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Quantum mechanics provides two fundamental examples of the duality between position and momentum, the Heisenberg uncertainty principle ΔxΔp ≥ ħ/2 stating that position and momentum cannot be simultaneously known to arbitrary precision, and the de Broglie relation p = ħk which states the momentum and wavevector of a free particle are ...
In mathematical physics, geometric quantization is a mathematical approach to defining a quantum theory corresponding to a given classical theory.It attempts to carry out quantization, for which there is in general no exact recipe, in such a way that certain analogies between the classical theory and the quantum theory remain manifest.
In light-front coordinates, + = +, =, the spatial coordinates ,, do not enter symmetrically: the coordinate is distinguished, whereas and do not appear at all. This non-covariant definition destroys the spatial symmetry that, in its turn, results in a few difficulties related to the fact that some transformation of the reference frame may ...
Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion. String theory, a leading candidate for a quantum theory of gravity, uses it to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions [clarification needed], minimal possible distance scale, and other effects that challenge intuition.
Canonical coordinates are defined as a special set of coordinates on the cotangent bundle of a manifold.They are usually written as a set of (,) or (,) with the x ' s or q ' s denoting the coordinates on the underlying manifold and the p ' s denoting the conjugate momentum, which are 1-forms in the cotangent bundle at point q in the manifold.
Canonical quantization develops quantum mechanics from classical mechanics. One introduces a commutation relation among canonical coordinates. Technically, one converts coordinates to operators, through combinations of creation and annihilation operators. The operators act on quantum states of the theory.
The implication is that a quantum field theory on noncommutative spacetime can be interpreted as a low energy limit of the theory of open strings. Two papers, one by Sergio Doplicher , Klaus Fredenhagen and John Roberts [ 5 ] and the other by D. V. Ahluwalia, [ 6 ] set out another motivation for the possible noncommutativity of space-time.
A reference frame can be treated in the formalism of quantum theory, and, in this case, such is referred as a quantum reference frame. Despite different name and treatment, a quantum reference frame still shares much of the notions with a reference frame in classical mechanics. It is associated to some physical system, and it is relational.