We discuss a generalization of the conventional bosonization procedure to the case of current-current interactions which get their natural representation in terms of current instead of fermion number density operators. A consistent bosonization procedure requires a geometrical quantization of the hamiltonian action of W ∞ on its coadjoint orbits. An integrable example of a nontrivial realizatio...

We present first results for masses of spin-3/2 baryons in lattice QCD, using a novel fat-link clover fermion action in which only the irrelevant operators are constructed using fat links. In the isospin-1/2 sector, we observe, after appropriate spin and parity projection, a strong signal for the J = 3 2 − state, and find good agreement between the 1 2 + mass and earlier nucleon mass simulation...

Systematic use of the infinite-dimensional spin representation simplifies and rigorizes several questions in Quantum Field Theory. This representation permutes “Gaussian” elements in the fermion Fock space, and is necessarily projective: we compute its cocycle at the group level, and obtain Schwinger terms and anomalies from infinitesimal versions of this cocycle. Quantization, in this framewor...

The search for Majorana fermions is quickly becoming an obsession in the condensed-matter community. To understand the intense interest, I will begin with a practical definition: a Majorana fermion is a fermion that is its own antiparticle. While sophisticated particle physics experiments are testing for Majorana character in neutrinos propagating in three dimensions [1], solid state physicists...

In a recent letter[1], Singh, Mobed and Papini (hereafter referred to as (I)) claim to show that the gravitaional field associated with the Lense-Thirring metric can distinguish between Dirac and Majorana neutrinos. According to these authors, the matrix element of the interaction Hamiltonian is significantly different, depending on the Dirac or Majorana nature of the neutrino. Here we point ou...

Schematic su(2)⊕ h3 interaction Hamiltonians, where su(2) plays the role of the pseudo-spin algebra of fermion operators and h3 is the Heisenberg algebra for bosons, are shown to be closely related to certain nonlinear models defined on a single quantum algebra suq(2) of quasifermions. In particular, suq(2) analogues of the Da ProvidenciaSchütte and extended Lipkin models are presented. The con...

We study four-point correlation functions with logarithmic behaviour in Liouville field theory on a sphere, which consist of one kind of the local operators. We study them as non-integrated correlation functions of the gravitational sector of two-dimensional quantum gravity coupled to an ordinary conformal field theory in the conformal gauge. We also examine, in the (p, q) minimal conformal fie...

Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as $\mathbb{Z}_2$-involutions in the passive transformation on coordinates; but together with a charge conjugation C, total C-P-R-T have enriched active transformations fields representations spacetime-internal symmetry groups quantum field theories (QFTs). In this work, we derive that these can be furth...

In this paper, the quantum theory of the infinite-component Majorana field for the fermionic tower is formulated. This study proves that the energy states with increasing spin are simply composite systems made by a bradyon and antitachyons with half-integer spin. The quantum field describing these exotic states is obtained by the infinite sum of four-spinor operators, which each operator depend...