Related papers: Conserving Lattice Gauge Theory for Finite Systems
In this contribution I discuss a recent proposal of a novel action for lattice gauge theory for finite systems, which accommodates non-periodic spatial boundary conditions. Drawing on the summation-by-parts formulation of finite differences…
We show that standard identities and theorems for lattice models with $U(1)$ symmetry get re-expressed discretely in the tensorial formulation of these models. We explain the geometrical analogy between the continuous lattice equations of…
Building on the principle of combinatorial gauge symmetry, lattice gauge theories can be formulated with only one- and two-body interactions that ensure the exact realization of the symmetry rather than its approximate emergence in a…
We study a lattice gauge theory in Wilson's Hamiltonian formalism. In view of the realization of a quantum simulator for QED in one dimension, we introduce an Abelian model with a discrete gauge symmetry $\mathbb{Z}_n$, approximating the…
A lattice Maxwell system is developed with gauge-symmetry, symplectic structure and discrete space-time symmetry. Noether's theorem for Lie group symmetries is generalized to discrete symmetries for the lattice Maxwell system. As a result,…
We derive non-perturbative sum rules in SU($N$) lattice gauge theory at finite temperature. They relate the susceptibilities of the trace anomaly and energy-momentum tensor to temperature derivatives of the thermodynamic potentials. Two of…
Real time evolution of classical gauge fields is relevant for a number of applications in particle physics and cosmology, ranging from the early Universe to dynamics of quark-gluon plasma. We present a lattice formulation of the interaction…
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter or quantum information theory. The recent progress in the control of artificial quantum systems already allows for studying Abelian lattice…
Protection of gauge invariance in experimental realizations of lattice gauge theories based on energy-penalty schemes has recently stimulated impressive efforts both theoretically and in setups of quantum synthetic matter. A major challenge…
We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a ``no go'' for simulating the original continuum classical gauge fields over a long time…
We consider a lattice discretization of a covariantly gauge-fixed abelian gauge theory. The gauge fixing is part of the action defining the theory, and we study the phase diagram in detail. As there is no BRST symmetry on the lattice,…
We discuss a particular lattice discretization of abelian gauge theories in arbitrary dimensions. The construction is based on gauging the center symmetry of a non-compact abelian gauge theory, which results in a Villain type action. We…
We derive an expression for the energy-momentum tensor in the discrete lattice formulation of pure glue QCD. The resulting expression satisfies the continuity equation for energy conservation up to numerical errors with a symmetric…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
We streamline and generalize the recent progress in understanding entanglement between spatial regions in Abelian gauge theories. We provide an unambiguous and explicit prescription for calculating entanglement entropy in a $\mathbb Z_N$…
Recent theoretical studies of various strongly-correlated systems in condensed matter physics reveal that the lattice gauge theory(LGT) developed in high-energy physics is quite a useful tool to understand physics of these systems.…
Non-Abelian gauge theories provide the most accurate description of fundamental interactions, showing remarkable agreement with experimental data in cosmology and particle physics. Highly precise predictions can be made using standard…
We present a comprehensive discussion on lattice techniques for the simulation of scalar and gauge field dynamics in an expanding universe. After reviewing the continuum formulation of scalar and gauge field interactions in Minkowski and…
Can high energy physics be simulated by low-energy, non-relativistic, many-body systems, such as ultracold atoms? Such ultracold atomic systems lack the type of symmetries and dynamical properties of high energy physics models: in…
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter, and quantum information science. Their local symmetries enforce the charge conservation observed in the laws of physics. Impressive…