Hamiltonian formulation of ferromagnetic hydrodynamics

The equations of ideal ferromagnetic hydrodynamics (FMHD) in three dimensions are formulated as a hamiltonian system in terms of a noncanonical Poisson bracket. The conservation laws for this system are determined and used to construct Lyapunov functionals that are potentially useful for dealing with stability properties of FMHD equilibrium solutions. Classes of equilibrium solutions are identified with critical points of these Lyapunov functionals. The FMHD system is also formulated in n dimensions and the relations among magnetic induction, magnetic field intensity, and magnetization density are discussed from a Lie-algebraic viewpoint.     

Hamiltonian formulation of the supermembrane

The hamiltonian formulation of the supermembrane theory in eleven dimensions is given. The covariant split of the first and second class constraints is exhibited, and their Dirac brackets are computed. Gauge conditions are imposed in such a way that the reparametrizations of the membrane with divergence-free 2-vectors are unfixed.     

Hamiltonian formulation of string field theory

Witten's string field theory is quantized in the hamiltonian formalism. The constraints are solved and the hamiltonian is expressed in terms of only physical degrees of freedom. Thus, no Faddeev-Popov ghosts are introduced. Instead, the action contains terms of arbitrarily high order in the string functionals. Agreement with the standard results is demonstrated by an explicit calculation of the residues of the first few poles of the four-tachyon tree amplitude.     

Hamiltonian formulation of Riemann ellipsoid dynamics

A Riemann ellipsoid is a classical fluid with an ellipsoidal boundary whose motion depends linearly on position. The Riemann ellipsoid Newtonian equations of motion are proven to form a Hamiltonian dynamical system. The co-adjoint orbits of a Lie group GCM(3) on which the inertia tensor is positive-definite are the reduced phase spaces of Riemann ellipsoids for which conservation of circulation has been exploited fully.     

Real Hamiltonian forms of Hamiltonian systems

We introduce the notion of a real form of a Hamiltonian dynamical system in analogy with the notion of real forms for simple Lie algebras. This is done by restricting the complexified initial dynamical system to the fixed point set of a given involution. The resulting subspace is isomorphic (but not symplectomorphic) to the initial phase space. Thus to each real Hamiltonian system we are able to associate another nonequivalent (real) ones. A crucial role in this construction is played by the assumed analyticity and the invariance of the Hamiltonian under the involution. We show that if the initial system is Liouville integrable, then its complexification and its real forms will be integrable again and this provides a method of finding new integrable systems starting from known ones. We demonstrate our construction by finding real forms of dynamics for the Toda chain and a family of Calogero-Moser models. For these models we also show that the involution of the complexified phase space induces a Cartan-like involution of their Lax representations.Received: 8 October 2003, Published online: 8 June 2004PACS: 02.30.Ik Integrable systems - 45.20.Jj Lagrangian and Hamiltonian mechanics     

Hamiltonian formulation of anomaly free chiral bosons

Starting out with an anomaly free lagrangian formulation for chiral scalars, which includes a Wess-Zumino term (to cancel the anomaly), we formulate the corresponding hamiltonian problem. Then we use the (quantum) Siegel invariance to choose a particular solution, which turns out to coincide with the one obtained by Floreanini and Jackiw.     

Hamiltonian formulation of theories with higher derivatives

A method of constructing the Hamiltonian formulation for a singular Lagrangian with higher derivatives is discussed. The method allows the specifics of the theory to be taken into account. It is shown that Hamiltonian formulations constructed from the same Lagrangian, but with different methods of introducing the additional generalized coordinates representing the higher derivatives, are related by a canonical point transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 65–68, September, 1985.     

Time-dependent formulation of the linear unitary transformation and the time evolution of general time-dependent quadratic Hamiltonian systems

A time-dependent closed-form formulation of the linear unitary transformation for harmonic-oscillator annihilation and creation operators is presented in the Schrödinger picture using the Lie algebraic approach. The time evolution of the quantum mechanical system described by a general time-dependent quadratic Hamiltonian is investigated by combining this formulation with the time evolution equation of the system. The analytic expressions of the evolution operator and propagator are found. The motion of a charged particle with variable mass in the time-dependent electric field is considered as an illustrative example of the formalism. The exact time evolution wave function starting from a Gaussian wave packet and the operator expectation values with respect to the complicated evolution wave function are obtained readily.     

Hamiltonian formulation for the positron trapping model

Summary A Hamiltonian formulation is used to build up an adequate Hamiltonian for the positron trapping model. The number of positrons annihilated in the free state,n _f, or the trapped one,n _v, are considered canonical conjugate variables; this point of view provides a route to propose a Hamiltonian which leads to the previously proposed phenomenological master equations.

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Riassunto Si usa una formulazione hamiltoniana per elaborare un'hamiltoniana adeguata per il modello a trappola dei positroni. Il numero di positroni annichilati nello stato libero,n _f, o in quello intrappolato,n _v, è considerato come variabili coniugate canoniche; in questo senso si fornisce una via per proporre un'hamiltoniana che porti alle equazioni principali fenomenologiche proposte precedentemente.

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Резюме Гамильтонова формулировка используется для конструирования адекватного Гамильтониана для модели захвата позитрона. Число аннигилированных позитронов в свободном состоянии,n _f, или число захваченных позитронов,n _v, рассматриваются как канонически сопряженные переменные. Этот подход приводит к Гамильтониану. Который дает ранее предположенные феноменологические ?управляющие? уравнения.

     

Conformal Hamiltonian systems

Vector fields whose flow preserves a symplectic form up to a constant, such as simple mechanical systems with friction, are called “conformal”. We develop a reduction theory for symmetric conformal Hamiltonian systems, analogous to symplectic reduction theory. This entire theory extends naturally to Poisson systems: given a symmetric conformal Poisson vector field, we show that it induces two reduced conformal Poisson vector fields, again analogous to the dual pair construction for symplectic manifolds. Conformal Poisson systems form an interesting infinite-dimensional Lie algebra of foliate vector fields. Manifolds supporting such conformal vector fields include cotangent bundles, Lie–Poisson manifolds, and their natural quotients.     

Hamiltonian formulation of d = 10 supergravity theories

A method is given for deriving the hamiltonian form of the d = 10 supergravity models. It is explicitly applied to the N = 1 theory.     

Hamiltonian formulation of the anomalous chiral Schwinger model

We construct the hamiltonian formulation of the anomalous chiral Schwinger model, which has recently been shown to yield a consistent unitary theory. The impact of the anomaly on the constraints of the system is exhibited and the system is quantized using an appropriate hamiltonian consistent with the constraints.     

Sequential contact transformation formulation of asymmetric-rotator vibration-rotation Hamiltonian

The sequential contact transformation technique recently described in this journal by Niroomand-Rad and Parker is applied to the Amat-Nielsen expansion of the Darling-Dennison Hamiltonian of asymmetric rotator type molecules. The resulting formalism for the calculation of fourth-order Hamiltonian coefficients is significantly simpler than the conventional Amat-Nielsen contact transformation formalism. Therefore the eventual development of detailed expressions for fourth-order vibration-rotation interaction coefficients in terms of fundamental molecular constants now appears much more feasible.     

Hamiltonian formulation of QED in the superaxial gauge

We present a hamiltonian formulation of QED in a fully fixed axial gauge. The equal-time commutators for all field variables are computed and are shown to lead to the correct equations of motion. The constraints and gauge conditions hold as strong operator relations.