  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. 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. 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.
