We study the fuzzy or noncommutative Dp-branes in terms of infinitely many unstable D0-branes, from which we can construct any Dp-branes. We show that the tachyon condensation of the unstable D0-branes induces the noncommutativity. In the infinite tachyon condensation limit, most of the unstable D0-branes disappear and remaining D0-branes are actually the BPS D0-branes with the correct noncommu...

We analyse the dynamics of an open membrane, both for the free case and when it is coupled to a background three-form, whose boundary is attached to p-branes. The role of boundary conditions and constraints in the Nambu-Goto and Polyakov formulations is studied. The low-energy approximation that effectively reduces the membrane to an open string is examined in detail. Noncommutative features of...

We consider the complexity of computing the determinant over arbitrary finite-dimensional algebras. We first consider the case that A is fixed. We obtain the following dichotomy: If A/ radA is noncommutative, then computing the determinant over A is hard. “Hard” here means #P-hard over fields of characteristic 0 and ModpP-hard over fields of characteristic p > 0. If A/ radA is commutative and t...

We investigate the transition from second to first order systems. This transforms configuration space into phase space and hence introduces noncommutativity in the former. Quantum mechanically, the transition may be described in terms of spectral flow. Gaps in the energy or mass spectrum may become large which effectively truncates the available state space. Using both operator and path integra...

In many aspects the most complicated foliated manifolds are those with nonvanishing Godbillon-Vey class. We argue that they probably do not appear in physics and that is due to gauge symmetry which prevents the foliation from becoming “too wild”; that means that the foliation does not develop resilient leaves which, at least in codim-1, by Duminy’s theorem are responsible for the nontriviality ...

We give substance to the motto “every partial algebra is the colimit of its total subalgebras” by proving it for partial Boolean algebras (including orthomodular lattices), the new notion of partial C*-algebras (including noncommutative C*-algebras), and variations such as partial complete Boolean algebras and partial AW*-algebras. Both pairs of results are related by taking projections. As cor...

Noncommutativity lays hidden in the proofs of classical dynamics. Modern frameworks can be used to bring it to light: *-products, groupoids, q-deformed calculus, etc.

This paper is an introduction to discrete physics based on a non-commutative calculus of finite differences. This gives a context for the Feynman-Dyson derivation of non-commutative electromagnetism, and for generalizations of this result. The paper discusses these ideas and their relations with quantum groups and topological quantum field theory.

We discuss various limits which transform configuration space into phase space, with emphasis on those related to lightfront field theory, and show that they are unified by spectral flow. Examples include quantising in ‘almost lightfront’ coordinates and the appearance of lightlike noncommutativity from a strong background laser field. We compare this with the limit of a strong magnetic field, ...

We apply the embedding method of Batalin-Tyutin for revealing noncommutative structures in the generalized Landau problem. Different types of noncommutativity follow from different gauge choices. This establishes a duality among the distinct algebras. An alternative approach is discussed which yields equivalent results as the embedding method. We also discuss the consequences in the Landau prob...