mty::gauge Namespace Reference

Namespace containing features concerning gauged groups and gauge choices. More...

Data Structures
class	Choice

Enumerations
enum	GroupType {   U1,   SU,   SO,   Sp,   E6,   E7,   E8,   F4,   G2 }
enum	Type {   NotDefined,   Lorenz,   Feynman,   Unitary }
	Different types of gauge ficing parameter for gauge boson propagators. More...

Functions
std::ostream &	operator<< (std::ostream &fout, GroupType type)

Detailed Description

Namespace containing features concerning gauged groups and gauge choices.

Enumeration Type Documentation

Type

enum mty::gauge::Type

Different types of gauge ficing parameter for gauge boson propagators.

The propagator of a gauge boson is

\[ -i\frac{g_{\mu\nu} - (1-\xi) \frac{p_\mu p_\nu}{p^2 - \xi M^2}}{p^2-M^2}, \]

\( M \) the mass of the particle, and \( p^\mu \) its momentum. The Lorenz gauge corresponds to \( \xi=0\), the propagator then reads

\[ -i\frac{g_{\mu\nu} - \frac{p_\mu p_\nu}{p^2}}{p^2-M^2}. \]

The Feynman gauge corresponds to \( \xi=1\), the propagator then reads

\[ -i\frac{g_{\mu\nu}}{p^2-M^2}. \]

The Unitary gauge corresponds to \( \xi=\infty\), the propagator then reads

\[ -i\frac{g_{\mu\nu} - \frac{p_\mu p_\nu}{M^2}}{p^2-M^2}. \]

Finally, the \( \mathcal{R}_\xi \) gauge does not fix \( \xi \), this corresponds to the choice NotDefined.

Enumerator
NotDefined	\(\xi \) is not fixed
Lorenz	\(\xi = 0\).
Feynman	\(\xi = 1\).
Unitary	\(\xi = \infty\).