conjugate momentum

conjugate momentum

[′kän·jə·gət mə′men·təm]
(mechanics)
If qj (j = 1,2, …) are generalized coordinates of a classical dynamical system, and L is its Lagrangian, the momentum conjugate to qj is pj = ∂ L /∂ qj. Also known as canonical momentum; generalized momentum.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
In the Nexus Paradigm, the labeling [q.sub.n] refers to a creation of a Nexus graviton in the n-th quantum state associated with a conjugate momentum [p.sub.n].
More concretely, in the case of one degree of freedom, besides [??] and the conjugate momentum [??], acting nontrivially in [H.sub.q], there should be [H.sub.t] where t, together with ?
where pr (i,t) is the conjugate momentum and can be determined from the relation
in terms of the conjugate momentum (p), the Hamiltonian density is
The Hamiltonian is expressed as a series expansion in terms of surface deformation coordinates and a conjugate momentum. We considered only the lowest kinetic energy terms, so that the eigen problem for our Hamiltonian reduces to Schrodinger equation in five dimensional spaces.
Considering that the scale factor a is positive, we require that the wave function of the universe vanishes at a = 0, in order for the conjugate momentum of a to be hermitic.
The fact that a [greater than or equal to] 0 can spoil hermiticity of the conjugate momentum of [[pi].sub.a].
Technically, every symmetry selects a constant conjugate momentum since, by the Euler-Lagrange equations we get
and the existence of a constant conjugate momentum means that a cyclic variable (a symmetry) exists.