Related papers: Gauge theories on quantum spaces
The nilpotent BRST, anti-BRST, dual-BRST and anti-dual-BRST symmetry transformations are constructed in the context of noncommutative (NC) 1-form as well as 2-form gauge theories. The corresponding Noether's charges for these symmetries on…
There is an interesting dichotomy between a space-time metric considered as external field in a flat background and the same considered as an intrinsic part of the geometry of space-time. We shall describe and compare two other external…
Gauge symmetries play a central role, both in the mathematical foundations as well as the conceptual construction of modern (particle) physics theories. However, it is yet unclear whether they form a necessary component of theories, or…
Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented. Some comparisons between them are made.
A review is made of recent efforts to add a gravitational field to noncommutative models of space-time. Special emphasis is placed on the case which could be considered as the noncommutative analog of a parallelizable space-time. It is…
A new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes…
In the groupoid approach to noncommutative quantization of gravity, gravitational field is quantized in terms of a C*-algebra A of complex valued funcions on a groupoid G (with convolution as multiplication). In the noncommutative quantum…
Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
We remark the importance of adding suitable pre-geometric content to tensor models, obtaining what has recently been called tensorial group field theories, to have a formalism that could describe the structure and dynamics of quantum…
This study of gauge field theories on kappa-deformed Minkowski spacetime extends previous work on field theories on this example of a noncommutative spacetime. We construct deformed gauge theories for arbitrary compact Lie groups using the…
We discuss how Moyal deformations of gauge theories, which arise naturally from open string theory, fit into the paradigm of colour-kinematics duality and the double copy of gauge theory to gravity. Along the way we encounter novel…
A consistent description of gauge theories on coordinate dependent non-commutative (NC) space-time is a long-standing problem with a number of solutions, none of which is free from criticism. In this work, we discuss the approach proposed…
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general…
We investigate non-commutative gauge theories in homogeneous spaces G/H. We construct such theories by adding cubic terms to IIB matrix model which contain the structure constants of G. The isometry of a homogeneous space, G must be a…
A description of motion is proposed, adapted to the composite bundle interpretation of Poincar\'e Gauge Theory. Reference frames, relative positions and time evolution are characterized in gauge-theoretical terms. The approach is…
We exploit the reparametrization symmetry of a relativistic free particle to impose a gauge condition which upon quantization implies space-time noncommutativity. We show that there is an algebraic map from this gauge back to the standard…
Spacetime manifolds that are not time orientable play a key role in a gravitational explanation of quantum theory. Such manifolds allow topology change, but also have fascinating additional properties such as net charge from source-free…
In this note we present a operator formulation of gauge theories in a quantum phase space which is specified by a operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport)…
We present a line by line derivation of canonical quantum mechanics stemming from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This viewpoint can…