Showing papers on "Conservation law published in 2019"
Proceedings Article•
04 Jun 2019
TL;DR: Inspiration from Hamiltonian mechanics is drawn to train models that learn and respect exact conservation laws in an unsupervised manner, and this model trains faster and generalizes better than a regular neural network.
Abstract: Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models that learn and respect exact conservation laws in an unsupervised manner. We evaluate our models on problems where conservation of energy is important, including the two-body problem and pixel observations of a pendulum. Our model trains faster and generalizes better than a regular neural network. An interesting side effect is that our model is perfectly reversible in time.
488 citations
TL;DR: In this paper, the authors use adversarial training to extract features of flow dynamics in an unsupervised manner and predict future flow fields at future occasions based on information on flow fields from previous occasions.
Abstract: Unsteady flow fields over a circular cylinder are used for training and then prediction using four different deep learning networks: generative adversarial networks with and without consideration of conservation laws; and convolutional neural networks with and without consideration of conservation laws. Flow fields at future occasions are predicted based on information on flow fields at previous occasions. Predictions of deep learning networks are made for flow fields at Reynolds numbers that were not used during training. Physical loss functions are proposed to explicitly provide information on conservation of mass and momentum to deep learning networks. An adversarial training is applied to extract features of flow dynamics in an unsupervised manner. Effects of the proposed physical loss functions and adversarial training on predicted results are analysed. Captured and missed flow physics from predictions are also analysed. Predicted flow fields using deep learning networks are in good agreement with flow fields computed by numerical simulations.
172 citations
TL;DR: In this paper, the Wigner function for massive particles in an inhomogeneous electromagnetic field to leading order in the Planck constant was calculated and a generalized Boltzmann equation was derived.
Abstract: We calculate the Wigner function for massive $\mathrm{spin}\text{\ensuremath{-}}1/2$ particles in an inhomogeneous electromagnetic field to leading order in the Planck constant $\ensuremath{\hbar}$. Going beyond leading order in $\ensuremath{\hbar}$ we then derive a generalized Boltzmann equation in which the force exerted by an inhomogeneous electromagnetic field on the particle dipole moment arises naturally. Furthermore, a kinetic equation for this dipole moment is derived. Carefully taking the massless limit we find agreement with previous results. The case of global equilibrium with rotation is also studied. Finally, we outline the derivation of fluid-dynamical equations from the components of the Wigner function. The conservation of total angular momentum is promoted as an additional fluid-dynamical equation of motion. Our framework can be used to study polarization effects induced by vorticity and magnetic field in relativistic heavy-ion collisions.
146 citations
TL;DR: A general group theory based formalism for harmonic generation from dilute and dense media, yielding new symmetries and selection rules that are not explained by currently known conservation laws.
Abstract: Symmetry is one of the most generic and useful concepts in science, often leading to conservation laws and selection rules. Here we formulate a general group theory for dynamical symmetries (DSs) in time-periodic Floquet systems, and derive their correspondence to observable selection rules. We apply the theory to harmonic generation, deriving closed-form tables linking DSs of the driving laser and medium (gas, liquid, or solid) in (2+1)D and (3+1)D geometries to the allowed and forbidden harmonic orders and their polarizations. We identify symmetries, including time-reversal-based, reflection-based, and elliptical-based DSs, which lead to selection rules that are not explained by currently known conservation laws. We expect the theory to be useful for ultrafast high harmonic symmetry-breaking spectroscopy, as well as in various other systems such as Floquet topological insulators. It is commonly assumed that a complete theory for selection rules in optical nonlinear harmonic generation was developed previously. Here, the authors present more general group theory based formalism for harmonic generation from dilute and dense media, yielding new symmetries and selection rules.
144 citations
TL;DR: By unambiguously demonstrating that the KPZ scaling function describes magnetization dynamics in the SU(2) symmetric Heisenberg spin chain, it is shown, for the first time, that this is so.
Abstract: Equilibrium spatiotemporal correlation functions are central to understanding weak nonequilibrium physics. In certain local one-dimensional classical systems with three conservation laws they show universal features. Namely, fluctuations around ballistically propagating sound modes can be described by the celebrated Kardar-Parisi-Zhang (KPZ) universality class. Can such a universality class be found also in quantum systems? By unambiguously demonstrating that the KPZ scaling function describes magnetization dynamics in the SU(2) symmetric Heisenberg spin chain we show, for the first time, that this is so. We achieve that by introducing new theoretical and numerical tools, and make a puzzling observation that the conservation of energy does not seem to matter for the KPZ physics.
