Lattice gauge theories and the continuum limit in two dimensions

1977 ◽  
Vol 15 (4) ◽  
pp. 1084-1093 ◽  
Author(s):  
M. W. Roth
Keyword(s):  
Continuum Limit ◽  
Gauge Theories ◽  
Two Dimensions ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
The Continuum

scholarly journals Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks

2017 ◽  
Vol 95 (9) ◽  
Author(s):  
Boye Buyens ◽  
Simone Montangero ◽  
Jutho Haegeman ◽  
Frank Verstraete ◽  
Karel Van Acoleyen
Keyword(s):  
Continuum Limit ◽  
Gauge Theories ◽  
Finite Representation ◽  
Lattice Gauge ◽  
Tensor Networks ◽  
Lattice Gauge Theories ◽  
The Continuum

scholarly journals Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization

2016 ◽  
Vol 31 (35) ◽  
pp. 1650192 ◽  
Author(s):  
Sinya Aoki ◽  
Etsuko Itou ◽  
Keitaro Nagata
Keyword(s):  
Pure State ◽  
Continuum Limit ◽  
Gauge Theories ◽  
Entanglement Entropy ◽  
Continuum Theory ◽  
Replica Method ◽  
Pure Gauge ◽  
Lattice Gauge ◽  
Lattice Regularization ◽  
The Continuum

We study the entanglement entropy (EE) for pure gauge theories in 1[Formula: see text]+[Formula: see text]1 dimensions with the lattice regularization. Using the definition of the EE for lattice gauge theories proposed in a previous paper,1 we calculate the EE for arbitrary pure as well as mixed states in terms of eigenstates of the transfer matrix in (1[Formula: see text]+[Formula: see text]1)-dimensional lattice gauge theory. We find that the EE of an arbitrary pure state does not depend on the lattice spacing, thus giving the EE in the continuum limit, and show that the EE for an arbitrary pure state is independent of the real (Minkowski) time evolution. We also explicitly demonstrate the dependence of EE on the gauge fixing at the boundaries between two subspaces, which was pointed out for general cases in the paper. In addition, we calculate the EE at zero as well as finite temperature by the replica method, and show that our result in the continuum limit corresponds to the result obtained before in the continuum theory, with a specific value of the counterterm, which is otherwise arbitrary in the continuum calculation. We confirm the gauge dependence of the EE also for the replica method.

P-CELL GAUGE THEORIES, MANIFOLD SPACE, AND MULTI-DIMENSIONAL INTEGRABILITY

1990 ◽  
Vol 05 (04) ◽  
pp. 255-264 ◽  
Author(s):  
T.A. LARSSON
Keyword(s):  
Classical Limit ◽  
Gauge Theories ◽  
Continuum Models ◽  
Dimensional Lattice ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
Infinite Set ◽  
P Cells ◽  
Conserved Currents ◽  
The Continuum

We construct lattice gauge theories where the gauge potentials live on p-cells, using ideas from the theory of multi-dimensional lattice integrability. The classical limit of these models can naturally be considered as chiral models in the space ΩPM of p-dimensional manifolds on M, or alternatively as gauge theories in ΩP−1M. The continuum models have an infinite set of functionally conserved currents in ΩPM, which are classical analogs of the simplex equations of lattice integrable systems.

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