Related papers: Quantum covariant derivative
This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief…
Over the years, Berry curvature, which is associated with the imaginary part of the quantum geometric tensor, has profoundly impacted many branches of physics. Recently, quantum metric, the real part of the quantum geometric tensor, has…
Quantum theory of the gauge models in the causal approach leads to some cohomology problems. We investigate these problems in detail.
We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector…
Quantum field theory is assumed to be gauge invariant. However it is well known that when certain quantities are calculated using perturbation theory the results are not gauge invariant. The non-gauge invariant terms have to be removed in…
Differences between vector potentials in different gauges contain no dynamics in both classical and quantum electrodynamics and chromodynamics. Consequently, once gauge invariance is established, results calculated in non-covariant gauges…
The elements of the quantum mechanical diffusion matrix, leading to a Gibbs equilibrium state for a set of $N$ coupled quantum harmonic oscillators are derived within Lindblad's axiomatic approach. Consequences of the fundamental…
Provided a quantum superconducting condensate is allowed to occupy a curved hyper-plane of space-time, a geometric potential from the kinetic term arises. An energy conservation relation involving the geometric field at every material point…
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum…
The BSSN and standard gauge equations are written in covariant form with respect to spatial coordinate transformations. The BSSN variables are defined as tensors with no density weights. This allows us to evolve a given set of initial data…
In this part of the series five-dimensional tangent vectors are introduced first as equivalence classes of parametrized curves and then as differential-algebraic operators that act on scalar functions. I then examine their basic algebraic…
A non-gauge dynamical system depending on parameters is considered. It is shown that these parameters can have such values that corresponding canonically quantized theory will be gauge invariant. The equations allowing to find these values…
One of the objectives of theories describing quantum dynamical geometry is to compute expectation values of geometrical observables. The results of such computations can be affected by whether or not matter is taken into account. It is thus…
The field equations in modified gravity theories possess an important decoupling property with respect to certain classes of nonholonomic frames. This allows us to construct generic off--diagonal solutions depending on all spacetime…
Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance…
Reflection and braid equations for rank two $q$-tensors are derived from the covariance properties of quantum vectors by using the $R$-matrix formalism.
The quantum derivatives of $e^{-A}, A^{-1}$ and $\log A$, which play a basic role in quantum statistical physics, are derived and their convergence is proven for an unbounded positive operator $A$ in a Hilbert space. Using the quantum…
It is shown with the help of skew-symmetric forms that the mathematical physics equations, on which no additional conditions are imposed, have quantum properties. And this is due to the integrability properties of differential equations,…
Covariant forms are given to a gauge theory of massive tensor field. This is accomplished by introducing another auxiliary field of scalar type to the system composed of a symmetric tensor field and an auxiliary field of vector type. The…
Quantum geometric tensor (QGT), including a symmetric real part defined as quantum metric and an antisymmetric part defined as Berry curvature, is essential for understanding many phenomena. We studied the photogalvanic effect of a…