138 citations
TL;DR: In this article, the semi-inverse method is used to establish a variational formulation for the thin-film equation, and a detailed derivation process is given, a special skill for construction of a heuristic trial-functional is elucidated.
Abstract: Thin film arises in various applications from electrochemistry to nano devices, many mathematical tools were adopted to study the problem, e.g. Lie symmetries and conservation laws, however, the variational approach is rare. This paper shows that the semi-inverse method is an effective approach to establishment of a variational formulation for the thin film equation. A detailed derivation process is given, a special skill for construction of a heuristic trial-functional is elucidated.
127 citations
TL;DR: In this article, it was shown that the geometry of a black hole horizon can be described as a Carrollian geometry emerging from an ultra-relativistic limit where the near-horizon radial coordinate plays the role of a virtual velocity of light tending to zero.
Abstract: We show that the geometry of a black hole horizon can be described as a Carrollian geometry emerging from an ultra-relativistic limit where the near-horizon radial coordinate plays the role of a virtual velocity of light tending to zero. We prove that the laws governing the dynamics of a black hole horizon, the null Raychaudhuri and Damour equations, are Carrollian conservation laws obtained by taking the ultra-relativistic limit of the conservation of an energy-momentum tensor; we also discuss their physical interpretation. We show that the vector fields preserving the Carrollian geometry of the horizon, dubbed Carrollian Killing vectors, include BMS-like supertranslations and superrotations and that they have non-trivial associated conserved charges on the horizon. In particular, we build a generalization of the angular momentum to the case of non-stationary black holes. Finally, we discuss the relation of these conserved quantities to the infinite tower of charges of the covariant phase space formalism.
121 citations
Posted Content•
TL;DR: In this article, the authors draw inspiration from Hamiltonian mechanics to train models that learn and respect exact conservation laws in an unsupervised manner and evaluate their models on problems where conservation of energy is important, including two-body problems and pixel observations of a pendulum.
Abstract: Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models that learn and respect exact conservation laws in an unsupervised manner. We evaluate our models on problems where conservation of energy is important, including the two-body problem and pixel observations of a pendulum. Our model trains faster and generalizes better than a regular neural network. An interesting side effect is that our model is perfectly reversible in time.
81 citations
TL;DR: In this paper, the authors consider the fluctuations of the net-baryon density which becomes the slow, critical mode near the critical point and study the real-time dynamics of the fluctuations.
Abstract: A quantitatively reliable theoretical description of the dynamics of fluctuations in nonequilibrium is indispensable in the experimental search for the QCD critical point by means of ultrarelativistic heavy-ion collisions. In this paper we consider the fluctuations of the net-baryon density which becomes the slow, critical mode near the critical point. Due to net-baryon number conservation the dynamics is described by the fluid dynamical diffusion equation, which we extend to contain a white noise stochastic current. Including nonlinear couplings from the 3d Ising model universality class in the free energy functional, we solve the fully interacting theory in a finite size system. We observe that purely Gaussian white noise generates non-Gaussian fluctuations, but finite size effects and exact net-baryon number conservation lead to significant deviations from the expected behavior in equilibrated systems. In particular the skewness shows a qualitative deviation from infinite volume expectations. With this benchmark established we study the real-time dynamics of the fluctuations. We recover the expected dynamical scaling behavior and observe retardation effects and the impact of critical slowing down near the pseudocritical temperature.
78 citations
TL;DR: In this paper, the M\"uller-Israel-Stewart theory and magnetohydrodynamics coupled to dynamical electric fields were derived from a (microscopic) dual gravitational description.
