相关论文: Fermions with spin 1/2 as global SO(3) vortices
From a geometric point of view, massless spinors in $3+1$ dimensions are composed of primary fields of weights $(\frac{1}{2},0)$ and $(0,\frac{1}{2})$, where the weights are defined with respect to diffeomorphisms of a sphere in momentum…
We realize the Weil representation of infinite dimensional symplectic group and spinor representation of infinite-dimensional group $GL$ by linear operators in the space of symmetric functions in infinite number of variables.
A FORTRAN code for generating the leading SU(3) irreducible representation (irrep) of N identical spin 1/2 fermions in a harmonic oscillator mean field is introduced. The basis states are labeled by N--the total number of particles, the…
We establish the functorial transfer of generic, automorphic representations from the quasi-split general spin groups to general linear groups over arbitrary number fields, completing an earlier project. Our results are definitive and, in…
The one-dimensional spin-orbital model is studied by means of Abelian bosonization. We derive the low-energy effective theory which enables us to study small deviations from the SU(4) symmetric point. We show that there exists a massless…
An analysis of generating fermion masses via cubic couplings in SO(10) grand unification with a unified Higgs sector is given. The new framework utilizes a single pair of vector--spinor representation $144+\bar{144}$ to break the gauge…
Parity-even cubic vertices of massless bosons of arbitrary spins in three dimensional Minkowski space are classified in the metric-like formulation. As opposed to higher dimensions, there is at most one vertex for any given triple…
The algebraic consistency of spin and isospin at the level of an unbroken SU(2) gauge theory suggests the existence of an additional angular momentum besides the spin and isospin and also produces a full quaternionic spinor operator. The…
We revisit the fermionic parton approach to S = 1/2 quantum spin liquids with SU(2) spin rotation symmetry, and the associated projective symmetry group (PSG) classification. We point out that the existing PSG classification is incomplete;…
A four dimensional Superstring is constructed starting from a twenty six dimensional bosonic string. Fermions are introduced by noting the Manselstam's proof of equivalence of two fermions to one boson in 1+1 dimensions. The action of the…
In this work we discuss an analytic bootstrap approach [1,2] in the context of spinning 4D conformal blocks [3,4]. As an example we study the simplest spinning case, the scalar-fermion correlator $\langle\phi\psi\phi\bar\psi\rangle$. We…
It is shown that the SO(3) isometries of the Euclidean Taub-NUT space combine a linear three-dimensional representation with one induced by a SO(2) subgroup, giving the transformation law of the fourth coordinate under rotations. This…
We formulate quantum mechanics on SO(3) using a non-commutative dual space representation for the quantum states, inspired by recent work in quantum gravity. The new non-commutative variables have a clear connection to the corresponding…
We propose a generalization of the supersymmetric representation of spins with symplectic symmetry, generalizing the rotation group of the spin from SU(2) to SP(N). As a test application of this new representation, we consider two toy…
In standard Poincare and anti de Sitter SO(2,3) invariant theories, antiparticles are related to negative energy solutions of covariant equations while independent positive energy unitary irreducible representations (UIRs) of the symmetry…
Unification based on the group SO(10)^3 \times S_3 is studied. Each family has its own SO(10) group, and the S_3 permutes the three families and SO(10) factors. This is the maximal local symmetry for the known fermions. Family unification…
We revisit the exact solution of the two space-time dimensional quantum field theory of a free massless boson with a periodic boundary interaction and self-dual period. We analyze the model by using a mapping to free fermions with a…
We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free…
We suggest a simple supersymmetric SO(10) grand unified theory in 6 dimensions which produces the suitable fermion mass hierarchies. The 5th and 6th dimensional coordinates are compactified on a $T^2/Z_2$ orbifold. The gauge and Higgs…
We generalize the worldline formalism to include spin 1/2 fields coupled to gravity. To this purpose we first extend dimensional regularization to supersymmetric nonlinear sigma models in one dimension. We consider a finite propagation time…