1,153 research outputs found
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
Notes on Connes' Construction of the Standard Model
The mathematical apparatus of non commutative geometry and operator algebras
which Connes has brought to bear to construct a rational scheme for the
internal symmetries of the standard model is presented from the physicist's
point of view. Gauge symmetry, anomaly freedom, conservation of electric
charge, parity violation and charge conjugation all play a vital role. When put
together with a relatively simple set of algebraic algorithms they deliver many
of the features of the standard model which otherwise seem rather ad hoc.Comment: 25 pages, Latex, no figure
Gravity in Non-Commutative Geometry
We study general relativity in the framework of non-commutative differential
geometry. In particular, we introduce a gravity action for a space-time which
is the product of a four dimensional manifold by a two-point space. In the
simplest situation, where the Riemannian metric is taken to be the same on the
two copies of the manifold, one obtains a model of a scalar field coupled to
Einstein gravity. This field is geometrically interpreted as describing the
distance between the two points in the internal space.Comment: ZU-TH-30/1992 and ETH/TH/92/44, 11 pages. (The earlier version of
this paper was the incomplete and unedited file which accidently replaced the
corrected file
Currents on Grassmann algebras
We define currents on a Grassmann algebra with generators as
distributions on its exterior algebra (using the symmetric wedge product). We
interpret the currents in terms of -graded Hochschild cohomology and
closed currents in terms of cyclic cocycles (they are particular multilinear
forms on ). An explicit construction of the vector space of closed
currents of degree on is given by using Berezin integration.Comment: 20 pages, CPT-93/P.2935 and ENSLAPP-440/9
Finite temperature corrections and embedded strings in noncommutative geometry and the standard model with neutrino mixing
The recent extension of the standard model to include massive neutrinos in
the framework of noncommutative geometry and the spectral action principle
involves new scalar fields and their interactions with the usual complex scalar
doublet. After ensuring that they bring no unphysical consequences, we address
the question of how these fields affect the physics predicted in Weinberg-Salam
theory, particularly in the context of the Electroweak phase transition.
Applying the Dolan-Jackiw procedure, we calculate the finite temperature
corrections, and find that the phase transition is first order. The new scalar
interactions significantly improve the stability of the Electroweak Z string,
through the ``bag'' phenomenon described by Watkins and Vachaspati. (Recently
cosmic strings have climbed back into interest due to new evidence). Sourced by
static embedded strings, an internal space analogy of Cartan's torsion is
drawn, and a possible Higgs-force-like `gravitational' effect of this
non-propagating torsion on the fermion masses is described. We also check that
the field generating the Majorana mass for the is non-zero in the
physical vacuum.Comment: 42 page
Algebraic treatment of compactification on noncommutative tori
In this paper we study the compactification conditions of the M theory on
D-dimensional noncommutative tori. The main tool used for this analysis is the
algebra A(Z^D) of the projective representations of the abelian group Z^D. We
exhibit the explicit solutions in the space of the multiplication algebra of
A(Z^D), that is the algebra generated by right and left multiplications.Comment: 8 pages, Latex, shortened version as accepted for publication in
Physics Letter
Does noncommutative geometry predict nonlinear Higgs mechanism?
It is argued that the noncommutative geometry construction of the standard
model predicts a nonlinear symmetry breaking mechanism rather than the orthodox
Higgs mechanism. Such models have experimentally verifiable consequences.Comment: 12 pages, LaTeX file, BI-TP 93/2
Non-linear sigma-models in noncommutative geometry: fields with values in finite spaces
We study sigma-models on noncommutative spaces, notably on noncommutative
tori. We construct instanton solutions carrying a nontrivial topological charge
q and satisfying a Belavin-Polyakov bound. The moduli space of these instantons
is conjectured to consists of an ordinary torus endowed with a complex
structure times a projective space .Comment: Latex, 10 page
Finite dimensional quantum group covariant differential calculus on a complex matrix algebra
Using the fact that the algebra M(3,C) of 3 x 3 complex matrices can be taken
as a reduced quantum plane, we build a differential calculus Omega(S) on the
quantum space S defined by the algebra C^\infty(M) \otimes M(3,C), where M is a
space-time manifold. This calculus is covariant under the action and coaction
of finite dimensional dual quantum groups. We study the star structures on
these quantum groups and the compatible one in M(3,C). This leads to an
invariant scalar product on the later space. We analyse the differential
algebra Omega(M(3,C)) in terms of quantum group representations, and consider
in particular the space of one-forms on S since its elements can be considered
as generalized gauge fields.Comment: 11 pages, LaTeX, uses diagrams.st
The Standard Model Fermion Spectrum From Complex Projective spaces
It is shown that the quarks and leptons of the standard model, including a
right-handed neutrino, can be obtained by gauging the holonomy groups of
complex projective spaces of complex dimensions two and three. The spectrum
emerges as chiral zero modes of the Dirac operator coupled to gauge fields and
the demonstration involves an index theorem analysis on a general complex
projective space in the presence of topologically non-trivial SU(n)xU(1) gauge
fields. The construction may have applications in type IIA string theory and
non-commutative geometry.Comment: 13 pages. Typset using LaTeX and JHEP3 style files. Minor typos
correcte
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