Generalized Hamiltonian dynamics
TL;DR: The equations of dynamics were put into a general form by Lagrange, who expressed them in terms of a set of generalized coordinates and velocities as discussed by the authors, and an alternative general form was later given by Hamilton, in the form of coordinates and momenta.
Abstract: 1. Introduction. The equations of dynamics were put into a general form
by Lagrange, who expressed them in terms of a set of generalized coordinates
and velocities. An alternative general form was later given by Hamilton, in
terms of coordinates and momenta. Let us consider the relative merits of the
two forms.
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TL;DR: In this article, the general dynamical system with constraints is quantized, and the S-matrix is constructed in the most general class of gauges including relativistic ones, and a new type of additional diagrams arises securing unitarity of the theory: the fourfermion interaction of ghost fields.
846 citations
TL;DR: The breaking of electroweak symmetry, and origin of the associated "weak scale" vweak = 1/ q 2 √ 2GF = 175 GeV, may be due to a new strong interaction as mentioned in this paper.
838 citations
Cites methods from "Generalized Hamiltonian dynamics"
...The other key ingredient of the Top Seesaw model, the seesaw (38)For a discussion of one possibility for extra dimensions of time, see [468]....
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TL;DR: In this article, the authors define a new representation for quantum general relativity, in which exact solutions of the quantum constraints may be obtained, by means of a noncanonical graded Poisson algebra of classical observables, defined in terms of Ashtekar's new variables.
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TL;DR: In this paper, the authors combine the restricted principle of relativity with the hamiltonian formulation of dynamics, which leads to the appearance of ten fundamental quantities for each dynamical system, namely the total energy, the total momentum and the 6-vector which has three components equal to the total angular momentum.
Abstract: For the purposes of atomic theory it is necessary to combine the restricted principle of relativity with the hamiltonian formulation of dynamics. This combination leads to the appearance of ten fundamental quantities for each dynamical system, namely the total energy, the total momentum, and the 6-vector which has three components equal to the total angular momentum. The usual form of dynamics expresses everything in terms of dynamical variables at one instant of time, which results in specially simple expressions for six or these ten, namely the components of momentum and of angular momentum. There are other forms for relativistic dynamics in which others of the ten are specially simple, corresponding to various sub-groups of the inhomogeneous lorentz group. These forms are investigated and applied to a system of particles in interaction and to the electromagnetic field.
1,724 citations
01 Jul 1933
TL;DR: The well-known methods of classical mechanics, based on the use of a Lagrangian or Hamiltonian function, are adequate for the treatment of nearly all dynamical systems met with in practice.
Abstract: The well-known methods of classical mechanics, based on the use of a Lagrangian or Hamiltonian function, are adequate for the treatment of nearly all dynamical systems met with in practice. There are, however, a few exceptional cases to which the ordinary methods are not immediately applicable. For example, the ordinary Hamiltonian method cannot be used when the momenta pr, defined in terms of the Lagrangian function L by the usual formulae pr = ∂L/∂qr, are not independent functions of the velocities. A practical case of this kind is provided by the electromagnetic field, considered as a dynamical system with an infinite number of degrees of freedom, since the momentum conjugate to the scalar potential at any point vanishes identically. Again, for the very simple example of the relativistic motion of a particle of zero rest-mass in field-free space, the Lagrangian function vanishes and the usual Lagrangian method is not applicable.
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