Gamma matrices Definition and 62 Threads

I'm reading an article (http://prb.aps.org/abstract/PRB/v82/i4/e045122) but I have some problems understanding certain definitions. The authors have introduced a basis of certain bands (four) and then continue to give the transformation matrices of the symmetry operators. One (rotation) of them...

Dear guys, I know that gamma matrices have some relations, like \gamma^0{\gamma^\mu}^\dagger\gamma^0 = \gamma^\mu \quad---(*) And I am wondering if this is representation independent? Consider, S\gamma^0S^{-1}S{\gamma^\mu}^\dagger S^{-1}S\gamma^0 S^{-1} = S\gamma^\mu S^{-1}...

Hi all, I'm interested in proving/demonstrating/understanding why the Dirac gamma matrices, plus the associated tensor and identity, form a complete basis for 4\times4 matrices. In my basic QFT course, the Dirac matrices were introduced via the Dirac equation, and we proved various...

I'm trying to show that the generators of the spinor representation: M^{\mu \nu}=\frac{1}{2}\sigma^{\mu \nu}=\frac{i}{4}[\gamma^\mu,\gamma^\nu] obey the Lorentz algebra: [M^{\mu \nu},M^{\rho \sigma}]=i(\delta^{\mu \rho}M^{\nu \sigma}-\delta^{\nu \rho}M^{\mu \sigma}+\delta^{\nu \sigma}M^{\mu...

Hi My QFT course assumes the following notation for gamma matrices: \gamma ^{\mu_1 \mu_2 \mu_3 \mu_4} = {\gamma ^ {[\mu_1}}{\gamma ^ {\mu_2}}{\gamma ^ {\mu_3}}{\gamma ^ {\mu_4 ]}} what does the thing on the right hand side actually mean? Its seems to be a commutator of some sort.

Dear guys, I read a derivation of the dimension of gamma matrices in a d dimension space, which I don't quite understand. First of all, in d dimension, where d is even. One assumes the dimension of gamma matrices which satisfy \{ \gamma^\mu , \gamma^\nu \} = 2\eta^{\mu\nu}...

I'm very confused By performing a lorentz transformation on a spinor \psi\rightarrow S(\Lambda)\psi(\Lambda x) and imposing covariance on the Dirac equation i\gamma^{\mu}\partial_{\mu}\psi=0 we deduce that the gamma matrices transform as S(\Lambda)\gamma^{\mu}...

It is well known that at times we do need explicit representations for the Dirac gamma matrices while doing calculations with fermions. Recently I found two different expressions for Majorana representation for the gamma matrices. In one paper, the form used is: \gamma_{0} = \left(...

Homework Statement Show that tr(\gamma^{\mu}\gamma^{\nu}\gamma^{5}) = 0 Homework Equations (anti-)commutation rules for the gammas, trace is cyclic The Attempt at a Solution I can do tr(\gamma^{\mu}\gamma^{\nu}\gamma^{5}) = -tr(\gamma^{\mu}\gamma^{5}\gamma^{\nu}) = -...

Hello everybody, I have to calculate the matrix element of the process gg-->ttbar-->lnub lnub (ttbar dileptonic decay) using FORM. I have three feynman dyagrams for such a process. When I calculate the interference term i have as output thousands of terms with Levi civita tensors inside (but...

Greetings, I've been asked to prove the following identity tr(\gamma^{\mu} \gamma^{\nu} \gamma^{\rho} \gamma^{\sigma}) = 4 (\eta ^{\mu \nu} \eta ^{\rho \sigma} - \eta ^{\mu \rho} \eta ^{\nu \sigma} + \eta ^{\mu \sigma} \eta ^{\nu \rho}) I know that tr(\gamma^{\mu} \gamma^{\nu}) = 4...

Hi everyone, From the condition: \gamma_{\mu}\gamma_{\nu}+\gamma_{\nu}\gamma_{\mu} = 2g_{\mu\nu} how does one formally proceed to show that the objects \gamma_{\mu} must be 4x4 matrices? I unfortunately know very little about Clifford algebras, and for this special relativity project...