We study the dynamics of multiparticle Carroll-Schrödinger (C-Sch) quantum systems in $1+1$ dimensions, where $x$ acts as the evolution variable and $t$ as the configuration coordinate. We derive the $N$-body theory on equal-$x$ slices as the post-Carrollian limit of a relativistic multitime Klein-Gordon model, introducing temporal interactions via minimal coupling to the temporal energy operators. An $x$-dependent gauge transformation maps this to an equivalent description with explicit many-body potentials, illustrated by a temporal coupled-oscillator model that exhibits synchronization. Adopting a complementary spatial viewpoint with a static potential $U_{\mathrm{tot}}(\mathbf{x})$, we show that the evolution is driven by the collective force ${\sum }_j{\partial }_{x_j}{U}_{\mathrm{tot}}$. For any translation-invariant interaction (such as a regularized Coulomb potential), these internal forces cancel, rendering the collective dynamics free and highlighting post-Carrollian ultralocality. We also construct coordinate duality mapping separable Schrödinger Hamiltonians to C-Sch generators via Schwarzian derivatives. Exchange symmetry is formulated in the time domain, yielding temporal bunching for bosons and antibunching for fermions via the second-order coherence function $g^{(2)}(t,t^{\prime })$. In second quantization, the contact limit yields a temporal derivative cubic-quintic nonlinear Schrödinger equation with a theoretically fixed nonlinearity coefficient $\beta =-3/16$. Finally, by coupling canonical pairs to external scalar and gauge fields, we identify an isomorphism with one-dimensional current density functional theory, outlining a post-Carrollian Hohenberg-Kohn mapping and Kohn-Sham scheme.

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• Classical solutions in field theory
• Dark energy
• Dark matter
• Particle dark matter
• Particle interactions
• Many-body techniques