Related papers: Dirac products and concurring Dirac structures

We develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result of this paper is that each symplectic foliation has an attached $L_\infty$-algebra controlling its…

We demonstrate that topological constraints do not only dictate the geometric part of the superfluid stiffness, but can also govern the total superfluid stiffness. By introducing a general adiabatic approach for superfluid responses, we…

Recently, type-II Dirac fermions characterized by strongly titled Dirac cones have been proposed. The new fermions exhibit unique physical properties different from the type-I Dirac fermions in graphene, and thus attract tremendous…

We propose an explicit construction of the deformation quantization of the general second-class constrained system, which is covariant with respect to local coordinates on the phase space. The approach is based on constructing the effective…

Understanding Dirac-like Fermions has become an imperative in modern condensed matter sciences: all across its research frontier, from graphene to high T$_c$ superconductors to the topological insulators and beyond, various electronic…

Many recently discovered advanced materials, such as high-Tc cuprates, iron pnictides and several heavy-fermions, exhibit a rich phase diagram suggesting the presence of different competing interactions that would lead to various types of…

This note elaborates on Th. Voronov's construction [math/0304038,math/0412202] of $L_\infty$-structures via higher derived brackets with a Maurer-Cartan element. It is shown that gauge equivalent Maurer-Cartan elements induce…

We theoretically study the effect of the motion and the merging of Dirac cone on the interlayer magnetoresistance in multilayer graphene like systems. This merging, which could be induced by a uniaxial strain, gives rise in monolayer Dirac…

The coadjoint orbits of compact Lie groups carry many K\"ahler structures, which include a Riemannian metric and a complex structure. We provide a fairly explicit formula for the Levi-Civita connection of the Riemannian metric, and we use…

We define a C*-algebraic quantization of constant Dirac structures on tori, which extends the standard quantization of Poisson structures. We prove that Dirac structures in the same orbit of a natural action of O(n,n|Z) give rise to Morita…

The $\mathrm{U}(1)$ Dirac spin liquid provides a useful organizing framework for frustrated magnets: it offers an algebraic parent state from which competing orders, confinement patterns, and low-energy spectral features can be understood.…

Superconductivity of a single two-dimensional Dirac fermion offers a natural route to topological superconductivity. While usually considered extrinsic -- arising from proximity to a conventional superconductor -- we investigate when a…

We introduce a class of first order G-structures, each of which has an underlying almost conformally symplectic structure. There is one such structure for each real simple Lie algebra which is not of type $C_n$ and admits a contact grading.…

We propose a correspondence between the description of emergent Lorentz symmetry in condensed-matter systems and the established general effective field theory for Lorentz violation in fundamental theories of spacetime and matter. This…

We formulate Dirac-Kaehler fermion action by introducing a new Clifford product with noncommutative differential form on a lattice. Hermiticity of the Dirac-Kaehler action requires to choose the lattice structure having both orientabilities…

In this paper we study the relationship between the extended symmetries of exact Courant algebroids over a manifold $M$, defined by Bursztyn, Cavalcanti and Gualtieri, and the Poisson algebras of admissible functions associated to twisted…

Let G be a torsion free discrete group with a finite dimensional classifying space BG. We show that G has a dual Dirac morphism if and only if a certain coarse (co)-assembly map is an isomorphism. Hence the existence of a dual Dirac…

In this present communication we provide a new derivation of the Dirac dual structure by employing a different approach from the originally proposed. Following a general and rigorous mathematical process to compute the dual structure, we…

Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…

We show that a generalized Dirac structure survives beyond the linear regime of the low-energy dispersion relations of graphene. A generalized uncertainty principle of the kind compatible with specific quantum gravity scenarios with a…