaohuamaoxiaohuamao
319111
319111
add a comment |
add a comment |
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