相关论文: Low energy theorem for scalar and vector interacti…

We consider a composite spin-half particle moving in spatially-varying scalar and vector fields. The vector field is assumed to couple to a conserved charge, but no assumption is made about either the structure of the composite or its…

For a relativistic particle moving in the presence of mean scalar and vector fields, the energy at second order in the scalar field is shown to contain two contributions in general. One is a momentum-dependent repulsive interaction…

We carefully study how the fermion-fermion interactions affect the low-energy states of a two-dimensional spin-$1/2$ fermionic system on the kagom\'{e} lattice with a quadratic band crossing point. With the help of the renormalization group…

We construct a lattice theory describing a system of interacting nonrelativistic spin s=1/2 fermions at nonzero chemical potential. The theory is applicable whenever the interparticle separation is large compared to the range of the…

One starts from a planar Maxwell-Chern-Simons model endowed with a Lorentz-violating term. The Dirac sector is introduced exhibiting a Yukawa and a minimal coupling with the scalar scalar and the gauge fields, respectively. One then…

We show that the conditions which originate the spin and pseudospin symmetries in the Dirac equation are the same that produce equivalent energy spectra of relativistic spin-1/2 and spin-0 particles in the presence of vector and scalar…

The spin-orbit interaction of light is a crucial concept for understanding the electromagnetic properties of a material and realizing the spin-controlled manipulation of optical fields. Achieving these goals requires a complete description…

Type-II semi-Dirac fermions in two dimensions have been proposed to describe topologically nontrivial low-energy excitations in titanium/vanadium oxide heterostructures. These quasiparticles appear at the merger of three Dirac cones,…

We discuss low-energy effective theories with a Dirac gravitino. Our main benchmark is Scherk--Schwarz supersymmetry breaking with anti-periodic boundary conditions for fermions on S^1/Z_2. In this case two Majorana spin-3/2 modes are…

The low-energy theory of electrons interacting via repulsive short-range interactions on graphene's honeycomb lattice at half filling is presented. The exact symmetry of the Lagrangian with local quartic terms for the Dirac field dictated…

We construct an action for the composite Dirac fermion consistent with symmetries of electrons projected to the lowest Landau level. First we construct a generalization of the $g=2$ electron that gives a smooth massless limit on any curved…

In the first part of the thesis we consider the constraints of causality and unitarity for particles interacting via strictly finite-range interactions. We generalize Wigner's causality bound to the case of non-vanishing partial-wave…

We present a framework to elucidate the existence of accidental contacts of energy bands, particularly those called Dirac points which are the point contacts with linear energy dispersions in their vicinity. A generalized von-Neumann-Wigner…

The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in particular case of interacting massless electrons in graphene and other…

The effects of interactions in a 2D electron system in a strong magnetic field of two degenerate Landau levels with opposite spins and at filling factors 1/2 are studied. Using the Chern-Simons gauge transformation, the system is mapped to…

We develop a second order formalism for spin 1/2 fermions based on the projection over Poincar\'{e} invariant subspaces in the $(1/2,0)\oplus(0,1/2)$ representation of the homogeneous Lorentz group. Using $U(1)_{em}$ gauge principle we…

We derive the spin Boltzmann equations for spin-1/2 fermions in a non-relativistic model with four-fermion contact interaction which conserves spin degrees of freedom. A great advantage of the model is that the spin matrix elements in…

We calculate, to second order in the scattering length between two fermions, the Landau quasiparticle interaction for a low-density mixture of two fermion species with unequal densities at temperature zero. From the Landau parameters we…

We consider a system of 2D fermions with short-range interaction. A straightforward perturbation theory is shown to be ill-defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near…

The lectures review some of the basic concepts relevant for an understanding of the low energy properties of the strong interactions: chiral symmetry, spontaneous symmetry breakdown, Goldstone bosons, quark condensate. The effective field…