Search results for "Sum rule in quantum mechanics"
showing 10 items of 153 documents
Analytic structure ofϕ4theory using light-by-light sum rules
2013
Abstract We apply a sum rule for the forward light-by-light scattering process within the context of the ϕ 4 quantum field theory. As a consequence of the sum rule a stringent causality criterion is presented and the resulting constraints are studied within a particular resummation of graphs. Such resummation is demonstrated to be consistent with the sum rule to all orders of perturbation theory. We furthermore show the appearance of particular non-perturbative solutions within such approximation to be a necessary requirement of the sum rule. For a range of values of the coupling constant, these solutions manifest themselves as a physical bound state and a K-matrix pole. For another domain …
Causality and the Coulomb sum rule in nuclei.
1989
The spectral function in the Jost-Lehmann-Dyson representation of causal commutators is determined for the nonrelativistic limit of inclusive lepton scattering from nuclei. From this an extrapolation of the Coulomb sum rule to higher-momentum transfers is performed which is consistent with the requirement of causality.
Process-independent strong running coupling
2016
We unify two widely different approaches to understanding the infrared behaviour of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realised via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running-coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann--Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be…
Novel patterns for vector mesons from the large-Nc limit
2008
We report on a relation between the decay constants of \rho-like J^{PC}=1^{--} vector mesons, which arises solely from the perturbative analysis of the VV, TT and VT correlators at order \alpha_s^0 in the large-N_c limit. We find f_{V}^T/f_{V}=1/\sqrt{2} for highly excited states together with a pattern of alternation in sign. Quite remarkably, recent lattice determinations reported f_{\rho}^T/f_{\rho}=0.72(2), in excellent agreement with our large-N_c result. This seems to suggest a pattern like f_{Vn}^T/f_{Vn}=(-1)^n/\sqrt{2} for the whole (1^{--}) states. In order to test this conjecture in real QCD we construct a set of spectral sum rules, which turn out to comply nicely with this scena…
Dynamics of a subconstituent picture of weak interactions
1985
We use sum rules in order to discuss the dynamics of the simplest subconstituent model of weak interactions with elementary spin 1/2 fermions and scalar bosons. Vacuum condensates of the scalars play an essential role and lead to features quite different from QCD. With a certain vacuum structure vector dominance of the composite W-mesons is a good approximation, and we also see a clear signal for massless fermions in the two-point function of composite fermions. Thus such a model is in good agreement with standard phenomenology. Composite Higgs particles are also investigated. The effective interaction is evidently of the gauge type.
Dipole surface plasmon in K+N clusters
1992
Abstract The technique of sum rules has been used to investigate the dipole surface plasmon for K + N clusters within a Density Functional Theory and the spherical jellium model. The role played by non-local effects is discussed comparing the results obtained from different functionals. Band-structure and core-polarization effects have been phenomenologically included in the calculation by means of an electron effective mass and a dielectric constant. Comparison with recent experimental data is presented.
Partial self-consistency and analyticity in many-body perturbation theory: Particle number conservation and a generalized sum rule
2016
We consider a general class of approximations which guarantees the conservation of particle number in many-body perturbation theory. To do this we extend the concept of $\Phi$-derivability for the self-energy $\Sigma$ to a larger class of diagrammatic terms in which only some of the Green's function lines contain the fully dressed Green's function $G$. We call the corresponding approximations for $\Sigma$ partially $\Phi$-derivable. A special subclass of such approximations, which are gauge-invariant, is obtained by dressing loops in the diagrammatic expansion of $\Phi$ consistently with $G$. These approximations are number conserving but do not have to fulfill other conservation laws, such…
Electromagnetic mass difference of pions at low temperature
1999
We compute low temperature corrections to the electromagnetic mass difference of pions in the chiral limit. The computation is done in a model independent way in the framework of chiral perturbation theory, using the background field method and the hard thermal loop approximation. We also generalize at low temperature the sum rule of Das et al. We find that the mass difference between the charged and neutral pions decreases at low temperature $T$ with respect to the T=0 value. This is so in spite of the fact that charged particles always get a thermal correction to their masses of order $\sim eT$, where $e$ is the gauge coupling constant. Our result can be understood as a consequence of the…
Radiative muon capture and the value of gP in nuclei
1990
Abstract Radiative muon capture by nuclei is analyzed by means of sum rule techniques, providing a total photon yield calculated with RPA precision. The measured yields relative to the ordinary muon capture rate are well reproduced for the nuclei 12C, 16O and 40Ca using a value of the pseudoscalar weak coupling constant gP enhanced by only 25% with respect to its canonical value. Therefore, the large renormalization of gP claimed up to now must be reconsidered.
Density gradient expansion of correlation functions
2013
We present a general scheme based on nonlinear response theory to calculate the expansion of correlation functions such as the pair-correlation function or the exchange-correlation hole of an inhomogeneous many-particle system in terms of density derivatives of arbitrary order. We further derive a consistency condition that is necessary for the existence of the gradient expansion. This condition is used to carry out an infinite summation of terms involving response functions up to infinite order from which it follows that the coefficient functions of the gradient expansion can be expressed in terms the local density profile rather than the background density around which the expansion is ca…