Final answer:
The helicity formalism and classical formalism in group representation theory are both constructed from the irreducible representations of the Poincaré group. The helicity formalism describes the spin state of a particle in terms of its projection along the direction of its momentum, particularly useful for massless particles. The classical formalism describes particles using the more general notion of spin.
Step-by-step explanation:
Group representation theory is used to describe the transformation properties of physical systems under the symmetry operations of a group.
In the context of particle physics, specifically the Poincaré group, helicity formalism and the classical formalism are both constructed from the irreducible representations of the group.
The helicity formalism is a way to describe the spin state of a particle in terms of its projection along the direction of its momentum.
It is particularly useful for massless particles, where the concept of helicity (spin projection) is well-defined.
The classical formalism, on the other hand, describes particles using the more general notion of spin.
The link between the two formalisms comes from the fact that the irreducible representations of the Poincaré group can be classified into two types: those that have a well-defined helicity (for massless particles) and those that do not.
The helicity formalism focuses on the former, while the classical formalism encompasses both types.