Abstract: Hydrodynamics is a theory of long-range excitations controlled by equations of motion that encode the conservation of a set of currents (energy, momentum, charge, etc.) associated with explicitly realized global symmetries. If a system possesses additional weakly broken symmetries, the low-energy hydrodynamic degrees of freedom also couple to a few other ``approximately conserved'' quantities with parametrically long relaxation times. It is often useful to consider such approximately conserved operators and corresponding new massive modes within the low-energy effective theory, which we refer to as quasihydrodynamics. Examples of quasihydrodynamics are numerous, with the most transparent among them hydrodynamics with weakly broken translational symmetry. Here, we show how a number of other theories, normally not thought of in this context, can also be understood within a broader framework of quasihydrodynamics: in particular, the M\"uller-Israel-Stewart theory and magnetohydrodynamics coupled to dynamical electric fields. While historical formulations of quasihydrodynamic theories were typically highly phenomenological, here, we develop a holographic formalism to systematically derive such theories from a (microscopic) dual gravitational description. Beyond laying out a general holographic algorithm, we show how the M\"uller-Israel-Stewart theory can be understood from a dual higher-derivative gravity theory and magnetohydrodynamics from a dual theory with two-form bulk fields. In the latter example, this allows us to unambiguously demonstrate the existence of dynamical photons in the holographic description of magnetohydrodynamics.
74 citations
TL;DR: The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities and it is found that the diffusive pole is shifted in the presence of nonlinear hydrodynamic self-interactions.
Abstract: The recently developed effective field theory of fluctuations around thermal equilibrium is used to compute late-time correlation functions of conserved densities. Specializing to systems with a single conservation law, we find that the diffusive pole is shifted in the presence of nonlinear hydrodynamic self-interactions, and that the density-density Green's function acquires a branch point halfway to the diffusive pole, at frequency $\ensuremath{\omega}=\ensuremath{-}(i/2)D{k}^{2}$. We discuss the relevance of diffusive fluctuations for strongly correlated transport in condensed matter and cold atomic systems.
TL;DR: In this paper, the conservation laws for optical solitons with anti-cubic nonlinearity and its generalized counterpart are given in terms of Gauss' hypergeometric functions.
TL;DR: In this article, a higher-order nonlinear Schrodinger system for the simultaneous propagation of two ultrashort optical pulses in an optical fiber was derived based on the Lax pair, with respect to the two-component electric fields, infinitely-many conservation laws and one/N-fold binary Darboux transformations.
Abstract: Optical fiber communication system is one of the core supporting systems of the modern internet age. In this paper, under investigation is a higher-order nonlinear Schrodinger system for the simultaneous propagation of two ultrashort optical pulses in an optical fiber. Based on the Lax pair, with respect to the two-component electric fields, infinitely-many conservation laws and one/N-fold binary Darboux transformations are derived, where N = 2 , 3 , … . Solitons are discussed: (1) Nondegenerate one dark–dark soliton, which is black or gray in each component, is obtained. ϵ has no relation with the soliton amplitude in each component, but has a linear correlation with the soliton velocities, where ϵ, σ1 and σ2 are the constant coefficients in the system; (2) Overtaking and head-on interactions between the two dark–dark solitons as well as the bound state are depicted. With the decreasing value of σ1, the gray solitons’ amplitudes increase, but the black solitons’ amplitudes decrease. With the decreasing value of σ2, the gray solitons’ amplitudes increase, but the black solitons’ amplitudes do not change; (3) Interaction among the three overtaking solitons and interaction between a bound state and one soliton are displayed. We find that the interactions between the two solitons and among the three solitons are elastic.
TL;DR: In this article, a time fractional nonlinear heat conduction equation with the sense of Riemann-Liouville (R-L) fractional derivative was investigated.
TL;DR: The Thermal-FIST package contains a class-based library which calculates relevant HRG observables for a specified setup, and contains a fast thermal event generator, which generates particle yields in accordance with the HRG chemistry, and particle momenta based on the Blast Wave model.
TL;DR: In this article, the (2+1)-dimensional KdV and mKdV equations were analyzed on the basis of the extended Lax pair and the symmetry generators were determined.
TL;DR: It is demonstrated that creating an entropy stable DG method in time is similar to the spatial discrete entropy analysis, but there are important (and subtle) differences.
Abstract: This work examines the development of an entropy conservative (for smooth solutions) or entropy stable (for discontinuous solutions) space-time discontinuous Galerkin (DG) method for systems of non ...
TL;DR: In this paper, the authors show that when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution.
