相关论文: Manifestations of quantum holonomy in interferomet…

A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral…

A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum…

As a hallmark of pure quantum effect, quantum entanglement has provided unconventional routes to condensed matter systems. Here, from the perspective of quantum entanglement, we disclose exotic quantum physics in non-Hermitian…

Holonomies are of great interest to quantum computation and simulation. The geometrical nature of these entities offers increased stability to quantum gates. Furthermore, symmetries of particle physics are naturally reflected in holonomies,…

By considering the most general metric which can occur on a contractable two dimensional symplectic manifold, we find the most general Hamiltonians on a two dimensional phase space to which equivariant localization formulas for the…

A new symmetry of $(1,0)$ supersymmetric non-linear $\sigma$-models in two dimensions with Fermi and mass sectors is introduced. It is a generalisation of the so-called special holonomy $W$-symmetry of Howe and Papadopoulos associated with…

We describe a midi-superspace quantization scheme for generic single horizon black holes in which only the spatial diffeomorphisms are fixed. The remaining Hamiltonian constraint yields an infinite set of decoupled eigenvalue equations: one…

A theory of position of massive bodies is proposed that results in an observable quantum behavior of geometry at the Planck scale, $t_P$. Departures from classical world lines in flat spacetime are described by Planckian noncommuting…

We consider an abelian holonomy operator in two-dimensional conformal field theory with zero-mode contributions. The analysis is made possible by use of a geometric-quantization scheme for abelian Chern-Simons theory on $S^1 \times S^1…

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…

We consider the phase space of the Maxwell field as a simplified framework to study the quantisation of holonomies (Wilson line operators) on lightlike (null) surfaces. Our results are markedly different from the spacelike case. On a…

Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which…

We show that non-abelian quantum statistics can be studied using certain topological invariants which are the homology groups of configuration spaces. In particular, we formulate a general framework for describing quantum statistics of…

There are not many tools to quantitatively monitor the emergence of classical geometric features from a quantum spacetime, whose microscopic structure may be a highly quantum-fluctuating "spacetime foam". To improve this situation, we…

The geometric properties of quantum states is fully encoded by the quantum geometric tensor. The real and imaginary parts of the quantum geometric tensor are the quantum metric and Berry curvature, which characterize the distance and phase…

In the context of (2+1)--dimensional gravity, we use holonomies of constant connections which generate a $q$--deformed representation of the fundamental group to derive signed area phases which relate the quantum matrices assigned to…

Geometric phases play a fundamental role in understanding quantum topology, yet extending the Uhlmann phase to non-Hermitian systems poses significant challenges due to parameter-dependent inner product structures. In this work, we develop…

We consider an ``integral'' extension of the classical notion of affine connection providing a correspondence between paths in the manifold and diffeomorphisms of the manifold. These path-diffeomorphisms are a generalization of parallel…

In the context of quantum gravity for spacetimes of dimension 2+1, we describe progress in the construction of a quantum Goldman bracket for intersecting loops on surfaces. Using piecewise linear paths in R^2 (representing loops on the…

We propose a generalized quantum geometric tenor to understand topological quantum phase transitions, which can be defined on the parameter space with the adiabatic evolution of a quantum many-body system. The generalized quantum geometric…