✦ LIBER ✦

Structures and Diagrammatics of Four Dimensional Topological Lattice Field Theories

✍ Scribed by J. Scott Carter; Louis H. Kauffman; Masahico Saito

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 1023 KB
Volume: 146
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1822

No coin nor oath required. For personal study only.

✦ Synopsis

Crane and Frenkel proposed a state sum invariant for triangulated 4-manifolds. They sketched the definition of a Hopf category that was to be used in their construction. Crane and Yetter studied Hopf categories and gave some examples using group cocycles that are associated to the Drinfeld double of a finite group. In this paper we define a state sum invariant of triangulated 4-manifolds using Crane Yetter cocycles as Boltzmann weights. Our invariant is analogous to the 3-dimensional invariants defined by Dijkgraaf and Witten and the invariants that are defined via Hopf algebras. We present diagrammatic methods for the study of such invariants that illustrate connections between Hopf categories and moves to triangulations.

📜 SIMILAR VOLUMES

Adjoint “quark” color fields in four-dim

Adjoint “quark” color fields in four-dimensional lattice gauge theory: Vacuum screening and penetration

✍ Howard D. Trottier 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 512 KB

Topological current structure of disloca

Topological current structure of dislocations in the 4-dimensional gauge field theory of disclocation and disclination continuum

✍ Yishi Duan; Shengli Zhang 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 611 KB

Topological current structure of disclin

Topological current structure of disclinations in the 4-dimensional gauge field theory of dislocation and disclination continuum

✍ Duan Yishi; Zhang Shengli 📂 Article 📅 1992 🏛 Elsevier Science 🌐 English ⚖ 477 KB

Stratification structures on a kind of c

Stratification structures on a kind of completely distributive lattices and their applications in the theory of topological molecular lattices

✍ Hongbin Cui; Chongyou Zheng 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 398 KB

In this paper, we shall introduce the concept of stratification structures on completely distributive lattices by direct product decompositions of completely distributive lattices, and prove that there is, up to isomorphism, a unique stratification structure on any normal completely distributive lat

A quantum field theory of lattice dynami

A quantum field theory of lattice dynamics and melting in sphalerite and diamond structure crystals

✍ T. Kitamura 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 276 KB

Hilbert space and structure constants of

Hilbert space and structure constants of descendant fields in two-dimensional conformal theories

✍ Michael Lässig; Giuseppe Mussardo 📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 859 KB

We have developed an algorithm to compute the Hubert-space basis and the operator algebra of descendant fields for (1 + 1)-dimensional conformal field theories. Implemented as a Marhematica computer program, this algorithm is used to obtain nonperturbatively the spectrum of the transfer matrix theor