Abstract: In driven-dissipative systems, the presence of a strong symmetry guarantees the existence of several steady states belonging to different symmetry sectors. Here we show that when a system with a strong symmetry is initialized in a quantum superposition involving several of these sectors, each individual stochastic trajectory will randomly select a single one of them and remain there for the rest of the evolution. Since a strong symmetry implies a conservation law for the corresponding symmetry operator on the ensemble level, this selection of a single sector from an initial superposition entails a breakdown of this conservation law at the level of individual realizations. Given that such a superposition is impossible in a classical stochastic trajectory, this is a a purely quantum effect with no classical analog. Our results show that a system with a closed Liouvillian gap may exhibit, when monitored over a single run of an experiment, a behavior completely opposite to the usual notion of dynamical phase coexistence and intermittency, which are typically considered hallmarks of a dissipative phase transition. We discuss our results on a coherently driven spin ensemble with a squeezed superradiant decay, a simple model that presents a wealth of nonergodic dynamics.
TL;DR: In this paper, the authors revisit the canonical framework for general relativity in its connection-vierbein formulation, recasting the Gauss law, the Bianchi identity and the space diffeomorphism bulk constraints as conservation laws for boundary surface charges, respectively electric, magnetic and momentum charges.
Abstract: We revisit the canonical framework for general relativity in its connection-vierbein formulation, recasting the Gauss law, the Bianchi identity and the space diffeomorphism bulk constraints as conservation laws for boundary surface charges, respectively electric, magnetic and momentum charges. Partitioning the space manifold into 3D regions glued together through their interfaces, we focus on a single domain and its punctured 2D boundary. The punctures carry a ladder of Kac-Moody edge modes, whose 0-modes represent the electric and momentum charges while the higher modes describe the stringy vibration modes of the 1D-boundary around each puncture. In particular, this allows to identify missing observables in the discretization scheme used in loop quantum gravity and leads to an enhanced theory upgrading spin networks to tube networks carrying Virasoro representations. In the limit where the tubes are contracted to 1D links and the string modes neglected, we do not just recover loop quantum gravity but obtain a more general structure: Poincar\'e charge networks, which carry a representation of the 3D diffeomorphism boundary charges on top of the $\mathrm{SU}(2)$ fluxes and gauge transformations.
TL;DR: In this article, the authors revisit the canonical framework for general relativity in its connection-vierbein formulation, recasting the Gauss law, the Bianchi identity and the space diffeomorphism bulk constraints as conservation laws for boundary surface charges, respectively electric, magnetic and momentum charges.
Abstract: We revisit the canonical framework for general relativity in its connection-vierbein formulation, recasting the Gauss law, the Bianchi identity and the space diffeomorphism bulk constraints as conservation laws for boundary surface charges, respectively electric, magnetic and momentum charges. Partitioning the space manifold into 3D regions glued together through their interfaces, we focus on a single domain and its punctured 2D boundary. The punctures carry a ladder of Kac-Moody edge modes, whose 0-modes represent the electric and momentum charges while the higher modes describe the stringy vibration modes of the 1D-boundary around each puncture. In particular, this allows to identify missing observables in the discretization scheme used in loop quantum gravity and leads to an enhanced theory upgrading spin networks to tube networks carrying Virasoro representations. In the limit where the tubes are contracted to 1D links and the string modes neglected, we do not just recover loop quantum gravity but obtain a more general structure: Poincare charge networks, which carry a representation of the 3D diffeomorphism boundary charges on top of the $\mathrm{SU}(2)$ fluxes and gauge transformations.
TL;DR: The formulation for parametrized aerodynamics problems governed by the compressible Euler and Navier-Stokes equations is demonstrated, and a direct quantitative control of the solution error induced by the hyperreduction is provided.
Abstract: We present a model reduction formulation for parametrized nonlinear partial differential equations (PDEs) associated with steady hyperbolic and convection-dominated conservation laws. Our formulation builds on three ingredients: a discontinuous Galerkin (DG) method which provides stability for conservation laws, reduced basis (RB) spaces which provide low-dimensional approximations of the parametric solution manifold, and the empirical quadrature procedure (EQP) which provides hyperreduction of the Galerkin-projection-based reduced model. The hyperreduced system inherits the stability of the DG discretization: (i) energy stability for linear hyperbolic systems, (ii) symmetry and non-negativity for steady linear diffusion systems, and hence (iii) energy stability for linear convection-diffusion systems. In addition, the framework provides (a) a direct quantitative control of the solution error induced by the hyperreduction, (b) efficient and simple hyperreduction posed as a l1 minimization problem, and (c) systematic identification of the reduced bases and the empirical quadrature rule by a greedy algorithm. We demonstrate the formulation for parametrized aerodynamics problems governed by the compressible Euler and Navier-Stokes equations.
