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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.
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 ...
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.
Front-form relativistic quantum mechanics was introduced by Paul Dirac in a 1949 paper published in Reviews of Modern Physics. [4] Light-front quantum field theory is the front-form representation of local relativistic quantum field theory.
In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle.. When the position operator is considered with a wide enough domain (e.g. the space of tempered distributions), its eigenvalues are the possible position vectors of the particle.
In quantum mechanics, idealized situations occur in rectangular Cartesian coordinates, such as the potential well, particle in a box, quantum harmonic oscillator, and more realistic approximations in spherical polar coordinates such as electrons in atoms and molecules. For generality, a formalism which can be used in any coordinate system is ...
In pure and applied mathematics, particularly quantum mechanics and computer graphics and their applications, a spherical basis is the basis used to express spherical tensors. [definition needed] The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions.
The phase-space formulation is a formulation of quantum mechanics that places the position and momentum variables on equal footing in phase space.The two key features of the phase-space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product.