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In physics, quantum triviality is the phenomenon in which a classical theory that describes interacting particles, when quantized, becomes a quantum field theory that describes noninteracting free particles. Charge screening can restrict the value of the observable charges that appear in the theory. If the only resulting value of the renormalized charge is zero, the theory is said to be "trivial" or noninteracting.

Modern considerations of triviality are usually formulated in terms of the real-space renormalization group, largely developed by Kenneth Wilson and others. Investigations of triviality are usually performed in the context of lattice gauge theory. A deeper understanding of the physical meaning and generalization of the renormalization process, which goes beyond the dilatation group of conventional renormalizable theories, came from condensed matter physics. Leo P. Kadanoff's paper in 1966 proposed the "block-spin" renormalization group. The blocking idea is a way to define the components of the theory at large distances as aggregates of components at shorter distances.

This approach covered the conceptual point and was given full computational substance in the work of Wilson. The power of Wilson's ideas was demonstrated by a constructive iterative renormalization solution of a long-standing problem, the Kondo problem, in 1974, as well as the preceding seminal developments of his new method in the theory of second-order phase transitions and critical phenomena in 1971.^{[citation needed]}

In more technical terms, let us assume that we have a theory described by a certain function ${\displaystyle Z}$ of the state variables ${\displaystyle \{s_{i}\}}$ and a certain set of coupling constants ${\displaystyle \{J_{k}\}}$. This function may be a partition function, an action, a Hamiltonian, etc. It must contain the whole description of the physics of the system.

Now we consider a certain blocking transformation of the state variables ${\displaystyle \{s_{i}\}\to \{{\tilde {s}}_{i}\}}$. The number of ${\displaystyle {\tilde {s}}_{i}}$ must be less than the number of ${\displaystyle s_{i}}$. Now let us try to rewrite the ${\displaystyle Z}$ function only in terms of the ${\displaystyle {\tilde {s}}_{i}}$. If this is achievable by a certain change in the parameters, ${\displaystyle \{J_{k}\}\to \{{\tilde {J}}_{k}\}}$, then the theory is said to be renormalizable. The most important information in the RG flow are its fixed points. The possible macroscopic states of the system, at a large scale, are given by this set of fixed points. If these fixed points correspond to a free field theory, the theory is said to be trivial.

The first evidence of possible triviality of quantum field theories was obtained in the context of quantum electrodynamics by Lev Landau, Alexei Abrikosov, and Isaak Khalatnikov who found the following relation between the observable charge g_obs and the "bare" charge g₀:

where m is the mass of the particle, and Λ is the momentum cut-off. If g₀ is finite, then g_obs tends to zero in the limit of infinite cut-off Λ.