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Fermion Hilbert space and fermion doubling in the noncommutative geometry approach to gauge theories
In this paper we study the structure of the Hilbert space for the recent noncommutative geometry models of gauge theories. We point out the presence of unphysical degrees of freedom similar to the
Geometry of the gauge algebra in noncommutative Yang-Mills Theory
A detailed description of the infinite-dimensional Lie algebra of -gauge transformations in non-commutative Yang-Mills theory is presented. Various descriptions of this algebra are given in terms of
The fuzzy disc
We introduce a finite dimensional matrix model approximation to the algebra of functions on a disc based on noncommutative geometry. The algebra is a subalgebra of the one characterizing the
Translation invariance, commutation relations and ultraviolet/infrared mixing
We show that the Ultraviolet/Infrared mixing of noncommutative field theories with the Gronewold-Moyal product, whereby some (but not all) ultraviolet divergences become infrared, is a generic
Infinitely many star products to play with
While there has been growing interest for noncommutative spaces in recent times, most examples have been based on the simplest noncommutative algebra: [x i ,x j ] = iθ ij . Here we present new
The Kirillov picture for the Wigner particle
We discuss the Kirillov method for massless Wigner particles, usually (mis)named "continuous spin" or "infinite spin" particles. These appear in Wigner's classification of the unitary representations
Bosonic spectral action induced from anomaly cancellation
We show how (a slight modification of) the noncommutative geometry bosonic spectral action can be obtained by the cancellation of the scale anomaly of the fermionic action. In this sense the standard
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