Related papers: From twistors to twisted geometries

In this paper, we show how the restriction of the Quantum Geometric Tensor to manifolds of states that can be generated through local interactions provides a new tool to understand the consequences of locality in physics. After a review of…

A geometrical description of three qubit entanglement is given. A part of the transformations corresponding to stochastic local operations and classical communication on the qubits is regarded as a gauge degree of freedom. Entangled states…

The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…

On the basis of the principle that topological quantum phases arise from the scattering around space-time defects in higher dimensional unification, a geometric model is presented that associates with each quantum phase an element of a…

The wave description of geometric phase uses the superposition of light waves to explain the geometric phase's origin. While our previous work focused on a basis of linearly polarized waves, here we show that the same concepts can be…

Many intracellular processes continue to oscillate during the cell cycle. Although it is not well-understood how they are affected by discontinuities in the cellular environment, the general assumption is that oscillations remain robust…

The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations,…

We follow up on previous work which found that commonly used graph evolution moves lead to conserved quantities that can be expressed in terms of the braiding of the graph in its embedding space. We study non-embedded graphs under three…

In this paper, we review two approaches that can describe, in a geometrical way, the kinematics of particles that are affected by Planck-scale departures, named Finsler and Hamilton geometries. By relying on maps that connect the spaces of…

The connection between the geometric phase and quantum phase transition has been discussed extensively in the two-band model. By introducing the twist operator, the geometric phase can be defined by calculating its ground-state expectation…

In this paper, I emphasize those features of the extended phase space approach to quantization of gravity that distinguish it among other approaches. First of all, it is the conjecture about non-trivial topology of the Universe which was…

For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…

A complete geometric unification of gravity and electromagnetism is proposed by considering two aspects of torsion: its relation to spin established in Einstein--Cartan theory and the possible interpretation of the torsion trace as the…

Quantum Graphity is an approach to quantum gravity based on a background independent formulation of condensed matter systems on graphs. We summarize recent results obtained on the notion of emergent geometry from the point of view of a…

Quantum geometry, i.e., the quantum theory of intrinsic and extrinsic spatial geometry, is a cornerstone of loop quantum gravity. Recently, there have been many new ideas in this field, and I will review some of them. In particular, after a…

In previous work by two of the present authors, twistors were re-interpreted as 4-d spinors with a position dependence within the formalism of geometric (Clifford) algebra. Here we extend that approach and justify the nature of the position…

We show how the theory of $\mathbb{Z}_2^n$ -manifolds - which are a non-trivial generalisation of supermanifolds - may be useful in a geometrical approach to mixed symmetry tensors such as the dual graviton. The geometric aspects of such…

Variational formalism in the extended phase space for fields is applied to gravity. It is shown that the requirement of invariance under arbitrary local inertial frames implies a coupling of torsion to a 3-form of matter fields on the one…

Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…