Theories are considered in which each interacting field possesses a definite spin (theories of class A). It is shown that the conservation laws of baryon charge, strangeness, isotopic spin, and electric charge are deeply connected with the space-time property of the vector spin-1 fields—the property of possessing a definite spin. So, the existence of truly neutral fields of spin 1 (e.g., photon or ω-meson) generates invariances corresponding to the conservation of additive quantum numbers (e.g., electric charge, baryon charge or strangeness). The existence of charged spin-1 fields (e.g., ϱ-meson) leads to invariances of the isotopic type etc. The proof proceeds by analyzing the most general local relativistically invariant Lagrangian for an arbitrary system of any number of interacting fields of spins 1, 1 2 , and 0. The only restriction accepted is the dimensionlessness of coupling constants. In the theories of class A each interacting massive vector field must satisfy the Lorentz condition which singles out spin 1 and is closely connected with the Lorentz inhomogeneous group. For zero-mass vector fields, instead of this, an arbitrariness of their 4-divergences is required. As a consequence, matrices constructed out of the coupling constants must constitute representations of the Lie algebras manifesting the abovementioned symmetry properties. The coupling constants for the vector field self-interaction are proved to be structure constants of the algebra.