Invariant combinations of coefficients in the rotational Hamiltonian

A general development of combinations of parameters in the asymmetric rotor Hamiltonian, which are independent of the coefficients of the contact transformation operators used in the reduction of that Hamiltonian, is given. These invariant combinations are obtained for a Hamiltonian containing up to eighth degree operators. The adaptation to the A and S forms of the Watson Hamiltonian and their utility in conversion of coefficients from one form to another is discussed.     

奇异拉氏量系统的正则对称性和Ward恒等式

给出了场论中约束Hamilton系统规范生成元的构成,说明了生成元中与第一类约束相联系的系数之间的关系.基于相空间中的生成泛函,导出了相应正则形式的Ward恒等式.讨论了与混合陈-Simons拉氏量等价的场论模型中的应用.     

More about superconformal field theory. Hamiltonian formalism

The Hamiltonian formalism for theN=1,d=4 superconformal system is given. The first-order formalism is found by starting from the canonical covariant one. As the conformal supergravity is a higher-derivative theory, to analyze the second-order Hamiltonian formalism the Ostrogradski transformation is introduced to define canonical momenta.     

Exponential Transformations for the Harmonic Chain with a Molecular Defect

The exponential transformation, developed in an earlier paper [1], is applied to the Hamiltonian of a linear harmonic chain with a molecular defect. The resulting eigenvalue equation is solved for the localized frequency. A discussion of the renormalized in-band frequencies shows that in good approximation the entire Hamiltonian is diagonalized by a single transformation. This is of great advantage, since in the classical Lifshitz formalism each single frequency has to be evaluated separately. Furthermore, a simpler transformation is discussed, which is derived from an U-matrix formalism. Numerical results of the two transformations are given for a chain with 999 lattice points and compared with the exact values from the classical Lifshitz formalism.     

Finding the Hamiltonian for Cosmological Models in Fourth-Order Gravity Theories Without Resorting to the Ostrogradski or Dirac Formalism

The Hamilton formalism of cosmological models in fourth-order theories of gravity is considered. An approach to constructing the Hamilton function is presented which starts by replacing the second order derivatives of configuration space coordinates by functions depending on these coordinates, its first order derivatives, and additional variables playing the role of configuration space coordinates. This formalism, which does not resort to the Ostrogradski or Dirac formalism, is elucidated and applied to examples. For a special class of Lagrange functions, it is demonstrated that the canonical coordinates of the considered formalism and of the Ostrogradski formalism are related via a canonical transformation. The canonical transformation is a transformation of the configuration space coordinates and a transformation of momentum components induced by the transformation of the configuration space coordinates for a special element of the class of Lagrange functions mentioned. The Wheeler-DeWitt equations belonging to this Lagrange function are related via minisuperspace coordinate transformations.     

Effective torsion-rotation Hamiltonian for methanol-type molecules

A fourth-order effective Hamiltonian has been derived for the torsion-rotation problem of a methanol-type molecule, i.e., for a C_3v top attached to a C_s frame. First, symmetry considerations based on a frame-fixed axis system are used to determine allowed terms in the Hamiltonian. These terms are then subjected to a contact transformation to remove the indeterminate ones. This procedure is essentially an extension of Watson's method for semirigid molecules to the torsion-rotation problem. It is demonstrated that the Hamiltonian derived in the present work is capable of improving the fittings of the millimeter and submillimeter absorption frequencies of CH₃OH and CH₃SH.     

Fourth-order centrifugal distortion coefficients for the nonlinear XYZ molecule

Detailed expressions in terms of fundamental molecular parameters are given for the ten fourth-order centrifugal distortion constants of the nonlinear XYZ molecule. The calculation of these coefficients is based on the Darling-Dennison Hamiltonian in the Nielsen-Amat-Goldsmith expansion.     

Hamiltonian description of barotropic Rossby waves

A transformation into the normal canonical variables is found in the beta-plane approximation for barotropic Rossby waves of an arbitrary amplitude. This transformation is used to derive a matrix of three-wave interaction and to find an expression for the fourth-order term in the interaction Hamiltonian, which describes the modulation instability of Rossby waves. An increment of this instability has been calculated and estimated numerically.     

Solution Transformations and Their Effects on the Systems with Open Boundary Conditions

The solution transformations and properties of the R-matrices for two-component systems under these transformations are analyzed in details.Not all transformed R-matrices can be put into the Skalyanin‘s formalism.For those R-matrices with all required properties,the effects of solution transformations to the six-and eight-vertex systems with open boundary conditions are discussed.these effects can be one of the following types:the Hamiltonian is invariant or transposition-invariant or made in a similarity transformation,or its coupling coefficients are multiplied by an overall factor,or the spin of the system is rotated around the z axis or/and reflected with respect to some plane.In these cases,the transformed systems remain to be integrable.     

Renormalization of a quadratic interaction in the Hamiltonian formalism

The method of the dressing transformation is used to perform a mass renormalization of a neutral scalar free field in the Hamiltonian formalism, for arbitrary space dimension. The resulting situation is analyzed by means of a Bogoliubov transformation, and seen to yield the expected results.Laboratoire associé au C.N.R.S.     

Hamiltonian description of bubble dynamics

The dynamics of a nonspherical bubble in a liquid is described within the Hamiltonian formalism. Primary attention is focused on the introduction of the canonical variables into the computational algorithm. The expansion of the Dirichlet-Neumann operator in powers of the displacement of a bubble wall from an equilibrium position is obtained in the explicit form. The first three terms (more specifically, the second-, third-, and fourth-order terms) in the expansion of the Hamiltonian in powers of the canonical variables are determined. These terms describe the spectrum and interaction of three essentially different modes, i.e., monopole oscillations (pulsations), dipole oscillations (translational motions), and surface oscillations. The cubic nonlinearity is analyzed for the problem associated with the generation of Faraday ripples on the wall of a bubble in an acoustic field. The possibility of decay processes occurring in the course of interaction of surface oscillations for the first fifteen (experimentally observed) modes is investigated.     

