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Grassmann Algebra

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ExploringClifford<strong>Algebra</strong>.nb 26<br />

� Γ p<br />

� Γ p<br />

Γ �Γ<br />

p p<br />

Γ �Γ �Γ<br />

p p p<br />

�Γ p<br />

� ����Γ<br />

�p<br />

† ���� Γp<br />

�<br />

�<br />

†<br />

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p<br />

à �à ��à p p p p<br />

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p p<br />

� ����Γ<br />

�p<br />

†<br />

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���� Γ<br />

†�����Γ<br />

�p<br />

p � p<br />

�<br />

���� ��� p�<br />

is an arbitrary repeated factor, Α m is arbitrary<br />

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� Γ<br />

†����<br />

�Γ<br />

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p � p<br />

�Γ p<br />

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� Α��� ���� Γ � ��1�<br />

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p<br />

mp � ����Α<br />

�<br />

�Γ��� ���� Γ<br />

�m<br />

p�<br />

p<br />

is an arbitrary repeated factor, Α m and Β k<br />

����Α<br />

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†����<br />

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�m<br />

p �<br />

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� Γ<br />

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�m<br />

p �<br />

�<br />

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���à p<br />

are arbitrary<br />

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k�<br />

mp � ����<br />

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k�<br />

p<br />

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mp � ����Α<br />

�<br />

�m<br />

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�<br />

Arbitrary and orthogonal elements<br />

� Γ p<br />

2001 4 26<br />

is arbitrary, Α m and Β k<br />

Α �<br />

m ����Γ<br />

�p<br />

are totally orthogonal<br />

�<br />

� ��� �<br />

k�<br />

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p�<br />

k<br />

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� ��� k�<br />

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� p<br />

Αi ���� Βj � 0<br />

12.33<br />

12.34<br />

12.35<br />

12.36<br />

12.37<br />

12.38<br />

12.39

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