Physlib

Physlib.Relativity.Fermions.Weyl.DualRightHanded

Dual right handed Weyl fermions

In this file we define dual right handed Weyl fermions. These sit in the dual-conjugate representation of `SL(2,ℂ)`, and we consider them to have down indices `ψ_\dot α}` with `α = 1,2`.

Underlying module structure

Basis

Representation

3 declarations

definition

Dual right-handed Weyl fermions C2\simeq \mathbb{C}^2

The equivalence `Fermion.DualRightHandedWeyl.toFin2ℂFun` defines an isomorphism between the space of dual right-handed Weyl fermions and the complex vector space C2\mathbb{C}^2, represented as the type of functions Fin 2C\text{Fin } 2 \to \mathbb{C}. This identifies the specific fermion structure with its underlying coordinate representation.

instance

`DualRightHandedWeyl` is an additive commutative monoid

The space of dual right-handed Weyl fermions, which is defined as a wrapper around C2\mathbb{C}^2, is equipped with the structure of an additive commutative monoid. This means that for any two dual right-handed Weyl fermions, there is a well-defined addition operation that is associative and commutative, and there exists a zero element that acts as the additive identity.

instance

Additive commutative group of dual right-handed Weyl fermions

The space of dual right-handed Weyl fermions is equipped with the structure of an additive commutative group. This defines the operations of addition, negation, and the zero element for these spinors, corresponding to the standard vector space operations on C2\mathbb{C}^2.