Hamiltonian Formalism of the Landau–Lifschitz Equation for a Spin Chain with an Easy Plane

With a suitable gauge transformation, the Hamiltonian formalism of the Landau–Lifschitz equation for a spin chain with an easy plane is established by standard procedure. Action-angle variables are obtained and the canonical equation is given.     

NEOCLASSICAL TRANSPORT IN A TOKAMAK WITH ELECTRIC SHEAR

Neoclassical transport theory for a tokamak in the presence of a large radial electric field with shear is developed using Hamiltonian formalism. Diffusion coefficients are derived in both the plateau and banana regimes where the squeezing factor in coefficients can greatly affect diffusion at the plasma edge. Rotation speeds are calculated in the scrape-off region. They are in good agreement with the measurements on the TdeV tokamak.     

Canonical symmetry of a constrained Hamiltonian system and canonical ward identity

An algorithm for the construction of the generators of the gauge transformation of a constrained Hamiltonian system is given. The relationships among the coefficients connecting the first constraints in the generator are made clear. Starting from the phase space generating function of the Green function, the Ward identity in canonical formalism is deduced. We point out that the quantum equations of motion in canonical form for a system with singular Lagrangian differ from the classical ones whether Dirac's conjecture holds true or not. Applications of the present formulation to the Abelian and non-Abelian gauge theories are given. The expressions for PCAC and generalized PCAC of the AVV vertex are derived exactly from another point of view. A new form of the Ward identity for gauge-ghost proper vertices is obtained which differs from the usual Ward-Takahashi identity arising from the BRS invariance.     

Extended view of classical contact transformations

Classical contact transformation theory is reconstructed from the concept of explicit rather than implicit transformation equations. This proves the existence of contact transformations from any given Hamiltonian to any prescribed Hamiltonian (with the same number of degrees of freedom).     

Hamilton's principle,covariant Hamiltonian,and canonical formalism in four and five dimensions

A discussion of the 1950s and 1960s on the existence of an explicit covariant canonical formalism is renewed. A new point of view is introduced where Hamilton's principle, based on the existence of a Hamiltonian, is postulated independently from the Lagrange formalism. The Hamiltonian is determined by transformation properties and dimensional considerations. The variation of the action without constraints leads to an explicit covariant canonical formalism and correct equations of motion. The introduction of the charge as a fifth momentum gives rise to a reformulation of classical relativistic point mechanics as a five-dimensionalU(1) gauge theory with a theoretically invisible extra dimension. A generalization to other gauge groups is given. The inversion of the proper time is introduced as a new particle-antiparticle symmetry that allows one to show that in the five-dimensional classical theory all particles have positive energy.     

Electro-optics of molecules. II

The formalism of polynomials of quantum numbers is generalized to the case of degenerate states and general recurrence relations are derived. A theorem of extraneous quantum numbers—the quantum numbers appearing in the anharmonic Hamiltonian as parameters—is formulated. With the help of this theorem the polynomial formalism is extrapolated to the case of rotation, and a simple and correct algorithm for deriving the coefficients of the Herman-Wallis factor is proposed. The expressions obtained for the first coefficients are more obvious than the conventional formulas and their application to the hydrogen iodide molecule leads to good agreement with modern experimental data. The necessity of taking into account the part of the magnetic dipole moment nonlinear in the spin variables—the magneto-optical anharmonicity—is shown for systems with the spin-spin interaction.     

Oscillations of charged particles in an external magnetic field about steady motion

We develop a Hamiltonian formalism that can be used to study the particle dynamics near stable equilibria. The construction of an original canonical transformation allowed us to prove the conservation of the linear momentum P₃, which permitted the expansion of the Hamiltonian about a fixed point. The definition of the rotational variable h whose Poisson algebra properties played the essential role in the diagonalization of the quadratic Hamiltonian yielding two uncoupled oscillators with definite frequencies and amplitudes. It is through applying this variable near a fixed point that come to light Heisenberg's and Harmonic Oscillator equations of motion of the particles, leading thus the association of the fixed point trajectories with arbitrary trajectories in its immediate neighborhood. The present formalism succeeded to treat the problem of free-electron laser dynamics and may be applied to similar cases. Received 20 October 2001     

Quantum Symmetries in the Maxwell–Chern–Simons Theory Coupled to Scalar Fields

The Maxwell-Chern-Simons gauge theory coupled to a complex scalar field is quantized in the Becchi-Rouet-Stora-Tyutin (BRST) path integral formalism. On the basis of the symmetries of a constrained canonical (Hamiltonian) system, we get the quantal conserved angular momentum of the system under the global symmetry transformation. It is shown that fractional spin also appears at the quantum level. The canonical Ward identities for this system are derived under local gauge transformation.     

Solutions of Two-Mode Bosonic and Transformed Hamiltonians

We have constructed the quasi-exactly-solvable two-mode bosonic realization of SU(2). Two-mode boson Hamiltonian is defined through a differential equation which is solved by quantum Hamilton-Jacobi formalism. The squeezed states of two-mode boson systems are characterized through canonical transformation. The illustrated concept of squeezed boson systems has been applied two-mode bosonic Hamiltonian which is a squeezed one and is determined through a differential equation. This differential equation is solved and energy eigenvalues are found approximately.