In this paper, we firstly re-present the results of Bondar et al. (2013). Then, following the approach taken in it, we use the method of Operational Dynamic Modeling (ODM) to deal with the situation where thebackground mechanics is varying between quantum and classical mechanics.

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Perspectives in Representation Theory: A Conference in Honor of Igor Frenkel’s 60th Birthday on Perspectives in Representation Theory, Yale University, New Haven, 12-17 May 2012

Distinct quantum vacua of topologically ordered states can be tunneled into each other via extended operators. The possible applications include condensed matter and quantum cosmology. We present a straightforward approach to calculate the partition function on various manifolds and ground state degeneracy (GSD), mainly based on continuum/cochain topological quantum field theories (TQFTs), in any dimension. This information can be related to the counting of extended operators of bosonic/fermionic TQFTs. On the lattice scale, anyonic particles/strings live at the ends of line/surface operators. Certain systems in different dimensions are related to each other through dimensional reduction schemes, analogous to (de)categorification. Examples include spin TQFTs derived from gauging the interacting fermionic symmetry-protected topological states (with fermion parity \mathbb{Z}_2^f) of symmetry groups \mathbb{Z}_2^f and \mathbb{Z}_2^f in

We consider N= 2 superconformal field theory with following properties: a) Coulomb branch operators have fractional scaling dimensions, b) there are exact marginal deformations. The weakly coupled gauge theory descriptions are found by decomposing 3d mirror into different components, and different decompositions correspond to different duality frames. The gauge theory is formed by gauging Argyres-Douglas matter, and we write down all duality frames for several classes with infinite sequence of theories.