FeynCalc manual (development version)

DiracSpinorNormalization

DiracSpinorNormalization is an option for SpinorChainEvaluate, DiracSimplify and other functions. It specifies the normalization of the spinor inner products $\bar{u}(p) u(p)$ and $\bar{v}(p) v(p)$. Following values are supported:

• "Relativistic" - this is the standard value corresponding to $\bar{u}(p) u(p) = 2 m$, $\bar{v}(p) v(p) = - 2 m$.

• "Rest" - this sets $\bar{u}(p) u(p) = 1$, $\bar{v}(p) v(p) = - 1$.

• "Nonrelativistic" - this sets $\bar{u}(p) u(p) = \frac{m}{p^0}$, $\bar{v}(p) v(p) = - \frac{m}{p^0}$.

See also

Overview, DiracSimplify, SpinorChainEvaluate.

Examples

SpinorUBar[p, m] . SpinorU[p, m] 
 
DiracSimplify[%]

$$\bar{u}(p,m).u(p,m)$$

$$2 m$$

SpinorUBar[p, m] . SpinorU[p, m] 
 
DiracSimplify[%, DiracSpinorNormalization -> "Rest"]

$$\bar{u}(p,m).u(p,m)$$

$$1$$

SpinorUBar[p, m] . SpinorU[p, m] 
 
DiracSimplify[%, DiracSpinorNormalization -> "Nonrelativistic"]

$$\bar{u}(p,m).u(p,m)$$

$$\frac{m}{p^0}$$