Abelian Constructivist Lagrangian

Constructivist lagrangian propiates a diverse approach to field theory. Introduce the set action. Consider fields families under a same symmetry group. The resulting fields set extends the standard atomist field theory to a whole field theory. An associative physics is proposed. The grouping physics. The relationship between the part and the whole is considered. A third quantum type beyond Planck granularity and quantum mechanics wave-particle is obtained. The quantum inserted in the whole. Differentiated energy packets are formed. A quantum system is constituted. The abelian grouping physics is considered. The simplest whole unity. Set action in terms of U(1) symmetry. The correspondent constructivist lagrangian is studied. A new type of individuation called whole quantum is derived.An abelian quantum system is constituted. The usual atomist gauge symmetry is preserved, but, constructivist properties are generated. Quantum system with own norm is a necessary theoretical argument. More is different, once time said P.W. Anderson. Physics is challenged to make the passage from an isolated particle to a quantum system. A theory to describe the physics of part in the whole. A challenge to be interpreted under gauge symmetry. A symmetry of difference is proposed. Quantum diversities enlarging the meanings of interaction, induction, connectivity. A quantum system is introduced. Its elementarity is identified as a third quantum type. It is called whole quantum or variety. This quantum of a many particles system appears with a new physicality. The correspondingset action derives antireductionist physical laws under gauge symmetry. Ruled by associativity, set transformation, evolution. Associativitity providing quantum under set, diversity, interdependence, nonlinearity, chance. Set transformations performing a whole determinism with directive conducted by gauge parameter and circumstances under lagrangian free coefficients. Generating a set physics with growth, evolution, emergence, complexity. An evolving quantum transforming their quantum numbers. The abelian constructivist lagrangian is explored. A quantum system assembled by fields families and gauge scalars is performed. It arises an environmental physics. Gauge scalars form substrutures with realities and potentialities. The volume of circumstances for each gauge scalar is calculated. Nonvirtual relationships are derived. Physical entities as masses, charges, coupling constants are expressed under constructivist properties. Functionalities will lead them to a physical behaviour beyond four interactions.