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  About Majorana spinor 1 form

+ 1 like - 0 dislike
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I am currently studying some basic materials about Majorana spinor 1 form.

I know usual (0-form) Majorana spinor very well(i guess). They satisfy the ψc=ψ for majoran spinor ψ and from them we can do some computation as follows ¯λχ=¯χλ¯λγμχ=¯χγμλ

Deriving above formula one use ψc=ψ and λaχb=χbλa. and so on.

Here come back to the problem, for Majorana spinor 1 form, only surviving form of majorana spinor is known as ¯ψγaψ0 and ¯ψγabψ0. From deriving above things i got stucked.


I think my main problem is the lack of concept for Majorna spinor 1 form

First usual spinor 1 form that i know is A=Aμdxμ

In that sense i can do for Majorana spinor 1 form ψ=ψμdxμ

What i want to know is for 1-form Majorna spinor case is still grassman property holds? i.e
Ψχ=χΨ

or it only holds for coefficient ψμ, χμ for one form? i.e for Ψ=ψμdxμ, χ=χμdxμ ψμχν=χνψμ

I know for the wedge product of p and q form gives w(p)w(q)=(1)pqw(q)w(p)


What i really want to do is following derivation for Majorna spinor 1 form ¯Ψγ5Ψ=0

¯Ψγ5Ψ=Ψa(Cγ5)abΨb=ΨaΨb(Cγ5)ab=(?)ΨbΨa(Cγ5)ab

Does the sign holds?

I can do the other leftover derivation except above parts.
If you know something please let me learn from you.

This post imported from StackExchange Physics at 2015-05-14 21:01 (UTC), posted by SE-user phy_math
asked May 10, 2015 in Theoretical Physics by phy_math (185 points) [ no revision ]
retagged May 14, 2015

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