122034057
Ground-state energy of two-dimensional weakly coupled Hamiltonians
It is observed' that a short-range attractive potential always produces a bound state in one or two dimensions. While this property has attracted considerable attention for one-dimensional potentials, leading to many general results, ' ' much less is known about the corresponding property in two dimensions. This may be due to the fact that the bound state is marginal in the case of two dimensions, and somewhat harder to analyze. Apart from the original result of Landau and Lifshitz, ' the only other results known for the two-dimensional problem are those obtained by Simon. ' For the two-dimensional Ham iltonian verse of the T matrix, thus allowing a perturbative description of the poles of the T matrix and hence the bound-state energies. In our present note, the ground-state energy of Hmniltonian (1) is analyzed using the Noyes form' of the T matrix. We find that for potentials satisfying conditions (2) and (3), the ground-state energy has an asymptotic series given by
120523186
s-WAVE SCATTERING LENGTHS, $pi$$pi$ DYNAMICS, AND A UNIVERSAL PARTIAL WIDTH FOR A REGGE TRAJECTORY.
124903228
Radiative Corrections to K(L) --> mu+ mu-
123365175
A renormalizable theory of weak interactions with a single massive spin-zero charged boson and neutral pseudoscalar hadrons as intermediate bosons
Abstract A renormalizable theory of weak interactions with a single spin-zero charged massive intermediate boson W ± and two charged massive leptons, L e ± , L μ ± is presented. The neutral intermediate boson is taken to be a combination of the usual pseudoscalar hadrons π O , η O and X O . The charged boson couples with unequal strengths to the leptons and octet hadron currents. An universality criterion is presented which enables us to understand this in a natural fashion. It is shown that such a theory is consistent with all the present data if the mass of W ± lies between few GeV and 20 GeV. Finally, some tests of the theory are suggested.
122539381
Nonperturbative approach to screened Coulomb potentials
The energy levels of two simple examples of screened Coulomb potentials have been analyzed using nonperturbative methods. The analysis indicates that the energy levels as a function of the perturbation parameter ) have a branch cut along the negative real axis; starting from the origin. Furthermore, there are singularities on the second sheet, along ~X~e '' for ~X ~0. As a consequence of these singularities, the energy levels have an asymptotic series in X, which means that orie cannot use a power series in X to describe the energy levels to an arbitrary accuracy, The approximate but nonperturbative expression for the energy levels, which has been obtained by using dispersion relations, predicts energy levels which are in good agreement with those obtained from variational calculations.
119717796
A non-polynomial Lee-like model without ghosts
Abstract A Lee-like non-polynomial Lagrangian is discussed. The fourth order calculations in the major coupling, for the propagator function are finite but dominate over the second order terms, asymptotically. This implies that for using non-polynomial Lagrangians at high energy, one must include the higheer order terms in the major coupling. It is shown that the model has no ghosts, but does not satisfy the theorem of Lehmann, Symanzik and Zimmermann.
119275413
On Semi-classical Degravitation and the Cosmological Constant Problems
In this report, we discuss a candidate mechanism through which one might address the various cosmological constant problems. We first observe that the renormalization of gravitational couplings (induced by integrating out various matter fields) manifests non-local modifications to Einstein’s equations as quantum corrected equations of motion. That is, at the loop level, matter sources curvature through a gravitational coupling that is a non-local function of the covariant d’Alembertian. If the functional form of the resulting Newton’s ‘constant’ is such that it annihilates very long wavelength sources, but reduces to 1=M 2 (Mpl being the 4d Planck mass) for all sources with cosmologically observable wavelengths, we would have a complimentary realization of the degravitation paradigm– a realization through which its non-linear completion and the corresponding modified Bianchi identities are readily understood. We proceed to consider various theories whose coupling to gravity may a priori induce non-trivial renormalizations of Newton’s constant in the IR, and arrive at a class of non-local effective actions which yield a suitably degravitating filter function for Newton’s constant upon subsequently being integrated out. We motivate this class of non-local theories through several considerations, discuss open issues, future directions, the inevitable question of scheme dependence in semi-classical gravitational calculations and comment on connections with other meditations in the literature on relaxing of the cosmological constant semi-classically.