- #1
LCSphysicist
- 645
- 161
- Homework Statement
- ...
- Relevant Equations
- ...
Suppose i have a term like this one (repeated indices are being summed)
$$x = \psi^a C_{ab} \psi^b$$
Such that ##C_{ab} = - C_{ba}##, and ##\{\psi^a,\psi^b\}=0##. How do i evaluate the derivative of this term with respect to ##\psi_r##?
I mean, my attempt g oes to here
$$\frac{\partial x}{\partial \psi_r} = C_{rb} \psi^b + \psi^r C_{ar}$$
But, i think this is zero!!, isnt? Ok, maybe we can't change a and b in ##x## because we have the anticommuting property of psi, but since in the term above we have one psi for each term, i can't see a problem in change a to b, using the C antisymmetry property and getting 0.
What is wrong?
$$x = \psi^a C_{ab} \psi^b$$
Such that ##C_{ab} = - C_{ba}##, and ##\{\psi^a,\psi^b\}=0##. How do i evaluate the derivative of this term with respect to ##\psi_r##?
I mean, my attempt g oes to here
$$\frac{\partial x}{\partial \psi_r} = C_{rb} \psi^b + \psi^r C_{ar}$$
But, i think this is zero!!, isnt? Ok, maybe we can't change a and b in ##x## because we have the anticommuting property of psi, but since in the term above we have one psi for each term, i can't see a problem in change a to b, using the C antisymmetry property and getting 0.
What is wrong?
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