Higgs field as the gauge field corresponding to parity in the usual space-time

We find that the local character of field theory requires the parity degree of freedom of the fields to be considered as an additional dicrete fifth dimension which is an artifact emerging due to the local description of space-time. Higgs field arises as the gauge field corresponding to this discrete dimension. Hence the noncommutative geometric derivation of the standard model follows as a manifestation of the local description of the usual space-time.Comment: 14 pages, latex, no figure

Noncommutative Geometry and The Ising Model

The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces using the introduced tools of discrete geometry. We write the action for few models, then we compare them with various models of statistical physics. We construct also the gauge theory with a discrete gauge group.Comment: 12 pages, LaTeX, TPJU - 18/92, December 199

EPD and Characterization of Graphite Oxide/Hydroxyapatite/Sodium Alginate Coatings Incorporated with Si3N4 or CuO Nanoparticles on Titanium Biomaterials

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BRST invariant Lagrangian of spontaneously broken gauge theories in noncommutative geometry

The quantization of spontaneously broken gauge theories in noncommutative geometry(NCG) has been sought for some time, because quantization is crucial for making the NCG approach a reliable and physically acceptable theory. Lee, Hwang and Ne'eman recently succeeded in realizing the BRST quantization of gauge theories in NCG in the matrix derivative approach proposed by Coquereaux et al. The present author has proposed a characteristic formulation to reconstruct a gauge theory in NCG on the discrete space $M_4\times Z_{_N}$. Since this formulation is a generalization of the differential geometry on the ordinary manifold to that on the discrete manifold, it is more familiar than other approaches. In this paper, we show that within our formulation we can obtain the BRST invariant Lagrangian in the same way as Lee, Hwang and Ne'eman and apply it to the SU(2)$\times$U(1) gauge theory.Comment: RevTeX, page

Scalar field theory on κ\kappa-Minkowski space-time and Doubly Special Relativity

In this paper we recall the construction of scalar field action on $\kappa$-Minkowski space-time and investigate its properties. In particular we show how the co-product of $\kappa$-Poincar\'e algebra of symmetries arises from the analysis of the symmetries of the action, expressed in terms of Fourier transformed fields. We also derive the action on commuting space-time, equivalent to the original one. Adding the self-interaction $\Phi^4$ term we investigate the modified conservation laws. We show that the local interactions on $\kappa$-Minkowski space-time give rise to 6 inequivalent ways in which energy and momentum can be conserved at four-point vertex. We discuss the relevance of these results for Doubly Special Relativity.Comment: 17 pages; some editing done, final version to be published in Int. J. Mod. Phys.

Chiral spinors and gauge fields in noncommutative curved space-time

The fundamental concepts of Riemannian geometry, such as differential forms, vielbein, metric, connection, torsion and curvature, are generalized in the context of non-commutative geometry. This allows us to construct the Einstein-Hilbert-Cartan terms, in addition to the bosonic and fermionic ones in the Lagrangian of an action functional on non-commutative spaces. As an example, and also as a prelude to the Standard Model that includes gravitational interactions, we present a model of chiral spinor fields on a curved two-sheeted space-time with two distinct abelian gauge fields. In this model, the full spectrum of the generalized metric consists of pairs of tensor, vector and scalar fields. They are coupled to the chiral fermions and the gauge fields leading to possible parity violation effects triggered by gravity.Comment: 50 pages LaTeX, minor corrections and references adde

Chiral Asymmetry and the Spectral Action

We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter

Parallel Transport in Gauge Theory on M4×Z2M_4 \times Z_2 Geometry

We apply the gauge theory on $M_4\times Z_2$ geometry previously proposed by Konisi and Saito to the Weinberg-Salam model for electroweak interactions, especially in order to clarify the geometrical meaning of curvatures in this geometry. Considering the Higgs field to be a gauge field along $Z_2$ direction, we also discuss the BRST invariant gauge fixing in this theory.Comment: 14 pages, LaTeX file. Change in title and minor changes in conten

Noncommutative Geometry of Finite Groups

A finite set can be supplied with a group structure which can then be used to select (classes of) differential calculi on it via the notions of left-, right- and bicovariance. A corresponding framework has been developed by Woronowicz, more generally for Hopf algebras including quantum groups. A differential calculus is regarded as the most basic structure needed for the introduction of further geometric notions like linear connections and, moreover, for the formulation of field theories and dynamics on finite sets. Associated with each bicovariant first order differential calculus on a finite group is a braid operator which plays an important role for the construction of distinguished geometric structures. For a covariant calculus, there are notions of invariance for linear connections and tensors. All these concepts are explored for finite groups and illustrated with examples. Some results are formulated more generally for arbitrary associative (Hopf) algebras. In particular, the problem of extension of a connection on a bimodule (over an associative algebra) to tensor products is investigated, leading to the class of `extensible connections'. It is shown that invariance properties of an extensible connection on a bimodule over a Hopf algebra are carried over to the extension. Furthermore, an invariance property of a connection is also shared by a `dual connection' which exists on the dual bimodule (as defined in this work).Comment: 34 pages, Late