Vevsfrakopling

Vevsfrakopling is a term used in theoretical physics to describe a class of couplings that arise when a scalar field acquires a vacuum expectation value (vev) and interacts with other fields organized under representations of a Lie algebra, often labeled in fraktur notation. The word blends the concept of a vacuum expectation value with the idea of couplings (oppling) and is encountered primarily in niche or informal discussions of symmetry breaking and group theory.

Conceptually, vevsfrakopling refers to the set of effective interaction terms that are generated by a background vev and controlled by the structure of the underlying Lie algebra. When a field φ develops a vev, ⟨φ⟩, it selects directions in internal space and induces mixings and mass terms for other fields transforming under related representations. The resulting couplings are governed by how the fields transform under the g-algebra and by the components of the vev in that algebra, often represented through generators written in fraktur style.

Formally, if φ transforms in a representation R of a gauge or flavor group with Lie algebra g, and ⟨φ⟩ = v^a T^a with T^a denoting the generators (often written in fraktur), then interactions with fermions ψ in a representation R_f can yield effective terms proportional to v^a and the corresponding representation matrices. This illustrates vevsfrakopling as a way to organize vev-induced couplings using the algebraic structure of the symmetry.

Applications and discussion typically appear in beyond-Standard-Model model-building, where flavor and symmetry-breaking patterns are explored. The term is not widely standardized; many discussions describe the same physics using vacuum expectation values, Yukawa couplings, and explicit symmetry-breaking terms instead of a distinct designation.

See also: vacuum expectation value, spontaneous symmetry breaking, Yukawa coupling, Lie algebra, fraktur notation, flavor symmetry.