121420070
T-matrix analysis of one-dimensional weakly coupled bound states
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.
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.
121285502
Nonpolynomial anharmonic oscillator
120196663
Dispersion relations for stark energy shifts in hydrogen atom
Abstract On the basis of an approximate but nonperturbative expression for the energy shift δE in the ground state of the hydrogen atom in the presence of an electric field of strength E , we deduce that δE has a branch point at E = 0, and an asymptotic behavior δE → −1 2 E ln E as E → ∞. These properties lead to a twice-subtracted dispersion relation for δE as a function of E . The dispersion relations in conjunction with the WKB approximation and the perturbation series allow us to (i) deduce the large-n behavior of the coefficient of E n in the perturbation series for δE( E ) including 1 n corrections and (ii) obtain the energy shift and the level width of the ground state for a large range of values of E . The agreement with the earlier numerical calculations is very satisfactory.
122881667
Wave functions for weakly coupled bound states
It has been observed' that a short-range attractive potential always produces a bound state in one or two dimensions. This property has been investigated in the weak-coupling limit, with the intention of obtaining perturbative expressions for the bound-state wave functions and energies. In particular, Hausmann has analyzed the bound states in one-dimensional, short-range potentials by using the homogeneous Lippmann-Schwinger equation for the bound-state wave functions. He showed that for the one-dimensional Hamiltonian V(x)~ —ax as x~+ ao, —2
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.
118823120
D0 matrix mechanics: New fuzzy solutions at large N
We wish to consider in this report the large-N limit of a particular matrix model introduced by Myers describing D-brane physics in the presence of an RR flux background. At finite N, fuzzy spheres appear naturally as non-trivial solutions to this matrix model and have been extensively studied. In this report, we wish to demonstrate several new classes of solutions which appear in the large-N limit, corresponding to the fuzzy cylinder,the fuzzy plane and a warped fuzzy plane. The latter two solutions arise from a possible ``central extension" to our model that arises after we account for non-trivial issues involved in the large-N limit. As is the case for finite N, these new solutions are to be interpreted as constituent D0-branes forming D2 bound states describing new fuzzy geometries.
119088066
UV/IR mode mixing and the CMB
It is well understood that spatial noncommutativity, if indeed realized in nature, is a phenomenon whose effects are not just felt at energy scales comparable to the noncommutativity scale. Loop effects can transmit signatures of any underlying noncommutativity to macroscopic scales (a manifestation of a phenomenon that has come to be known as UV/IR mode mixing) and offer a potential lever to constrain the amount of noncommutativity present in nature, if present at all. Field theories defined on noncommutative spaces (realized in string theory when D-branes are coupled to backgrounds of nontrivial RR background flux), can exhibit strong UV/IR mode mixing, manifesting in a nonlocal one-loop effective action. In the context of inflation in the presence of any background noncommutativity, we demonstrate how this UV/IR mixing at the loop level can allow us to place severe constraints on the scale of noncommutativity if we presume inflation is responsible for large-scale structure. We demonstrate that any amount of noncommutativity greatly suppresses the cosmic microwave background power at all observable scales, independent of the scale of inflation, and independent of whether or not the noncommutativity tensor redshifts during inflation, therefore nullifying a very salient and successful prediction of inflation.
18075993
Inflation with a stringy minimal length, reworked
In this paper we revisit the formulation of scalar field theories on de Sitter backgrounds subject to the generalized uncertainty principle (GUP). The GUP arises in several contexts in string theory, but is most readily thought of as resulting from using strings as effective probes of geometry, which suggests an uncertainty relation incorporating the string scale ls. After reviewing the string theoretic case for the GUP, which implies a minimum length scale ls, we follow in the footsteps of Kempf and concern ourselves with how one might write down field theories which respect the GUP. We uncover a new representation of the GUP, which unlike previous studies, readily permits exact analytical solutions for the mode functions of a scalar field on de Sitter backgrounds. We find that scalar fields cannot be quantized on inflationary backgrounds with a Hubble radius H−1 smaller than the string scale, implying a sensibly stringy (as opposed to Planckian) cutoff on the scale of inflation resulting from the GUP. We also compute (Hls)2 corrections to the two point correlation function analytically and comment on the future prospects of observing such corrections in the fortunate circumstance our universe is described by a very weakly coupled string theory.
119299896
Mass hierarchies and non-decoupling in multi-scalar field dynamics
In this work we study the effects of field space curvature on scalar field perturbations around an arbitrary background field trajectory evolving in time. Non-trivial imprints of the 'heavy' directions on the low energy dynamics arise when the vacuum manifold of the potential does not coincide with the span of geodesics defined by the sigma model metric of the full theory. When the kinetic energy is small compared to the potential energy, the field traverses a curve close to the vacuum manifold of the potential. The curvature of the path followed by the fields can still have a profound influence on the perturbations as modes parallel to the trajectory mix with those normal to it if the trajectory turns sharply enough. We analyze the dynamical mixing between these non-decoupled degrees of freedom and deduce its non-trivial contribution to the low energy effective theory for the light modes. We also discuss the consequences of this mixing for various scenarios where multiple scalar fields play a vital role, such as inflation and low-energy compactifications of string theory.