Abstract
We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al.) and condensed matter properties (Kane et al.), where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Highlights
Topological Quantum Field Theories TQFT’s are possible realisations of the invariance under general local field transformations general coordinates invariant symmetries
The first non-trivial example of a TQFT was introduced by Witten [1] showing that the genuine N = 2 supersymmetric gauge theories contains observables that describe the Donaldson invariants
This unambiguous definition of observables from the cohomology of a BRST operator is perfectly suited for the gauge theories of elementary particles
Summary
Topological Quantum Field Theories TQFT’s are possible realisations of the invariance under general local field transformations general coordinates invariant symmetries. Hilbert space as the cohomology of Q (states which are annihilated by Q without being the Q transformation of other states) This unambiguous definition of observables from the cohomology of a BRST operator is perfectly suited for the gauge theories of elementary particles Our model generalises [5] and gives a sort of conformally vibrating lattice where each site is a particle interacting by superconformal interactions with its nearest neighbours (two in this present case). This model exhibits non-trivial instanton solutions and has some topological observables
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