Related papers: Geodesic nature and quantization of shift vector
We explore how the quantum geometric properties of the Bloch wave function, characterized by the Hilbert-Schmidt quantum distance, impact magnetic phases in solid-state systems. To this end, we investigate the spin susceptibility within the…
The importance of simple geometrical invariants, such as the Berry curvature and quantum metric, constructed from the Bloch states of a crystal has become well-established over four decades of research. More complex aspects of geometry…
Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to…
Modeling the propagation of gravitational waves (GWs) through matter is complicated by the gauge freedom of linearized gravity in that once nonlinearities are taken into consideration, gauge artifacts can cause spurious acceleration of the…
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
In this article, the quantum representation of the algebra among reduced twisted geometries (with respect to the Gauss constraint) is constructed in the gauge invariant Hilbert space of loop quantum gravity. It is shown that the reduced…
It is argued that the massive non-Abelian gauge field theory without involving Higgs bosons may be well established on the basis of gauge-invariance principle because the dynamics of the field is gauge-invariant in the physical space…
We write down the Yang-Mills partition function and the average Wilson loop in terms of local gauge-invariant variables being the six components of the metric tensor of dual space. The Wilson loop becomes the trace of the parallel…
We present a formalism for analysis of linear Cauchy data on a Kottler metric. Our method removes redundancy due to gauge transformations and constraints. A set of four gauge-invariant, scalar functions on the Cauchy surface is produced and…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
The quantum metric and Berry curvature capture essential properties of non-trivial Bloch states and underpin many fascinating phenomena. However, it becomes increasingly evident that a more comprehensive understanding of quantum state…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
The Loop Variable method that has been developed for the U(1) bosonic open string is generalized to include non-Abelian gauge invariance by incorporating "Chan-Paton" gauge group indices. The scale transformation symmetry $k(s) \to k(s)…
The Hamiltoinian analysis of the vector-tensor theory of gravity is performed. The resulting geometrical dynamics is reformulated into the connection dynamics, with the real SU(2)-connection serving as one of the configuration variables.…
For (2+2)-dimensional nonholonomic distributions, the physical information contained into a spacetime (pseudo) Riemannian metric can be encoded equivalently into new types of geometric structures and linear connections constructed as…
Classical methods of differential geometry are used to construct equations of motion for particles in quantum, electrodynamic and gravitational fields. For a five dimensional geometrical system, the equivalence principle can be extended.…
We prove that $\W_3$ is the gauge symmetry of the scale-invariant rigid particle, whose action is given by the integrated extrinsic curvature of its world line. This is achieved by showing that its equations of motion can be written in…
Quantum geometry characterizes the variation of wavefunctions in momentum space through their overlaps and relative phases, providing a general framework for understanding many transport and optical properties. It is generally formulated in…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
In recent work on Einstein gravity in four dimensions using the Ashtekar variables, non-local loop variables have played an important role in attempts to formulate a quantum theory. The introduction of such variables is guided by gauge…