Conventions and Formulae

Units

We use natural units, $[\hslash ]=[c]=1$

Metric

$x^{\mu }=(ct,\vec{x})p^{\mu }=(\frac{E_p}{c},\vec{p})$

where $\mu =0,1,2,3$ are the indices (temporal and spatial) corresponding to $t,x,y,z$.

• Minkowski Metric,

-1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1 \end{pmatrix}$$ such that $$x_\mu=\eta_{\mu \nu}x^\nu=(-ct,\vec{x})$$ ## Partial Derivatives $$\partial_x \implies \frac{\partial}{\partial x}$$ ## Dirac Delta Function $$\int_{-\infty}^{\infty}dke^{ikx}=2\pi\delta(x)$$ $$\int_{-\infty}^{\infty}d^nke^{ikx}=(2\pi)^n\delta^{(n)}(x)$$ ## Commutators - $$[A,B]=AB-BA$$ - $$[A,BC]=[A,B]C + B[A,C]$$ - $$\{A,B\} = AB+BA\:\:(called \:the\:anti-commutator)$$