Electromagnetic and weak current operators for interacting systems should properly commute with the Poincaré generators and satisfy Hermiticity. The electromagnetic current should also satisfy P and T covariance and continuity equation. In frontform dynamics the current can be constructed from auxiliary operators, defined in a Breit frame where initial and final three-momenta of the system are directed along the z axis. Poincaré covariance constraints reduce for auxiliary operators to the ones imposed only by kinematical rotations around the z axis; while Hermiticity requires a suitable behaviour of the auxiliary operators under rotations by π around the x or y axes. Applications to deep inelastic structure functions and electromagnetic form factors are discussed. Elastic and transition form factors can be extracted without any ambiguity and in the elastic case the continuity equation is automatically satisfied, once Poincaré, P and T covariance, together with Hermiticity, are imposed.
The modular analog of representations of the so(1,4) algebra for a system of two spinless particles is considered in the framework of approach (proposed by the author earlier), in which physical systems are described by the elements of a linear space over a finite field, and operators of physical quantities by linear operators in this space. The eigenvalues of the free mass operator and corresponding eigenvectors are found. It is shown that if the finite field under consideration satisfies some properties then the particles necessarily interact with each other. The corresponding interaction is universal, since it is fully defined by the masses of particles and characteristics of the finite field. The formula for the kernel of the interaction operator is derived, but since the kernel is defined by the sum over the Galois field and this sum cannot be calculated explicitly, then it cannot be determined how far the above interaction manifests itself in the usual conditions.
In standard Poincare and anti de Sitter SO(2,3) invariant theories, antiparticles are related to negative energy solutions of covariant equations while independent positive energy unitary irreducible representations (UIRs) of the symmetry group are used for describing both a particle and its antiparticle. Such an approach cannot be applied in de Sitter SO(1,4) invariant theory. We argue that it would be more natural to require that (*) one UIR should describe a particle and its antiparticle simultaneously. This would automatically explain the existence of antiparticles and show that a particle and its antiparticle are different states of the same object. If (*) is adopted then among the above groups only the SO(1,4) one can be a candidate for constructing elementary particle theory. It is shown that UIRs of the SO(1,4) group can be interpreted in the framework of (*) and cannot be interpreted in the standard way. By quantizing such UIRs and requiring that the energy should be positive in the Poincare approximation, we conclude that i) elementary particles can be only fermions. It is also shown that ii) C invariance is not exact even in the free massive theory and iii) elementary particles cannot be neutral. This gives a natural explanation of the fact that all observed neutral states are bosons.
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