Related papers: The Fuzzy Onion: An Initial Study
The fuzzy disc, introduced by the authors of Ref.[1], is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. In this paper we show that one can introduce a concept of angles to the fuzzy disc,…
The matrix model with mass term has a nontrivially classical solution which is known to represent a noncommutative fuzzy sphere. The fuzzy sphere has a lower energy then that of the trivial solution. In this letter we investigate the…
The highly influential framework of conceptual spaces provides a geometric way of representing knowledge. Instances are represented by points in a high-dimensional space and concepts are represented by convex regions in this space. After…
We briefly review the connection between the fuzzy field theories and matrix models and describe the main features of the models that appear. We summarize the different approaches to their analysis, some of the recent results and the…
Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then…
We discuss various properties of the variational class of continuous matrix product states, a class of ansatz states for one-dimensional quantum fields that was recently introduced as the direct continuum limit of the highly successful…
We investigate the phase structure of a special class of multi-trace hermitian matrix models, which are candidates for the description of scalar field theory on fuzzy spaces. We include up to the fourth moment of the eigenvalue distribution…
A variational equation of the third order in three-dimensional space is proposed which describes autoparallel curves of some connection.
The notion of Intuitionistic fuzzy hypervector space has been generalized and a few basic properties on this concept are studied. It has been shown that the intersection and union of an arbitrary family of Intuitionistic fuzzy hypervector…
We discuss the second quantization of scalar field theory on the q-deformed fuzzy sphere S^2_{q,N} for q \in \R, using a path-integral approach. We find quantum field theories which are manifestly covariant under U_q(su(2)), have a smooth…
The model of a scalar field with quartic self-interaction on the fuzzy sphere has three known phases: a uniformly ordered phase, a disordered phase and a non-uniformly ordered phase, the last of which has no classical counterpart. These…
One-dimensional quantum optical models usually rest on the intuition of large scale separation or frozen dynamics associated with the different spatial dimensions, for example when studying quasi one-dimensional atomic dynamics, potentially…
A monistic framework is set up where energy is the only fundamental substance. Different states of energy are ordered by a set of scalar qunatum-phase-fields. The dual elements of matter, mass and space, are described as volume- and…
Lattice QCD with an even number of degenerate quark flavours is shown to be a limit of a local bosonic field theory. The action of the bosonic theory is real and bounded from below so that standard simulation algorithms can be expected to…
Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle…
Quantum Field Theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantum mechanics to QFT for students at early…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
We study the q-deformed fuzzy sphere, which is related to D-branes on SU(2) WZW models, for both real q and q a root of unity. We construct for both cases a differential calculus which is compatible with the star structure, study the…
Quantum simulation provides quantum systems under study with analogous controllable quantum systems and has wide applications from condensed-matter physics to high energy physics and to cosmology. The quantum system of a homogeneous and…
A detailed Monte Carlo calculation of the phase diagram of bosonic IKKT Yang-Mills matrix models in three and six dimensions with quartic mass deformations is given. Background emergent fuzzy geometries in two and four dimensions are…