منابع مشابه
On Noncommutative Classical Mechanics
In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, [1]. I treat some classical systems with various potentials and some Physical interpretations are given concerning the presence of noncommutativity at large scales (Celeste Mechanics) directly tied to the one present at small scales (Quant...
متن کاملNoncommutative Classical and Quantum Mechanics for Quadratic Lagrangians (Hamiltonians)
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the algebra by linear transformation of coordinates and transmitted to the Hamiltonian (Lagrangian). Since linear transformations do not change the quadratic form of ...
متن کاملNoncommutative Quantum Mechanics
We consider Feynman’s path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the another one with usual commutative coordinates and momenta. We found connection between quadratic classical Hamiltonians, as well as Lagrangians, in their co...
متن کاملNoncommutative Lagrange Mechanics
It is proposed how to impose a general type of “noncommutativity” within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy, which are extensively applied within noncommutative quantum theories. Newton–Lagrange noncommutative equations of motion are formulated and their properties are...
متن کاملClassical Mechanics
here xi = (xi1, . . . , xid) are coordinates of the i-th particle and ∂xi is the gradient (∂xi1 , . . . , ∂xid); d is the space dimension (i.e. d = 3, usually). The potential energy function will be supposed “smooth”, i.e. analytic except, possibly, when two positions coincide. The latter exception is necessary to include the important cases of gravitational attraction or, when dealing with ele...
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ژورنال
عنوان ژورنال: International Journal of Theoretical Physics
سال: 2004
ISSN: 0020-7748
DOI: 10.1023/b:ijtp.0000028864.02161.a3