Analyzing the constraint structure of electrodynamics, massive vector bosons, Dirac fermions and electrodynamics coupled to fermions, we show that Dirac quantization method leads to appropriate creationannihilation algebra among the Forier coefficients of the fields. e-mail: [email protected]

Differential structure of a d-dimensional lattice, which essentially is a noncommutative exterior algebra, is defined using both reductions in 1-order plus 2-order of universal differential calculus in the context of NCG developed by Dimakis et al , and the formalism adopting a Dirac-Connes operator proposed by us recently within Connes’ NCG. Metric structure on this lattice and on differential...

Understanding the structure of the wavefunction is essential for depicting the surface states of a topological insulator. Owing to the inherent strong spin–orbit coupling, the conventional hand-waving picture of the Dirac surface state with a single chiral spin texture is incomplete, as this ignores the orbital components of the Dirac wavefunction and their coupling to the spin textures. Here, ...

Materials harbouring exotic quasiparticles, such as massless Dirac and Weyl fermions, have garnered much attention from physics and material science communities due to their exceptional physical properties such as ultra-high mobility and extremely large magnetoresistances. Here, we show that the highly stable, non-toxic and earth-abundant material, ZrSiS, has an electronic band structure that h...

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i) A weak formulation of the underlying geometric (Stokes-Dirac) structure with a segmented boundary according to the causality of the boundary ports. (ii) The...

Network modeling of complex physical systems leads to a class of nonlinear systems called port-Hamiltonian systems, which are defined with respect to a Dirac structure (a geometric structure which formalizes the power-conserving interconnection structure of the system). A power conserving interconnection of Dirac structures is again a Dirac structure. In this paper we study interconnection prop...

In this paper, we prove that, when the ne structure constant is small enough, the energy of the \ground state" of the Dirac-Fock model can be obtained by a nonlinear max-min principle. 1. The Dirac-Fock model. In 6] we proved that solutions of Dirac-Fock equations converge, in a certain sense, towards solutions of the Hartree-Fock equations when the speed of light tends to innnity. This limitin...

For a Hamiltonian, proper and free action of a Lie group G on a Dirac manifold (M,L), with a regular moment map μ :M → g∗, the manifolds M/G, μ−1(0) and μ−1(0)/G all have natural induced Dirac structures. If (M,L) is an integrable Dirac structure, we show thatM/G is always integrable, but μ−1(0) and μ−1(0)/G may fail to be integrable, and we describe the obstructions to their integrability.

Simplicial Dirac structures as finite analogues of the canonical Stokes-Dirac structure, capturing the topological laws of the system, are defined on simplicial manifolds in terms of primal and dual cochains related by the coboundary operators. These finite-dimensional Dirac structures offer a framework for the formulation of standard input-output finite-dimensional portHamiltonian systems that...

We prove upper and lower bounds for the eigenvalues of the Dirac operator and the Laplace operator on 2-dimensional tori. In particluar we give a lower bound for the first eigenvalue of the Dirac operator for non-trivial spin structures. It is the only explicit estimate for eigenvalues of the Dirac operator known so far that uses information about the spin structure. As a corollary we obtain lo...