相关论文: Left-Ideals, Dirac Fermions and SU(2)-Flavour
This report deals with the quantum theory of flavor oscillations in vacuum, extended to fermionic particles in the several subtle aspects of the first and second quantization theories. In this scenario, the use of the Dirac equation is…
Requiring the effective mass term for a category of fundamental Dirac or Majorana fermions of the same electric charge to be invariant under the translational transformations $\psi^{}_{\alpha \rm L (R)} \to \psi^{}_{\alpha \rm L (R)} +…
Two mathematical models based on Pauli transformations including U(1) chiral group and Pauli SU(2) group, that mixes particle and antiparticle states, are developed for description of Majorana properties of neutral particles. The first one…
We report about recent results on Dirac wave packets in the treatment of neutrino flavor oscillation where the initial localization of a spinor state implies an interference between positive and negative energy components of mass-eigenstate…
We present a fermion model characterized by an anticommuting-parameter shift symmetry. The Hamiltonian formulation exhibits a combination of first-class and second-class constraints. We derive the well-known Dirac equation by fixing the…
We present a new unification of the electro-weak and gravitational interactions based on the joining the weak SU(2) gauge fields with the left handed part of the space-time connection, into a single gauge field valued in the…
It has recently been proposed that all fundamental fermion masses (whether Dirac or Majorana) come from effective dimension-five operators in the context of a truly minimal left-right model. We show how a particularly economical scheme…
Motivated by recent examples of three-dimensional lattice Hamiltonians with massless Dirac fermions in their (bulk) spectrum, I revisit the problem of fermion doubling on bipartite lattices. The number of components of the Dirac fermion in…
We present a non-perturbative lattice study of SU(4) gauge theory with two flavors of fermions in the fundamental representation and two in the two-index antisymmetric representation: a theory closely related to a minimal…
Let $G$ be a simple finite graph. A famous theorem of Dirac says that $G$ is chordal if and only if $G$ admits a perfect elimination order. It is known by Fr\"oberg that the edge ideal $I(G)$ of $G$ has a linear resolution if and only if…
We consider $SU(N)$ Yang-Mills theories in $(2n+1)$-dimensional Euclidean spacetime, where $N\geq n+1$, coupled to an even flavour number of Dirac fermions. After integration over the fermionic degrees of freedom the wave functional for the…
I found an extended duality (triality) between Dirac fermions in periodic spacetime metrics, nonrelativistic fermions in gauge fields (e.g., Harper-Hofstadter model), and in periodic scalar fields on a lattice (e.g., Aubry-Andr\'e model).…
We construct the grand partition function of the system of massive Dirac fermions in a uniform magnetic field from Landau levels, through which all thermodynamic quantities can be obtained. Making use of the Abel-Plana formula, these…
A U(2) flavor symmetry can successfully describe the charged fermion masses and mixings, and supress SUSY FCNC processes, making it a viable candidate for a theory of flavor. We show that a direct application of this U(2) flavor symmetry…
I show that there exist twelve independent Dirac equations for spin 1/2 fermions. The Dirac fields that satisfy these equations can be grouped into six pairs according to the way they transform under continuous space-time transformations.…
After some introductory comments on the peculiar features of slowly running theories, I will report results obtained using the Schrodinger functional technique for two gauge theories that are believed to lie near the bottom of the conformal…
We employ the Dirac-like equation for the gauge field proposed by Majorana to obtain an action that is symmetric under duality transformation. We also use the equivalence between duality and chiral symmetry in this fermion-like formulation…
An unorthodox unified theory is developed to describe external and internal attributes and symmetries of fundamental fermions, quarks and leptons. Basic ingredients of the theory are an algebra which consists of all the…
We posit that the distinct patterns observed in fermion masses and mixings are due to a minimally broken $\mathrm{U}(2)_{q+e}$ flavor symmetry acting on left-handed quarks and right-handed charged leptons, giving rise to an accidental…
We analyse how $U(3)^5$ and $U(2)^5$ flavour symmetries act on the Standard Model Effective Field Theory, providing an organising principle to classify the large number of dimension-six operators involving fermion fields. A detailed…