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## Main Question or Discussion Point

**"No-Interaction" Theorem**

THEOREM. "No-Interaction" Theorem.

Suppose we seek a many-particle direct-interaction theory with the

following properties:

1. the theory is Lorentz invariant,

2. the theory is based on a Hamiltonian dynamics, and

3. the theory is based on independent (canonical) particle variables.

Then such a theory is only compatible with noninteracting particles.

"No-Interaction" Theorem in Classical Relativistic Mechanics

http://prola.aps.org/abstract/PR/v182/i5/p1397_1

Relativistic particle dynamics—Lagrangian proof of the no-interaction theorem

http://prola.aps.org/abstract/PRD/v30/i10/p2110_1

G. Marmo and N. Mukunda

Instituto di Fisica Teorica, Universita di Napoli, Napoli, Italy and Istituto Nazionale di Física Nucleare, Gruppo Teorico, Sezione di Napoli, Napoli, Italy

E. C. G. Sudarshan

Center for Particle Theory, Department of Physics, The University of Texas at Austin, Austin, Texas 78712

Received 28 November 1983

An economical proof is given, in the Lagrangian framework, of the no-interaction theorem of relativistic particle mechanics. It is based on the assumption that there is a Lagrangian, which if singular is allowed to lead at most to primary first-class constraints. The proof works with Lagrange rather than Poisson brackets, leading to considerable simplifications compared to other proofs.