The mystery of relationship of mechanics and field in the many-body quantum world

TL;DR

This paper critiques the misuse of quantum field methods in quantum mechanics, proposing a new framework that corrects foundational errors and offers fresh insights into symmetry breaking, superconductivity, and quasiparticle concepts.

Contribution

It introduces a novel approach separating field and mechanical patterns, leading to revised models for symmetry breaking and quasiparticle behavior in many-body quantum systems.

Findings

Identifies critical errors in applying field methods to quantum mechanics.

Proposes a new form of Bohr's complementarity at the composite system level.

Reveals a unified view of Jahn-Teller effect and superconductivity as symmetry-breaking phenomena.

Abstract

We have revealed three fatal errors incurred from a blind transferring of quantum field methods into the quantum mechanics. This had tragic consequences because it produced crippled model Hamiltonians, unfortunately considered sufficient for a description of solids including superconductors. From there, of course, Fr\"ohlich derived wrong effective Hamiltonian, from which incorrect BCS theory arose. 1) Mechanical and field patterns cannot be mixed. Instead of field methods applied to the mechanical Born-Oppenheimer approximation we have entirely to avoid it and construct an independent and standalone field pattern. This leads to a new form of the Bohr's complementarity on the level of composite systems. 2) We have correctly to deal with the center of gravity, which is under the field pattern "materialized" in the form of new quasipartiles - rotons and translons. This leads to a new type of relativity of internal and external degrees of freedom and one-particle way of bypassing degeneracies (gap formation). 3) The possible symmetry cannot be apriori loaded but has to be aposteriori obtained as a solution of field equations, formulated in a general form without translational or any other symmetry. This leads to an utterly revised view of symmetry breaking in non-adiabatic systems, namely Jahn-Teller effect and superconductivity. These two phenomena are synonyms and share a unique symmetry breaking.