Gamma matrices Definition and 58 Threads

  1. R

    Gamma matrices and lorentz algebra

    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...
  2. V

    Notation relating to gamma matrices

    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.
  3. I

    Dimension of the gamma matrices in general dimension

    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}...
  4. B

    Reps of lorentz group and pauli and gamma matrices

    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}...
  5. A

    Majorana representation of Gamma matrices.

    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(...
  6. W

    Proving the Trace of Gamma Matrices with (Anti-)Communtation Rules

    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}) = -...
  7. K

    Proving an Identity Involving Gamma Matrices

    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...
  8. K

    Formal Proof: 4x4 Gamma Matrices in Special Relativity Project

    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...
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