Related papers: Geometry of Quantum Group invariant systems
From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have…
Anyonic oscillators with fractional statistics are built on a two-dimensional square lattice by means of a generalized Jordan-Wigner construction, and their deformed commutation relations are thoroughly discussed. Such anyonic oscillators,…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…
We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive…
We study two--loop renormalization in $(2+\epsilon)$--dimensional quantum gravity. As a first step towards the full calculation, we concentrate on the divergences which are proportional to the number of matter fields. We calculate the…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
How complex is the structure of quantum geometry? In several approaches, the spacetime atoms are obtained by the SU(2) intertwiner called quantum tetrahedron. The complexity of this construction has a concrete consequence in recent efforts…
The quantum geometric tensor (QGT) characterizes the local geometry of quantum states, and its components directly account for the dynamical effects observed, e.g., in condensed matter systems. In this work, we address the problem of…
The purpose of this overview article, which can be viewed as a supplement to our previous review on quantum rings, [S. Viefers {\it et al}, Physica E {\bf 21} (2004), 1-35], is to highlight the differences of boson and fermion systems in…
We argue that fermion-boson mapping techniques represent a natural tool for studying many-body supersymmetry in fermionic systems with pairing. In particular, using the generalized Dyson mapping of a many-level fermion superalgebra with the…
Toroidal classification and geometric duality in quantum spin systems is presented. Through our classification and duality, we reveal that various bipartite quantum features in magnon-systems can manifest equivalently in both bipartite…
All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…
The Skyrme model is considered quantum mechanically ab initio in various irreducible representations of the SU(2) group. The canonical quantization procedure yields negative mass correction ensuring existence of stabile soliton solution…
Quantum phase transitions in a system of N bosons with angular momentum L=0,2 (s,d) and a single fermion with angular momentum j are investigated both classically and quantum mechanically. It is shown that the presence of the odd fermion…
We study a conformal field theory that arises in the infinite-volume limit of a spin chain with $U_q(sl_2)$ global symmetry. Most operators in the theory are defect-ending operators which allows $U_q(sl_2)$ symmetry transformations to act…
The properties of the deformed bosonic oscillator, and the quantum groups ${\cal U}_q(SL(2))$ and $GL_q(2)$ in the limit as their deformation parameter $q$ goes to a root of unity are investigated and interpreted physically. These…
The geometry of Hamiltonian's eigenstates is encoded in the quantum geometric tensor (QGT). It contains both the Berry curvature, central to the description of topological matter and the quantum metric. So far the full QGT has been measured…
The implementation of physical symmetries into problem descriptions allows for the reduction of parameters and computational complexity. We show the integration of the permutation symmetry as the most restrictive discrete symmetry into…
The possible role of gravity in a noncommutative geometry is investigated. Due to the Moyal *-product of fields in noncommutative geometry, it is necessary to complexify the metric tensor of gravity. We first consider the possibility of a…
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered…