Abstract It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schrödinger equation are derived from the causal action principle. The dynamics of the statistical operator is described by a deterministic equation of Kossakowski–Lindblad form. Moreover, the quantum state undergoes a dynamical collapse compatible with the Born rule. The effective model has similarities with the continuous spontaneous localization model, but differs from it by a conservation law for the probability integral as well as a non-locality in time on a microscopic length scale ℓ min .Abstract It is shown that, in the non-relativistic limit, causal fermion systems give rise to an effective collapse theory. The nonlinear and stochastic correction terms to the Schrödinger equation are derived from the causal action principle. The dynamics of the statistical operator is described by a deterministic equation of Kossakowski–Lindblad form. Moreover, the quantum state undergoes a dynamical collapse compatible with the Born rule. The effective model has similarities with the continuous spontaneous localization model, but differs from it by a conservation law for the probability integral as well as a non-locality in time on a microscopic length scale ℓ min .

arXiv:2405.19254Journal of Physics A Mathematical and TheoreticalSep 2, 20243 citations

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

Tejinder P. Singh

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.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.

physics.gen-phCross-listedarXiv:2602.15044Feb 5, 20260 citations

FERMIONIC MODELS WITH SELF-INTERACTION

WORLD SCIENTIFIC eBooksAug 1, 19910 citations

Probabilities of many-body decays of fermions

K. R. Nasriddinov, N.A. Sarikov

Uzbekiston Fizika ZhurnaliJan 1, 19920 citations

In Models of Spontaneous Wave-Function Collapse, Why Only Fermions Collapse, Not Bosons?

Tejinder P. Singh

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 Q̇1 and Q̇2, 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 unequal odd-grade Grassmann elements β1 ≠ β2. 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.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 Q̇1 and Q̇2, 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 unequal odd-grade Grassmann elements β1 ≠ β2. 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.

Feb 11, 20261 citation

\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.