Related papers: Quantum covariant derivative
We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…
Adaptive perturbation is a new method for perturbatively computing the eigenvalues and eigenstates of quantum mechanical Hamiltonians that heretofore were not believed to be obtainable by such methods. The novel feature of adaptive…
We discuss the covariant formulation of the dynamics of particles with abelian and non-abelian gauge charges in external fields. Using this formulation we develop an algorithm for the construction of constants of motion, which makes use of…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
The systematic derivation of constants of the motion, based on Killing tensors and the gauge covariant approach, is outlined. Quantum dots are shown to support second-, third- and fourth-rank Killing tensors.
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…
Vector is a physical quantity and it does not depend on any co-ordinate system. It need to be expanded in some basis for practical calculation and its components do depend on the chosen basis. The expansion in orthonormal basis is…
We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We…
We study the derivation of the effective equation of motion for a pointlike particle in the framework of quantum gravity. Just like the geodesic motion of a classical particle is a consequence of classical field theory coupled to general…
Noncommutative quantum mechanics can be considered as a first step in the construction of quantum field theory on noncommutative spaces of generic form, when the commutator between coordinates is a function of these coordinates. In this…
In these lecture notes, partly based on a course taught at the Karpacz Winter School in March 2014, we explore the close connections between non-adiabatic response of a system with respect to macroscopic parameters and the geometry of…
A recent surge of research in many-body quantum entanglement has uncovered intriguing properties of quantum many-body systems. A prime example is the modular commutator, which can extract a topological invariant from a single wave function.…
Among various approaches in proving gauge independence, models containing an explicit gauge dependence are convenient. The well-known example is the gauge parameter in the covariant gauge fixing which is of course most suitable for the…
Local observables in (perturbative) quantum gravity are notoriously hard to define, since the gauge symmetry of gravity -- diffeomorphisms -- moves points on the manifold. In particular, this is a problem for backgrounds of high symmetry…
The familiar concepts of state vectors and operators in quantum mechanics rely on associative products of observables. However, these notions do not apply to some exotic systems such as magnetic monopoles, which have long been known to lead…
Coherent-state representations are a standard tool to deal with continuous-variable systems, as they allow one to efficiently visualize quantum states in phase space. Here, we work out an alternative basis consisting of monomials on the…
Quantum computation is the suitable orthogonal encoding of possibly holistic functional properties into state vectors, followed by a projective measurement.
It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…
Gauge-invariant observables for quantum gravity are described, with explicit constructions given primarily to leading order in Newton's constant, analogous to and extending constructions first given by Dirac in quantum electrodynamics.…
Using stochastic quantization method we derive gauge-invariant equations, connecting multilocal vacuum correlators of nonperturbative field configurations immersed into the quantum background. Three alternative methods of stochastic…