We derive an effective Hamiltonian for a quantum system constrained to a submanifold ~the constraint manifold! of configuration space ~the ambient space! by an infinite restoring force. We pay special attention to how this Hamiltonian depends on quantities which are external to the constraint manifold, such as the extrinsic curvature of the constraint manifold, the curvature of the ambient spac...

We study the problem of the phonon–induced electron–electron interaction in a solid. Starting with a Hamiltonian that contains an electron–phonon interaction, we perform a similarity renormalization transformation to calculate an effective Hamiltonian. Using this transformation singularities due to degeneracies are avoided explicitely. The effective interactions are calculated to second order i...

We begin with a discussion of the general properties of eigenvectors and eigenvalues for an effective Hamiltonian governing time evolution in a two state subspace of the state space of the total system under consideration. Next, the Lee, Oehme and Yang (LOY) theory of time evolution in such a subspace is considered. The CPT– and CP–symmetry properties of the LOY effective Hamiltonian are discus...

We propose a new formulation to compute effective Hamiltonians for homogenization of a class of Hamilton-Jacobi equations. Our formulation utilizes an observation made by BarronJensen [3] about viscosity supersolutions of Hamilton-Jacobi equations. The key idea is to link the effective Hamiltonian to a suitable effective equation. The main advantage of our formulation is that only one auxiliary...

We formulate the quark meson coupling model as a many-body effective Hamiltonian. This leads naturally to the appearance of many-body forces. We investigate the zero range limit of the model and compare its Hartree-Fock Hamiltonian to that corresponding to the Skyrme effective force. By fixing the three parameters of the model to reproduce the binding and symmetry energy of nuclear matter, we f...

The experimental and theoretical evidence relating spin dependence and long range confinement is reviewed. One of the simplest confinement ideas, the dynamic electric flux tube picture of Buchmüller, can be exploited to yield a complete effective Hamiltonian. In addition to pure Thomas spin-orbit splitting the other relativistic corrections are calculated. It is shown that our effective Hamilto...

The effective nonleptonic weak Hamiltonian is examined beyond the leading-logarithm approximation. In the AS=l, AC=1 part of the Hamiltonian no significant contribution is found. In the AS=l, AC=0 sector coefficients of the "penguin" operators depend strongly on added corrections. The momentum subtraction scheme has been used in the calculation. The independence of the result on the renormaliza...

The properties of open quantum systems are described well by an effective Hamiltonian H that consists of two parts: the Hamiltonian H of the closed system with discrete eigenstates and the coupling matrix W between discrete states and continuum. The eigenvalues of H determine the poles of the S matrix. The coupling matrix elements W(cc')(k) between the eigenstates k of H and the continuum may b...

The ↑↓-model has produced the physical masses of all flavor-asymmetric mesons like the π or the ρ. Can the same model also account for the flavor-symmetric mesons like the π or the ρ? — By adjusting one parameter in a 5× 5-matrix, the π-η degeneracy is lifted and the η − η splitting falls into the right ball park. The isospin triplets for pions and rhos are caused the mass-degeneracy of the up ...

The canonical front form Hamiltonian for non-Abelian SU(N) gauge theory in 3+1 dimensions is mapped non-perturbatively on an effective Hamiltonian which acts only in the Fock space of a quark and an antiquark. Emphasis is put on dealing with the many-body aspects of gauge field theory, and it is shown explicitly how the higher Fockspace amplitudes can be retrieved self-consistently from solutio...