Related papers: Group Theoretic Approach to Fermion Production
We show that each unitary representation of the N=2 superVirasoro algebra can be realized in terms of ``collective excitations'' over a filled Dirac sea of fermionic operators satisfying a generalized exclusion principle. These are…
The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the…
We study the quantum fermions+gravity system, that is, the gravitational counterpart of QED. We start from the standard Einstein-Weyl theory, reformulated in terms of Ashtekar variables; and we construct its non- perturbative quantum theory…
Based on the generalized gauge theory on $M^4\times Z_2\times Z_3$, we reconstructed the realistic SU(5) Grand Unified model by a suitable assignment of fermion fields. The action of group elements $Z_2$ on fermion fields is the charge…
In this paper we start from a basic notion of process, which we structure into two groupoids, one orthogonal and one symplectic. By introducing additional structure, we convert these groupoids into orthogonal and symplectic Clifford…
One of the interesting features in unification models and supersymmetric unification models is that the chiral states of quarks and leptons in a family including a right-handed neutrino can be fitted neatly into a fundamental spinor…
Fermionic linear optics corresponds to the dynamics of free fermions, and is known to be efficiently simulable classically. We define fermionic anyon models by deforming the fermionic algebra of creation and annihilation operators, and…
Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and…
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It…
We construct a four dimensional lattice gauge theory in which fermions acquire mass without breaking symmetries as a result of gauge interactions. Our model consists of reduced staggered fermions transforming in the bifundamental…
We construct a gauge theory based in the supergroup $G=SU(2,2|2)$ that generalizes MacDowell-Mansouri supergravity. This is done introducing an extended notion of Hodge operator in the form of an outer automorphism of $su(2,2|2)$-valued…
Previously one of us presented a conjecture [APF-4 Proceedings] to model antiferromagnetism and high temperature superconductivity and their 'unification' by quantum group symmetry rather than the corresponding classical symmetry in view of…
In a previous paper we introduced two linear spinor equations equivalent to the Lorentz Force and stated that these equations were fairly general and could be applied to any force field compatible with Special Relativity. In this paper, via…
We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…
Is there more to Dirac's gamma matrices than meets the eye? It turns out that gamma zero can be factorized into a product of three operators. This revelation facilitates the expansion of Dirac's space-time algebra to Clifford algebra…
We suggest the model with the gauge group $ ... \otimes SU(6) \otimes SU(5)\otimes SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$. This group is the infinite continuation of the gauge group $SU(4) \otimes SU(3) \otimes SU(2) \otimes U(1)$…
We proposed a viable and predictive model based on the $SU(3)_C \times SU(3)_L \times U(1)_X$ gauge symmetry, supplemented by the global $U(1)_{Lg}$ symmetry, the $S_4$ family symmetry and several auxiliary cyclic symmetries, which…
It has been proposed several times in the past that one can obtain an equivalent, but in many aspects simpler description of fermions by first reformulating their first-order (Dirac) Lagrangian in terms of two-component spinors, and then…
We present a new predictive approach based on SUSY $SO(10)$ theory. The inter-family hierarchy is first generated in the sector of hypothetical superheavy fermions and then transfered inversely to ordinary quarks and leptons by means of the…
Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of…