scholarly journals STRUCTURE OF TOPOLOGICAL LATTICE FIELD THEORIES IN THREE DIMENSIONS

1994 ◽  
Vol 09 (08) ◽  
pp. 1305-1360 ◽  
Author(s):  
STEPHEN-WEI CHUNG ◽  
MASAFUMI FUKUMA ◽  
ALFRED SHAPERE
Keyword(s):  
Hopf Algebras ◽  
Lattice Gauge Theory ◽  
Three Dimensions ◽  
Field Theories ◽  
Arbitrary Topology ◽  
Lattice Gauge ◽  
Lattice Field ◽  
Topological Lattice ◽  
Local Lattice ◽  
Zero Coupling

We construct and classify topological lattice field theories in three dimensions. After defining a general class of local lattice field theories, we impose invariance under arbitrary topology-preserving deformations of the underlying lattice, which are generated by two new local lattice moves. Invariant solutions are in one-to-one correspondence with Hopf algebras satisfying a certain constraint. As an example, we study in detail the topological lattice field theory corresponding to the Hopf algebra based on the group ring C[G], and show that it is equivalent to lattice gauge theory at zero coupling, and to the Ponzano-Regge theory for G = SU (2).

scholarly journals ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES

2009 ◽  
Vol 24 (32) ◽  
pp. 6105-6121 ◽  
Author(s):  
P. TEOTONIO-SOBRINHO ◽  
C. MOLINA ◽  
N. YOKOMIZO
Keyword(s):  
Hopf Algebras ◽  
Gauge Theories ◽  
Local Symmetry ◽  
Two Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Wilson Loops ◽  
Two Dimensional ◽  
Lattice Field ◽  
Expected Values

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.

scholarly journals Structures and Diagrammatics of Four Dimensional Topological Lattice Field Theories

1999 ◽  
Vol 146 (1) ◽  
pp. 39-100 ◽  
Author(s):  
J. Scott Carter ◽  
Louis H. Kauffman ◽  
Masahico Saito
Keyword(s):  
Field Theories ◽  
Lattice Field ◽  
Topological Lattice

scholarly journals Cold atoms meet lattice gauge theory

2021 ◽  
Vol 380 (2216) ◽  
Author(s):  
Monika Aidelsburger ◽  
Luca Barbiero ◽  
Alejandro Bermudez ◽  
Titas Chanda ◽  
Alexandre Dauphin ◽  
...  
Keyword(s):  
Particle Physics ◽  
Cold Atoms ◽  
Lattice Gauge Theory ◽  
New Physics ◽  
Theme Issue ◽  
Central Idea ◽  
Hubbard Models ◽  
Lattice Gauge ◽  
Lattice Field ◽  
New Information

The central idea of this review is to consider quantum field theory models relevant for particle physics and replace the fermionic matter in these models by a bosonic one. This is mostly motivated by the fact that bosons are more ‘accessible’ and easier to manipulate for experimentalists, but this ‘substitution’ also leads to new physics and novel phenomena. It allows us to gain new information about among other things confinement and the dynamics of the deconfinement transition. We will thus consider bosons in dynamical lattices corresponding to the bosonic Schwinger or Z 2 Bose–Hubbard models. Another central idea of this review concerns atomic simulators of paradigmatic models of particle physics theory such as the Creutz–Hubbard ladder, or Gross–Neveu–Wilson and Wilson–Hubbard models. This article is not a general review of the rapidly growing field—it reviews activities related to quantum simulations for lattice field theories performed by the Quantum Optics Theory group at ICFO and their collaborators from 19 institutions all over the world. Finally, we will briefly describe our efforts to design experimentally friendly simulators of these and other models relevant for particle physics. This article is part of the theme issue ‘Quantum technologies in particle physics’.

scholarly journals A MODEL OF THREE-DIMENSIONAL LATTICE GRAVITY

1992 ◽  
Vol 07 (18) ◽  
pp. 1629-1646 ◽  
Author(s):  
D.V. BOULATOV
Keyword(s):  
Cohomology Group ◽  
Lattice Gauge Theory ◽  
Finite Abelian Group ◽  
Three Dimensional ◽  
Dimensional Lattice ◽  
Lattice Gauge ◽  
Topological Lattice ◽  
First Cohomology Group ◽  
Definition Of ◽  
Topological Expansion

A model is proposed which generates all oriented 3D simplicial complexes weighted with an invariant associated with a topological lattice gauge theory. When the gauge group is SUq(2), qn=1, it is the Turaev-Viro invariant and the model may be regarded as a nonperturbative definition of 3D simplicial quantum gravity. If one takes a finite Abelian group G, the corresponding invariant gives the rank of the first cohomology group of a complex C:IG(C)=rank(H1(C,G)), which means a topological expansion in the Betti number b1. In general, it is a theory of the Dijkgraaf-Witten type, i.e., determined completely by the fundamental group of a manifold.

Sign in / Sign up

Export Citation Format

Share Document