Abstract
It is taken for granted that bound systems are made of massive constituents that interact through particle exchanges (charged particles interacting via photon exchanges, quarks in elementary particles interacting via gluon exchanges, and nucleons in nuclei interacting via meson exchanges). However, as was recently theoretically found, there exist systems dominated by exchange particles (at least for the zero exchange masses). In these systems, the contribution of massive constituents is negligible. These systems have a relativistic nature (since they are mainly made of massless particles moving at the speed of light), and therefore, they cannot be described by the Schrödinger equation. Though these results were found so far in the simple Wick–Cutkosky model (spinless constituents interacting via the ladder of spinless massless exchanges), the physical ground for their existence seems to be rather general.
Highlights
Bound states have an essentially non-perturbative nature
It is taken for granted that bound systems are made of massive constituents that interact through particle exchanges
A natural question arises: Why, in view of the infinite number of exchanges, are we dealing with a system containing massive constituents, not with a system containing, in addition to massive constituents, an indefinite number of massless exchange particles?
Summary
Bound states have an essentially non-perturbative nature. They appear if the coupling constant exceeds some critical value (for an interaction of a finite radius). With the interaction approximated by a static potential, a few-body system is described by the Schrödinger equation In this way, the intermediate states with many-body exchange particles are cut from the very beginning. If systems of the second type (with many massless exchange particles in the intermediate states) exist, they should be described by a relativistic equation. Since a relativistic approach covers the full domain of momenta, both small and large, it can be applied to the systems of both types simultaneously: (i) the non-relativistic ones, described by the Schrödinger equation—the limiting case of the initial relativistic equation (the hydrogen atom in our case)—and (ii) purely relativistic systems, dominated by exchange particles, which cannot be discovered in the Schrödinger framework. Some technical details of calculating the full norm of the state vector are included in Appendix A
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