TL;DR: An analytic family of quasilocal conservation laws that break the spin-reversal symmetry and compute a lower bound on the spin Drude weight, which is found to be a fractal function of the anisotropy parameter.
Abstract: We demonstrate ballistic spin transport of an integrable unitary quantum circuit, which can be understood either as a paradigm of an integrable periodically driven (Floquet) spin chain, or as a Trotterized anisotropic (XXZ) Heisenberg spin-1/2 model. We construct an analytic family of quasilocal conservation laws that break the spin-reversal symmetry and compute a lower bound on the spin Drude weight, which is found to be a fractal function of the anisotropy parameter. Extensive numerical simulations of spin transport suggest that this fractal lower bound is in fact tight.
TL;DR: In this article, the authors investigated the characteristics of integrability, bidirectional solitons and localized solutions for a (€ 3+1$$ )-dimensional breaking soliton (GBS) equation with general forms.
Abstract: The characteristics of integrability, bidirectional solitons and localized solutions are investigated for a (
$$3+1$$
)-dimensional breaking soliton (GBS) equation with general forms. Firstly, starting from the GBS equation, we perform the singularity manifold analysis and obtain a new integrable model in the sense of Painleve property. Secondly, taking advantage of the Bell polynomial approach, we construct the Backlund transformation, Lax pair and an infinite sequence of conservation laws. Subsequently, this new equation is also found to allow bidirectional soliton solutions, and the head-on and overtaking collisions between solitons are illustrated by some illustrative graphs. Finally, some localized excitations, such as lump solution, multi-dromions, periodic solitary waves solution, are obtained.
TL;DR: In this article, the authors numerically study the dynamics on the ergodic side of the many-body localization transition in a periodically driven Floquet model with no global conservation laws.
Abstract: We numerically study the dynamics on the ergodic side of the many-body localization transition in a periodically driven Floquet model with no global conservation laws. We describe and employ a nume ...
TL;DR: A general variational principle for the dynamics of impurity particles immersed in a quantum-mechanical medium is presented and it is found that it can successfully model the results of recent Ramsey interference experiments on ^{40}K atoms in a ^{6}Li Fermi gas.
Abstract: We present a general variational principle for the dynamics of impurity particles immersed in a quantum-mechanical medium. By working within the Heisenberg picture and constructing approximate time-dependent impurity operators, we can take the medium to be in any mixed state, such as a thermal state. Our variational method is consistent with all conservation laws and, in certain cases, it is equivalent to a finite-temperature Green's function approach. As a demonstration of our method, we consider the dynamics of heavy impurities that have suddenly been introduced into a Fermi gas at finite temperature. Using approximate time-dependent impurity operators involving only one particle-hole excitation of the Fermi sea, we find that we can successfully model the results of recent Ramsey interference experiments on ^{40}K atoms in a ^{6}Li Fermi gas. We also show that our approximation agrees well with the exact solution for the Ramsey response of a fixed impurity at finite temperature. Our approach paves the way for the investigation of impurities with dynamical degrees of freedom in arbitrary quantum-mechanical mediums.
TL;DR: T theoretical simulations are presented that demonstrate that this process also conserves a mixture of the torus-knot angular momentum J_{γ}, by producing high-order harmonics with driving pulses that are invariant under coordinated rotations.
Abstract: High-order harmonic generation stands as a unique nonlinear optical up-conversion process, mediated by a laser-driven electron recollision mechanism, which has been shown to conserve energy, linear momentum, and spin and orbital angular momentum. Here, we present theoretical simulations that demonstrate that this process also conserves a mixture of the latter, the torus-knot angular momentum J_{γ}, by producing high-order harmonics with driving pulses that are invariant under coordinated rotations. We demonstrate that the charge J_{γ} of the emitted harmonics scales linearly with the harmonic order, and that this conservation law is imprinted onto the polarization distribution of the emitted spiral of attosecond pulses. We also demonstrate how the nonperturbative physics of high-order harmonic generation affect the torus-knot angular momentum of the harmonics, and we show that this configuration harnesses the spin selection rules to channel the full yield of each harmonic into a single mode of controllable orbital angular momentum.
