We study the dynamics of multiparticle Carroll-Schrödinger (CS) 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 Carrollian limit of a relativistic multi-time 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
Utot(x), we show that the evolution is driven by the collective force
∑j∂xjUtot; for any translation-invariant interaction (such as a regularized Coulomb potential), these internal forces cancel, rendering the collective dynamics free and highlighting Carrollian ultralocality. We also construct a coordinate duality mapping separable Schrödinger Hamiltonians to CS 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′). In second quantization, the contact limit yields a temporal derivative cubic--quintic nonlinear Schrödinger equation with a theoretically fixed nonlinearity coefficient
β=−3/16. Finally, by coupling canonical pairs to external scalar and gauge fields, we establish an isomorphism with one-dimensional current-density functional theory, outlining a Carrollian Hohenberg-Kohn mapping and Kohn-Sham scheme.
A bstract We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the general constraints of the quantum group symmetry, given by Ward identities, that correlation functions of the theory should satisfy. We also show that generators of the symmetry can be represented by topological lines with some novel properties. We then discuss a particular example of U q ( sl 2 ) symmetric CFT, which we solve using bootstrap techniques and relying on the symmetry. We finally show strong evidence that for a special value of q a subsector of this theory reproduces the fermionic formulation of the Ising model. This suggests that a quantum group can act on local operators as well, however, it generically transforms them into non-local ones.
In this paper we give a derivation of the virial expansion and some of its generalizations. Our derivation is based on the generating functional which defines a representation of the density operator ρ (x) in a nonrelativistic local current algebra. The virial expansion results from solving a functional differential equation for this quantity. We exploit the well-known analogy between quantum field theory and classical statistical mechanics to explore the use of the virial expansion in Euclidean quantum field theory. Specifically, we show that the virial expansion can be used to derive Feynman’s rules and to provide a perturbation expansion about a static ultralocal model. The latter is worked out in detail in the case of a free neutral scalar model, and outlined in the case of a λφ4 model.
It has been discussed earlier that ( weak quasi-) quantum groups allow for conventional interpretation as internal symmetries in local quantum theory. From general arguments and explicit examples their consistency with (braid-) statistics and locality was established. This work addresses to the reconstruction of quantum symmetries and algebras of field operators. For every algebra A of observables satisfying certain standard assumptions, an appropriate quantum symmetry is found. Field operators are obtained which act on a positive definite Hilbert space of states and transform covariantly under the quantum symmetry. As a substitute for Bose/Fermi (anti-) commutation relations, these fields are demonstrated to obey local braid relation. Contents 1 Introduction 1 2 The Notion of Quantum Symmetry 5 3 Algebraic Methods for Field Construction 9 3.1 Observables and superselection sectors in local quantum field theory . . . . 10 3.2 Localized endomorphisms and fusion structure . . . . . ....
According to the standard classification of conformal quantum field theory (CQFT) in two dimensions, the massless continuum limit of the O(2) model at the Kosterlitz-Thouless transition point should be given by the massless free scalar field; in particular the Noether current of the model should be proportional to (the dual of) the gradient of the massless free scalar field, reflecting a symmetry enhanced from O(2) to $\mathrm{O}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{}\mathrm{O}(2)$. More generally, the massless continuum limit of a spin model with a symmetry given by a Lie group
G should have an enhanced symmetry $G\ifmmode\times\else\texttimes\fi{}G$. We point out that the arguments leading to this conclusion contain two serious gaps: (i) the possibility of ``nontrivial local cohomology'' and (ii) the possibility that the current is an ultralocal field. For the two-dimensional O(2) model we give analytic arguments that rule out the first possibility and use numerical methods to dispose of the second one. We conclude that the standard CQFT predictions appear to be borne out in the O(2) model, but give an example where they would fail. We also point out that all our arguments apply equally well to any
G symmetric spin model, provided it has a critical point at a finite temperature.