Quick search Find article
Quick search
Find article

Differential calculus and gauge theory on finite sets

A Dimakis and F Muller-Hoissen

Show affiliations


We develop differential calculus and gauge theory on a finite set G. An elegant formulation is obtained when G is supplied with a group structure and in particular for a cyclic group. Connes' two-point model (1986) (which is an essential ingredient of his reformulation of the standard model of elementary particle physics) is recovered in our approach. Reductions of the universal differential calculus to 'lower-dimensional' differential calculi are considered. The 'complete reduction' leads to a differential calculus on a periodic lattice.


PACS

11.15.-q Gauge field theories

02.30.-f Function theory, analysis

02.10.Yn Matrix theory

02.40.-k Geometry, differential geometry, and topology

02.10.Ab Logic and set theory

MSC

81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)

53Cxx Global differential geometry (See also 51H25, 58-XX; for related bundle theory, see 55Rxx, 57Rxx)

15A57 Other types of matrices (Hermitian, skew-Hermitian, etc.)

Subjects

Mathematical physics

Particle physics and field theory

Dates

Issue 9 (7 May 1994)



  1. Differential calculus and gauge theory on finite sets

    A Dimakis and F Muller-Hoissen 1994 J. Phys. A: Math. Gen. 27 3159

  2. The Hausdorf dimension of the Apollonian packing of circles

    P B Thomas and D Dhar 1994 J. Phys. A: Math. Gen. 27 2257

  3. Coupled dynamics of fast spins and slow interactions in neural networks and spin systems

    R W Penney et al 1993 J. Phys. A: Math. Gen. 26 3681

  4. Noncommutative differential calculus and lattice gauge theory

    A Dimakis et al 1993 J. Phys. A: Math. Gen. 26 1927

  5. Exact solution of a 1D asymmetric exclusion model using a matrix formulation

    B Derrida et al 1993 J. Phys. A: Math. Gen. 26 1493

  6. Information capacity of a perceptron

    N Brunel et al 1992 J. Phys. A: Math. Gen. 25 5017

  7. A generalization of Handscomb's quantum Monte Carlo scheme-application to the 1D Hubbard model

    A W Sandvik 1992 J. Phys. A: Math. Gen. 25 3667

  8. Thermodynamics of the strongly correlated Hubbard model

    Y S Yang and C J Thompson 1991 J. Phys. A: Math. Gen. 24 L279

  9. A gauge theory for a quantum system with isospin

    E B Lin 1991 J. Phys. A: Math. Gen. 24 L1045

  10. Localization and spectral statistics in a banded random matrix ensemble

    M Wilkinson et al 1991 J. Phys. A: Math. Gen. 24 175

Related review articles

What's this?
View review articles related to this research to gain an insight into the key trends in this subject area. Related review articles are selected based on PACS/MSC codes, and are no more than three years old.

  1. Chern–Simons forms in gravitation theories
  2. Supersymmetric many-particle quantum systems with inverse-square interactions
  3. Superconformal mechanics
More

View by subject




Export








Please login to access our web services, or create an account if you don't yet have one.

You must have cookies enabled in your web browser to be able to login.

Username
Password

Forgotten your password? Get a new one here.