TL;DR: A sampling method for the transition from relativistic hydrodynamics to particle transport, commonly referred to as particlization, which preserves the local conservation of energy, momentum, baryon number, strangeness, and electric charge microcanonically, i.e., in every sample is presented.
Abstract: We present a sampling method for the transition from relativistic hydrodynamics to particle transport, commonly referred to as particlization, which preserves the local conservation of energy, momentum, baryon number, strangeness, and electric charge microcanonically, i.e., in every sample. The proposed method is essential for studying fluctuations and correlations by means of stochastic hydrodynamics. It is also useful for studying small systems. The method is based on Metropolis sampling applied to particles within distinct patches of the switching space-time surface, where hydrodynamic and kinetic evolutions are matched.
TL;DR: In this article, it was shown that the geometry of a black hole horizon can be described as a Carrollian geometry emerging from an ultra-relativistic limit where the near-horizon radial coordinate plays the role of a virtual velocity of light tending to zero.
Abstract: We show that the geometry of a black hole horizon can be described as a Carrollian geometry emerging from an ultra-relativistic limit where the near-horizon radial coordinate plays the role of a virtual velocity of light tending to zero. We prove that the laws governing the dynamics of a black hole horizon, the null Raychaudhuri and Damour equations, are Carrollian conservation laws obtained by taking the ultra-relativistic limit of the conservation of an energy-momentum tensor; we also discuss their physical interpretation. We show that the vector fields preserving the Carrollian geometry of the horizon, dubbed Carrollian Killing vectors, include BMS-like supertranslations and superrotations and that they have non-trivial associated conserved charges on the horizon. In particular, we build a generalization of the angular momentum to the case of non-stationary black holes. Finally, we discuss the relation of these conserved quantities to the infinite tower of charges of the covariant phase space formalism.
Book•
15 Jan 2019TL;DR: In this article, the authors considered the problem of finding a hypersurface in spacetime which is acoustically timelike as viewed from its future, acoustic spacelike from its past, and across which the physical variables suffer discontinuities obeying jump conditions in accordance with the integral form of the particle and energymomentum conservation laws.
Abstract: The subject of this work is the shock development problem in fluid mechanics. A shock originates from an acoustically spacelike surface in spacetime at which the 1st derivatives of the physical variables blow up. The solution requires the construction of a hypersurface in spacetime which is acoustically timelike as viewed from its future, acoustically spacelike as viewed from its past, the shock hypersurface, across which the physical variables suffer discontinuities obeying jump conditions in accordance with the integral form of the particle and energy-momentum conservation laws. Mathematically, this is a free boundary problem, with nonlinear conditions at the free boundary, for a 1st order quasilinear hyperbolic system of p.d.e., with characteristic initial data which are singular at the past boundary of the initial characteristic hypersurface, that boundary being the surface of origin. This work solves, in any number of spatial dimensions, a restricted form of the problem which retains the essential difficulties due to the singular nature of the surface of origin. The solution is accomplished through the introduction of new geometric and analytic methods.
TL;DR: In this article, the massless scalar field in terms of a dual two-form gauge field has been treated as a generator of large gauge transformations of the scalar soft theorem.
Abstract: In recent years soft factorization theorems in scattering amplitudes have been reinterpreted as conservation laws of asymptotic charges. In gauge, gravity, and higher spin theories the asymptotic charges can be understood as canonical generators of large gauge symmetries. Such a symmetry interpretation has been so far missing for scalar soft theorems. We remedy this situation by treating the massless scalar field in terms of a dual two-form gauge field. We show that the asymptotic charges associated to the scalar soft theorem can be understood as generators of large gauge transformations of the dual two-form field. The dual picture introduces two new puzzles: the charges have very unexpected Poisson brackets with the fields, and the monopole term does not always have a dual gauge transformation interpretation. We find analogues of these two properties in the Kramers-Wannier duality on a finite lattice, indicating that the free scalar theory has new edge modes at infinity that canonically commute with all the bulk degrees of freedom.