Exact bosonization in two spatial dimensions and a new class of lattice gauge theories

We describe a 2d analog of the Jordan-Wigner transformation which maps an arbitrary fermionic system on a 2d lattice to a lattice gauge theory while preserving the locality of the Hamiltonian. When the space is simply-connected, this bosonization map is an equivalence. We describe several examples of 2d bosonization, including free fermions on square and honeycomb lattices and the Hubbard model. We describe Euclidean actions for the corresponding lattice gauge theories and find that they contains Chern-Simons-like terms. Finally, we write down a fermionic dual of the gauged Ising model (the Fradkin-Shenker model).Comment: 30 pages, 8 figure

Exact bosonization in arbitrary dimensions

We extend the previous results of exact bosonization, mapping from fermionic operators to Pauli matrices, in 2D and 3D to arbitrary dimensions. This bosonization map gives a duality between any fermionic system in arbitrary n spatial dimensions and a class of (n−1)-form Z₂ gauge theories in n dimensions with a modified Gauss's law. This map preserves locality and has an explicit dependence on the second Stiefel-Whitney class and a choice of spin structure on the spatial manifold. A formula for Stiefel-Whitney homology classes on lattices is derived. In the Euclidean path integral, this exact bosonization map is equivalent to introducing a topological Steenrod square term to the space-time action

The Intention to Download Music Files in a P2P Environment: Rational Choice, Fashion, and Ethical Decision Perspectives

Downloading unauthorized music file is deemed illegal and immoral, but the peer-to-peer systems have boosted its popularity. Many authors attributed this phenomenon to the low morality of Internet users, but inconclusive evidence to this argument was found. Extant literature seldom noticed that downloading music files is a new mean of music consumption. People, especially young generation, might rationally choose between downloading music files and buying CDs for greater utility for enjoying and pursuing after the fashion of music. This paper presents a conceptual model of file downloading by looking at and integrating these perspectives. An analysis of 834 samples drew from a questionnaire survey of P2P users in Taiwan generally supports the above assertion

Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way

We extend the periodic table of phases of free fermions in the ten-fold way symmetry classes to a classification of free fermionic phases protected by an arbitrary on-site unitary symmetry $\hat G$ in an arbitrary dimension. The classification is described as a function of the real representation theory of $\hat G$ and the data of the original periodic table. We also systematically study in low dimensions the relationship between the free invariants and the invariants of short-range entangled interacting phases of fermions. Namely we determine whether a given symmetry protected phase of free fermions is destabilized by sufficiently strong interactions or it remains stable even in the presence of interactions. We also determine which interacting fermionic phases cannot be realized by free fermions. Examples of both destabilized free phases and intrinsically interacting phases are common in all dimensions.Comment: 18 page