相关论文: Numerical Computations in the Worldsheet Formulati…

Quantum simulation of synthetic dynamic gauge field has attracted much attentions in recent years. There are two traditional ways to simulate gauge theories. One is to directly simulate the full Hamiltonian of gauge theories with local…

We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to…

We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (which is an essential…

The methods of lattice gauge theory may be applied to gauge theories besides QCD, in fact to any gauge group and any representation of matter fields (as long as the coupling is not chiral). Such theories are useful for model building beyond…

The Weyl fermion belonging to the real representation of the gauge group provides a simple illustrative example for L\"uscher's gauge-invariant lattice formulation of chiral gauge theories. We can explicitly construct the fermion…

In this paper we propose a new approach to formulate the field theory on a lattice. This approach can eliminate the Fermion doubling problem, preserve the chiral symmetry and get the same dispersion relation for both Fermion and Boson…

A formulation of chiral gauge theories on a lattice which is both reflection positive and gauge invariant is discussed.

Path integration over Euclidean chiral fermions is replaced by the quantum mechanics of an auxiliary system of non--interacting fermions. Our construction avoids the no--go theorem and faithfully maintains all the known important features…

In these proceedings, we review recent advances in applying quantum computing to lattice field theory. Quantum computing offers the prospect to simulate lattice field theories in parameter regimes that are largely inaccessible with the…

We explain, in a slightly modified form, an old construction allowing to reformulate the U(N) gauge theory defined on a D-dimensional lattice as a theory of lattice strings (a statistical model of random surfaces). The world surface of the…

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…

Lattice perturbation theory is discussed in the overlap formulation for the Yukawa and gauge interactions. One and two point functions are studied for fermion, scalar and gauge fields, taking the Standard Model as an example. The formulae…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…

Quantum computing promises the possibility of studying the real-time dynamics of nonperturbative quantum field theories while avoiding the sign problem that obstructs conventional lattice approaches. Current and near-future quantum devices…

We introduce a way to express compact quantum electrodynamics with dynamical matter on two- and three-dimensional spatial lattices in a gauge redundancy-free manner while preserving translational invariance. By transforming to a rotating…

In this paper, we propose that a simple model, in which fermions coupled to a dynamical lattice gauge field, can be engineered via the Floquet approach. The model possess both a independent Maxwell term and the local $Z_{2}$ gauge symmetry.…

We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree…

The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now…

In the framework of the Connes-Lott model based on noncommutative geometry, the basic features of a gauge theory in the presence of gravity are reviewed, in order to show the possible physical relevance of this scheme for inflationary…

In this contribution we give an introduction to the foundations and methods of lattice gauge theory. Starting with a brief discussion of the quantum mechanical path integral, we develop the main ingredients of lattice field theory:…