相关论文: Quantum differential forms

Differential forms provide a coordinate-free way to express many quantities and relations in mathematical physics. In particular, they are useful in plasma physics. This tutorial gives a guide so that you can read the plasma physics…

A simple mathematical extension of quantum theory is presented. As well as opening the possibility of alternative methods of calculation, the additional formalism implies a new physical interpretation of the standard theory by providing a…

In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…

Starting from the concept of the universal exterior algebra in non-commutative differential geometry we construct differential forms on the quantum phase-space of an arbitrary system. They bear the same natural relationship to quantum…

In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…

We generalize Maxwell equations which describe the vacuum of quantum electrodynamics into the quantum form. This nontraditional approach is different from the widely used theory|-Quantum Electrodynamics. From another viewpoint, it could be…

Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.

Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…

Heisenberg motion equations in Quantum mechanics can be put into the Hamilton form. The difference between the commutator and its principal part, the Poisson bracket, can be accounted for exactly. Canonical transformations in Quantum…

A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…

A non--commutative analogue of the classical differential forms is constructed on the phase--space of an arbitrary quantum system. The non--commutative forms are universal and are related to the quantum mechanical dynamics in the same way…

The non-individuals interpretation of quantum mechanics is presented with the aim of clarifying it and highflying some of its salient features. Alternative formulations of it are proposed and examined.

A new quantum-stochastic differential calculus is derived for representing continuous quantum measurement of the position operator. Closed nonlinear quantum-stochastic differential equation is given for the quantum state of the observed…

Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.

We develop Cresson's nondifferentiable calculus of variations on the space of H\"{o}lder functions. Several quantum variational problems are considered: with and without constraints, with one and more than one independent variable, of first…

Various aspects of q-differential equations are examined in the contexts of quantum groups and spaces, differential calculi, zero curvature, and Lax-Sato hierarchies. There are many explicit formulas and examples along with some survey…

We outline the recent classification of differential structures for all main classes of quantum groups. We also outline the algebraic notion of `quantum manifold' and `quantum Riemannian manifold' based on quantum group principal bundles, a…

The non-commutative differential calculus on the quantum groups $SL_q(N)$ is constructed. The quantum external algebra proposed contains the same number of generators as in the classical case. The exterior derivative defined in the…

A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…

We introduce an explicit construction for realizing of the space of invariant deformation quantizations on an arbitrary symmetric bounded domain.