SU (2) Yang-Mills field theory is considered in the framework of the generalized Hamiltonian approach and the equivalent unconstrained system is obtained using the method of Hamiltonian reduction. A canonical transformation to a set of adapted coordinates is performed in terms of which the Abelianization of the Gauss law constraints reduces to an algebraic operation and the pure gauge degrees of freedom drop out from the Hamiltonian after projection onto the constraint shell. For the remaining gauge invariant fields two representations are introduced where the three fields which transform as scalars under spatial rotations are separated from the three rotational fields. An effective low energy nonlinear sigma model type Lagrangian is derived which out of the six physical fields involves only one of the three scalar fields and two rotational fields summarized in a unit vector. Its possible relation to the effective Lagrangian proposed recently by Faddeev and Niemi is discussed. Finally the unconstrained analog of the well-known nonnormalizable groundstate wave functional which solves the Schrödinger equation with zero energy is given and analysed in the strong coupling limit.
The SU (2) gauge invariant Dirac-Yang-Mills mechanics of spatially homogeneous isospinor and gauge fields is considered in the framework of the generalized Hamiltonian approach. The unconstrained Hamiltonian system equivalent to the model is obtained using the gaugeless method of Hamiltonian reduction. The latter includes the Abelianization of the first class constraints, putting the second class constraints into the canonical form and performing a canonical transformation to a set of adapted coordinates such that a subset of the new canonical pairs coincides with the second class constraints and part of the new momenta is equal to the Abelian constraints. In the adapted basis the pure gauge degrees of freedom automatically drop out from the consideration after projection of the model onto the constraint shell. Apart from the elimination of these ignorable degrees of freedom a further Hamiltonian reduction is achieved due to the three dimensional group of rigid symmetry possessed by the system.
A strong coupling expansion of the SU (2) Yang-Mills quantum Hamiltonian is carried out in the form of an expansion in the number of spatial derivatives, using the symmetric gauge ǫ ijk A jk = 0. Introducing an infinite lattice with box length a, I obtain a systematic strong coupling expansion of the Hamiltonian in λ ≡ g −2/3 , with the free part being the sum of Hamiltonians of Yang-Mills quantum mechanics of constant fields for each box, and interaction terms of higher and higher number of spatial derivatives connecting different boxes. The corresponding deviation from the free glueball spectrum, obtained earlier for the case of the Yang-Mills quantum mechanics of spatially constant fields, is calculated using perturbation theory in λ. As a first step, the interacting glueball vacuum and the energy spectrum of the interacting spin-0 glueball are obtained to order λ 2 . Its relation to the renormalisation of the coupling constant in the IR is discussed, indicating the absence of infrared fixed points. *
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