In models of spontaneous wave-function collapse, why only fermions collapse, not bosons?

TL;DR

Within generalized trace dynamics, the paper analyzes the STM-atom trace Lagrangian written with two inequivalent matrix velocities $Q_1$ and $Q_2$ to explain why spontaneous localization couples only to fermionic degrees of freedom. By computing the trace Hamiltonian via trace-derivative canonical momenta and separating bosonic and fermionic variations, it shows the purely bosonic sector has a self-adjoint Hamiltonian $\mathcal{H}_{BB}$, whereas the fermionic sector carries a purely anti-self-adjoint term $\mathcal{H}_{FF}$, made nontrivial by $\beta_1 \neq \beta_2$. The ASA part of the full Hamiltonian is $\mathcal{H}_{asa} = \tfrac{1}{2}(\mathcal{H}-\mathcal{H}^\dagger) = \tfrac{1}{2}(\mathcal{H}_{BF}-\mathcal{H}_{BF}^\dagger) + \mathcal{H}_{FF}$, ensuring that all ASA contributions involve fermionic variables and vanish in their absence. Consequently, this provides a first-principles mechanism for fermion-only collapse within GTD, while bosonic fields can become classical indirectly through correlations with localized fermions, and connects to CSL-like nonunitary dynamics upon coarse-graining.

Abstract

Objective collapse models are often implemented so that collapse acts only on the fermionic (matter) sector, while bosonic fields do not undergo fundamental collapse. In generalized trace dynamics (GTD), spontaneous localization is expected to arise when the trace Hamiltonian has a significant anti-self-adjoint component. In this note we show, starting from the STM-atom (spacetime-matter atom) trace Lagrangian written in terms of two inequivalent matrix velocities $\dot Q_1$ and $\dot Q_2$, that the purely bosonic subsector admits a self-adjoint Hamiltonian, whereas the fermionic sector carries an intrinsic anti-self-adjoint contribution. The key structural input is that making the trace Lagrangian bosonic requires insertion of two \emph{unequal} odd-grade Grassmann elements $β_1\neq β_2$. Assuming natural adjoint properties for these elements, we compute the trace Hamiltonian explicitly via trace-derivative canonical momenta (with bosonic and fermionic variations treated separately) and isolate the resulting anti-self-adjoint term. This provides a first-principles mechanism, within GTD, for why only fermionic degrees of freedom act as collapse channels.