Related papers: Lectures on Matrix Field Theory I
Quantization of spacetime by means of finite dimensional matrices is the basic idea of fuzzy spaces. There remains an issue of quantizing time, however, the idea is simple and it provides an interesting interplay of various ideas in…
We show that after the Seiberg-Witten map is performed the action for noncommutative field theories can be regarded as a coupling to a field dependent gravitational background. This gravitational background depends only on the gauge field.…
I recall the main motivation to study quantum field theories on noncommutative spaces and comment on the most-studied example, the noncommutative R^4. That algebra is given by the *-product which can be written in (at least) two ways: in an…
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has…
We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that…
In this contribution to the proceedings of the Corfu Summer Institute 2015, I give an overview over quantum field theories on non-commutative Moyal space and renormalization. In particular, I review the new features and challenges one faces…
These lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate…
Non-Perturbative Quantum Field Theory has played an important role in the study of phenomena where a fermion condensate can appear under certain physical conditions. The familiar phenomenon of electric superconductivity, the color…
The paper investigates relations between the phase space structure of a quantum field theory ("nuclearity") and the concept of pointlike localized fields. Given a net of local observable algebras, a phase space condition is introduced that…
We show that the matrix formulation of non-commutative field theories is equivalent, in the continuum, to a formulation in a mixed configuration-momentum space. In this formulation, the non-locality of the interactions, that leads to the…
We explore the origins of non-geometric fluxes within the context of M theory described as a matrix model. Building upon compactifications of Matrix theory on non-commutative tori and twisted tori, we formulate the conditions which describe…
This is an introduction to the basic ideas and to a few further selected topics in conformal quantum field theory and in the theory of Kac-Moody algebras.
We review some selected aspects of the construction of gauge invariant operators in field theories on non-commutative spaces and their relation to the energy momentum tensor as well as to the non-commutative loop equations.
Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory for large $N$ is described by q-deformed quantum field. The master fields for large N theories satisfy to standard equations of relativistic field theory but fields…
It is shown that all possible N sheeted coverings of the cylinder are contained in type IIA matrix string theory as non-trivial gauge field configurations. Using these gauge field configurations as backgrounds the large $N$ limit is shown…
The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quaternion) form. It was shown that the plane…
Techniques of zero-temperature field theory that have found application in the analysis of field theory at finite temperature are revisited. Specifically, several of the results that are discussed are relevant to the study of…
Recent progress in the understanding of gravity on noncommutative spaces is discussed. A gravity theory naturally emerges from matrix models of noncommutative gauge theory. The effective metric depends on the dynamical Poisson structure,…
During the last century the tensor theory of the gravitational field was developed. We propose and develop the novel, pure mathematical, matrix theory of the field in n-dimensional metric space. The definition of the mathematical field…
A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define…