Quantum field theory and link invariants
نویسندگان
چکیده
منابع مشابه
Knot Invariants and New Quantum Field Theory
We propose a new gauge theory of quantum electrodynamics (QED) and quantum chromodynamics (QCD) from which we derive knot invariants such as the Jones polynomial. Our approach is inspired by the work of Witten who derived knot invariants from quantum field theory based on the Chern-Simon Lagrangian. From our approach we can derive new knot invariants which extend the Jones polynomial and give a...
متن کاملQuantum Harmonic Oscillator Algebra and Link Invariants
The q–deformation Uq(h4) of the harmonic oscillator algebra is defined and proved to be a Ribbon Hopf algebra. Associated with this Hopf algebra we define an infinite dimensional braid group representation on the Hilbert space of the harmonic oscillator, and an extended Yang–Baxter system in the sense of Turaev. The corresponding link invariant is computed in some particular cases and coincides...
متن کاملIntegrality and Symmetry of Quantum Link Invariants
0. Introduction. Quantum invariants of framed links whose components are colored by modules of a simple Lie algebra g are Laurent polynomials in v1/D (with integer coefficients), where v is the quantum parameter and D an integer depending on g. We show that quantum invariants, with a suitable normalization, are Laurent polynomials in v2. We also establish two symmetry properties of quantum link...
متن کاملSpin networks, quantum automata and link invariants
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with purely discrete unitary gates, the simulator is naturally modelled as families of quantum automata which in turn represent discrete versions of topological qua...
متن کاملLink Homology and Unoriented Topological Quantum Field Theory
We investigate Khovanov homology of stable equivalence classes of link diagrams on oriented surfaces. We apply Bar-Natan’s geometric formalism to this setting and using unoriented 1+1-dimensional topological quantum field theories we define new link homology theories for stable equivalences classes.
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ژورنال
عنوان ژورنال: Nuclear Physics B
سال: 1990
ISSN: 0550-3213
DOI: 10.1016/0550-3213(90)90123-u