Separable Nucleon-Nucleon Potential with Experimental Off-Shell Information

By means of solving the Lippman-Schwinger equation and Faddeev equation, fitting the two-body and three-body low energy experimental data in a unified way, a set of rank-1 central separable potential is constructed to provide the applications of the nuclear theoretical calculation.     

Geometry of Lagrangian First-order Classical Field Theories

We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism.     

Second Order Lagrangian and Angular Momentum of Scalar Field

The class of second order Lagrangian for the scalar field is including free divergence terms giving rise to new canonical conservation laws by means of Noethers theorem. The appearance of a spin like tensor S within angular momentum is nothing but a redefinition of orbital angular momentum. S is mainly giving a new definition of center of mass for the field, indicating that the variation for the motion of singularities is nothing but a redefinition for the motion, since the sum for the additional forces, coming from divergence part of Lagrangian, is zero. Thus, the physical content of the theory will not be affected by the divergence part of Lagrangian, is zero. Thus, the physical content of the theory will not be affected by the divergence termes; it is only an other formulation.     

The Calculation of Off-Shell Interaction Vq-qqq Revised

Various methods for calculating the off-shell interaction is discussed. The Hermitian conjugation property of V_q-qqq is restored. But different methods give rise to a little different results and raise an uncertainty of the off-shell interaction. The origin of the non-Galilean invariant term is still unknown. The reason of a too small πNN coupling constant is clarified.     

A Generalized Lagrangian Formalism in Particle Mechanics and Classical Field Theory

A geometric generalization of the first-order Lagrangian formalism is proposed, following the original ideas of Poincaré and Cartan and the extension to field theory due to Krupka, Betounes and Rund. The method is particularly suited for the study of Noetherian symmetries. This point is proved by explicit study of many interesting systems with groups of symmetries appearing in theoretical physics.     

Field equations of the gauge theory of gravitation originate from a quadratic Lagrangian with torsion

The equations of the gauge theory of gravitation [Debney et al.General Relativity and Gravitation,9, 879–887 (1978)] are derived from a complex quadratic Lagrangian with torsion. The derivation is performed in a coordinate basis in a completely covariant way.     

An Off-Shell qq Potential and Its Effect on the Meson Spectrum

An off-shell qq potential is derived from the effective interaction Harniltonian which appears in the relativistic Pauli-Schrödinger equation for quark-antiquark bound states. This potential gives considerable theoretical improvements on meson spectra.     

Off-Shell Relativistic Quantum Mechanics and Formulation of Dirac's Equation Using Characteristic Matrices

It is argued that the Klein-Gordon equation isan equation for characteristic functions, i.e.,Fourier-transformed Wigner functions, not for wavefunctions. This statement is derived starting from theoff-shell formulation of relativistic quantum mechanicsby expressing the condition that the mass of theparticle is exactly known. A particular class ofsolutions of the Klein–Gordon equation is formedby the integrable superpositions of pure momentum states. Adirect sum of four copies of the associatedGelfand–Naimark–Segal representation isconsidered. Then one can derive from the Klein-Gordonequation an equation for spinor wave functions. Solutions of the latterequation are in one-to-one correspondence to thesolutions of the Fourier-transformed Dirac equation.Finally, the equation is reformulated as an equation for characteristic matrices.     

Symplectic manifolds with Lagrangian fibration

A structure theorem is presented for certain kinds of symplectic manifold with a Lagrangian fibration. As a corollary, the class of cotangent bundles is characterized up to the appropriat equivalence, as the type of symplectic manifold considered in the theorem for which in addition, a certain cohomology class vanishes. These results and techniques are then applied to two situations in classical mechanics where symplectic manifolds foliated by Lagrangian submanifolds arise, namely, the Legendre transformation and Hamilton-Jacobi theory.     

On the Lagrangian and Canonical Formalism of the Complex Vector-Pseudovector Field at the Dual Symmetrical Way

A correct Lagrangian as well as canonical formalism for a complex vector-pseudovector classical field in the dual symmetrical form is developed. The negative energies were possible to being extruded eliminating the corresponding fields. The existence of the pseudocharge enables a statistical interpretation of the field, like spin 1 particles, without charge and with two signs of pseudocharge.     

Cartesian and Lagrangian Momentum

Historical, physical, and geometrical relations between two different momenta, characterized here as Cartesian and Lagrangian, are explored. Cartesian momentum is determined by the mass tensor, and gives rise to a kinematical geometry. Lagrangian momentum, which is more general, is given by the fiber derivative, and produces a dynamical geometry. This differs from the kinematical in the presence of a velocity-dependent potential. The relation between trajectories and level surfaces in Hamilton-Jacobi theory can also be Cartesian and kinematical or, more generally, Lagrangian and dynamical.     

Lagrangian and Hamiltonian constraints

We give a procedure for constructing all the Lagrangian constraints of a degenerate system from the Hamiltonian constraints.     

Relative equilibria of Lagrangian systems with symmetry

We discuss the characterization of relative equilibria of Lagrangian systems with symmetry.