相关论文: Non-Commutative Geometry, Spin and Quarks
In [1], Connes presented axioms governing noncommutative geometry. He went on to claim that when specialised to the commutative case, these axioms recover spin or spin^c geometry depending on whether the geometry is ''real'' or not. We…
We consider the Quasilocal Quark Model of NJL type (QNJLM) as an effective theory of non-perturbative QCD including scalar (S), pseudoscalar (P), vector (V) and axial-vector (A) four-fermion interaction with derivatives. In the presence of…
We discuss the role that interactions play in the non-commutative structure that arises when the relative coordinates of two interacting particles are projected onto the lowest Landau level. It is shown that the interactions in general…
Analysing two models of four-quark interactions which are of intrinsic difference in the behaviours of their correlation lengths some issues of quark condensations are considered. It is demonstrated that the quark condensates substantially…
We investigate the relationship between mass and spin of quark anti-quark bound state in non-commutative gauge theory with N=4 supersymmetry. In the large N and large 't Hooft coupling limit, these bound states correspond to rotating open…
In this talk I shall first make some brief remarks on quaternionic quantum mechanics, and then describe recent work with A.C. Millard in which we show that standard complex quantum field theory can arise as the statistical mechanics of an…
Based on the permutation group formalism, we present a discrete symmetry algebra in QCD. The discrete algebra is hidden symmetry in QCD, which is manifest only on a space-manifold with non-trivial topology. Quark confinement in the presence…
Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum…
From the mass term for the transformed quark fields, we obtain effective contact interactions of the NJL type. The parameters of the model that maps a system of non-interacting transformed fields into quarks interacting via NJL contact…
With the bare essentials of noncommutative geometry (defined by a spectral triple), we first describe how it naturally gives rise to gauge theories. Then, we quickly review the notion of twisting (in particular, minimally) noncommutative…
In these proceedings we review the main results concerning superspace geometries with nonanticommutative spinorial variables and field theories formulated on them. In particular, we report on the quantum properties of the WZ model…
In a previous paper we developed a formalism to construct (potentially) supersymmetric theories in the context of noncommutative geometry. We apply this formalism to explore the existence of a noncommutative version of the minimal…
The interaction between static quarks is derived by applying many-body techniques to QCD in Coulomb gauge. The result is shown to be exact in the IR and UV limits, and agrees remarkably well with lattice computations.
We analyse the causality condition in noncommutative field theory and show that the nonlocality of noncommutative interaction leads to a modification of the light cone to the light wedge. This effect is generic for noncommutative geometry.…
We investigate the effect of the noncommutative geometry on the classical orbits of particles in a central force potential. The relation is implemented through the modified commutation relations $[x_i, x_j]=i \theta_{ij} $. Comparison with…
In the QCD analysis, when quarks are expressed in quaternion basis, the quark and its charge conjugate together are expressed by octonions and the octonion posesses the triality symmetry. Gluos are expressed by Pl\"ucker coordinates of…
I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.
In this paper, we use methods from differential geometry and statistical mechanics to investigate a model for the concept of mass. The theory is not quantum mechanical in the usual sense, although certain features like multiple histories…
A review is given of some 2-dimensional metrics for which noncommutative versions have been found. They serve partially to illustrate a noncommutative extension of the moving-frame formalism. All of these models suggest that there is an…
The main properties of the leading-twist transverse momentum dependent parton distributions in a light-cone constituent quark model of the nucleon are reviewed, with focus on the role of the spin-spin and spin-orbit correlations of quarks.…