Return to Question

I need to obtain this using package FeynCalc: $$ \begin{align} [\gamma_{0},\gamma_{i}]=& 2 \gamma_{0}\gamma_{i}, \\ [\gamma_{i},\gamma_{0}]=& 2 \gamma_{i}\gamma_{0} , \\ [\gamma_{0},\gamma_{0}]=& 0, \\ \gamma_{0}.\gamma_{i}.\gamma_{0}.\gamma_{i} =& 1 , \\ \gamma_{0}.\gamma_{i}.\gamma_{i}.\gamma_{0} =& -1. \end{align}$$.

My gamma matrices are:

$\gamma_{0}= \lbrace \lbrace 0, \ \ \mathbb{I}_{2\times 2} \rbrace,\lbrace \mathbb{I}_{2\times 2}, \ \ 0 \rbrace \rbrace $

$\gamma_{i}= \lbrace \lbrace 0, \ \ -\sigma^{i} \rbrace,\lbrace \sigma^{i}, \ \ 0 \rbrace \rbrace $

and

$\sigma_{1}=\lbrace \lbrace 0, \ \ 1 \rbrace,\lbrace 1, \ \ 0 \rbrace \rbrace $

$\sigma_{2}=\lbrace \lbrace 0, \ \ -i \rbrace,\lbrace i, \ \ 0 \rbrace \rbrace $

$\sigma_{3}=\lbrace \lbrace 1, \ \ 0 \rbrace,\lbrace 0, \ \ -1 \rbrace \rbrace $

I'm working in D-4 space.

I need to obtain this using package FeynCalc: $$ \begin{align} [\gamma_{0},\gamma_{i}]=& 2 \gamma_{0}\gamma_{i}, \\ [\gamma_{i},\gamma_{0}]=& 2 \gamma_{i}\gamma_{0} , \\ [\gamma_{0},\gamma_{0}]=& 0, \\ \gamma_{0}.\gamma_{i}.\gamma_{0}.\gamma_{i} =& 1 , \\ \gamma_{0}.\gamma_{i}.\gamma_{i}.\gamma_{0} =& -1. \end{align}$$.

My gamma matrices are:

$\gamma_{0}= \lbrace \lbrace 0, \ \ \mathbb{I}_{2\times 2} \rbrace,\lbrace \mathbb{I}_{2\times 2}, \ \ 0 \rbrace \rbrace $

$\gamma_{i}= \lbrace \lbrace 0, \ \ -\sigma^{i} \rbrace,\lbrace \sigma^{i}, \ \ 0 \rbrace \rbrace $

and

$\sigma_{1}=\lbrace \lbrace 0, \ \ 1 \rbrace,\lbrace 1, \ \ 0 \rbrace \rbrace $

$\sigma_{2}=\lbrace \lbrace 0, \ \ -\mathrm i \rbrace,\lbrace \mathrm i, \ \ 0 \rbrace \rbrace $

$\sigma_{3}=\lbrace \lbrace 1, \ \ 0 \rbrace,\lbrace 0, \ \ -1 \rbrace \rbrace $

I'm working in D-4 space.

I need to obtain this using FeynCalc

$[\gamma_{0},\gamma_{i}]= 2 \gamma_{0}\gamma_{i} \\\\$, $[\gamma_{i},\gamma_{0}]= 2 \gamma_{i}\gamma_{0} \\\\$, $[\gamma_{0},\gamma_{0}]= 0$, $\gamma_{0}.\gamma_{i}.\gamma_{0}.\gamma_{i} = 1 $, $\gamma_{0}.\gamma_{i}.\gamma_{i}.\gamma_{0} = -1$ $.

My gamma matrices are:

$\gamma^{0}= \lbrace \lbrace 0, \ \ \mathbb{I}_{2\times 2} \rbrace,\lbrace \mathbb{I}_{2\times 2}, \ \ 0 \rbrace \rbrace $

$\gamma^{i}= \lbrace \lbrace 0, \ \ -\sigma^{i} \rbrace,\lbrace \sigma^{i}, \ \ 0 \rbrace \rbrace $

and

$\sigma^{1}=\lbrace \lbrace 0, \ \ 1 \rbrace,\lbrace 1, \ \ 0 \rbrace \rbrace $

$\sigma^{2}=\lbrace \lbrace 0, \ \ -i \rbrace,\lbrace i, \ \ 0 \rbrace \rbrace $

$\sigma^{3}=\lbrace \lbrace 1, \ \ 0 \rbrace,\lbrace 0, \ \ -1 \rbrace \rbrace $

I'm working in D-4 space.

I need to obtain this using package FeynCalc: $$ \begin{align} [\gamma_{0},\gamma_{i}]=& 2 \gamma_{0}\gamma_{i}, \\ [\gamma_{i},\gamma_{0}]=& 2 \gamma_{i}\gamma_{0} , \\ [\gamma_{0},\gamma_{0}]=& 0, \\ \gamma_{0}.\gamma_{i}.\gamma_{0}.\gamma_{i} =& 1 , \\ \gamma_{0}.\gamma_{i}.\gamma_{i}.\gamma_{0} =& -1. \end{align}$$.

My gamma matrices are:

$\gamma_{0}= \lbrace \lbrace 0, \ \ \mathbb{I}_{2\times 2} \rbrace,\lbrace \mathbb{I}_{2\times 2}, \ \ 0 \rbrace \rbrace $

$\gamma_{i}= \lbrace \lbrace 0, \ \ -\sigma^{i} \rbrace,\lbrace \sigma^{i}, \ \ 0 \rbrace \rbrace $

and

$\sigma_{1}=\lbrace \lbrace 0, \ \ 1 \rbrace,\lbrace 1, \ \ 0 \rbrace \rbrace $

$\sigma_{2}=\lbrace \lbrace 0, \ \ -i \rbrace,\lbrace i, \ \ 0 \rbrace \rbrace $

$\sigma_{3}=\lbrace \lbrace 1, \ \ 0 \rbrace,\lbrace 0, \ \ -1 \rbrace \rbrace $

I'm working in D-4 space.