Pure spinor formalism and non-integrable exponential factors are used for constructing the conformal-invariant wave equation and Lagrangian density for massive fermion. It is proved that canonical Dirac Lagrangian for massive fermion is invariant under induced projective conformal transformations.

S.-X. Yang,1,2,* P. Haase,3 H. Terletska,1,4 Z. Y. Meng,1,2 T. Pruschke,3 J. Moreno,1,2 and M. Jarrell1,2 1Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA 2Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA 3Department of Physics, University of Göttingen, 37077 Göttingen, Germany 4Condensed Matt...

The local composite operator A2 is analysed in pure Yang-Mills theory in the Landau gauge within the algebraic renormalization. It is proven that the anomalous dimension of A2 is not an independent parameter, being expressed as a linear combination of the gauge β function and of the anomalous dimension of the gauge fields. Research Assistant of The Fund For Scientific Research-Flanders, Belgium...

Composite optical vortices may form when two or more beams interfere. Using analytical and numerical techniques, we describe the motion of these optical phase singularities as the relative phase or amplitude of two interfering collinear nonconcentric beams is varied. The creation and the annihilation of vortices are found, as well as vortices having translational velocities exceeding the speed ...

Neutrinos can have naturally small Dirac masses if the Standard Model singlet right-handed neutrinos are light composite fermions. Theories which produce light composite fermions typically generate many of them, three of which can marry the left-handed neutrinos with small Dirac masses. The rest can serve as sterile states which can mix with the Standard Model neutrinos. We present explicit mod...

Using a four fermion interaction Lagrangian, we demonstrate that the spontaneous breaking of vector symmetries requires the existence of a light (comparing with the heavy fermion mass) scalar particle and the low energy effective theory (the σ model) obtained after integrating out heavy fermion degrees of freedom is asymptotically a renormalizable one. When applying the idea to the electroweak ...

The Jordan-Wigner transformation is known as a powerful tool in condensed matter theory, especially in the theory of low-dimensional quantum spin systems. The aim of this chapter is to review the application of the Jordan-Wigner fermionization technique for calculating dynamic quantities of low-dimensional quantum spin models. After a brief introduction of the Jordan-Wigner transformation for o...