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Journal ArticleDOI

Volume dependence of the energy spectrum in massive quantum field theories. II. Scattering states

01 Jun 1986-Communications in Mathematical Physics (Springer-Verlag)-Vol. 105, Iss: 2, pp 153-188
TL;DR: The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L as mentioned in this paper.
Abstract: The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L The coefficients in these expansions are related to the appropriate elastic scattering amplitude in a simple and apparently universal manner At low energies, the scattering amplitude can thus be determined, if an accurate calculation of two-particle energy values is possible (by numerical simulation, for example)

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Citations
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Journal ArticleDOI
TL;DR: In this article, the nuclear forces can be derived using effective chiral Lagrangians consistent with the symmetries of QCD, and the status of the calculations for two and three nucleon forces and their applications in few-nucleon systems are reviewed.
Abstract: Nuclear forces can be systematically derived using effective chiral Lagrangians consistent with the symmetries of QCD. I review the status of the calculations for two- and three-nucleon forces and their applications in few-nucleon systems. I also address issues like the quark mass dependence of the nuclear forces and resonance saturation for four-nucleon operators.

1,455 citations

Journal ArticleDOI
TL;DR: In this article, the authors review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecule, and are discussed in both the continuum and finite volumes.
Abstract: A large number of experimental discoveries especially in the heavy quarkonium sector that did not at all fit to the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy Among various explanations of the internal structure of these excitations, hadronic molecules, being analogues of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty We review experimental evidences of various candidates of hadronic molecules, and methods of identifying such structures Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules, and are discussed in both the continuum and finite volumes Also pertinent lattice QCD results are presented Further, we discuss the production mechanisms and decays of hadronic molecules, and comment on the reliability of certain assertions often made in the literature

1,016 citations


Cites background from "Volume dependence of the energy spe..."

  • ...He derived a relation between the energy shift in the finite volume and the scattering phase shift in the continuum (Lüscher, 1986, 1991), see also Refs....

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Journal ArticleDOI
TL;DR: In this paper, the energy spectrum of a system of two particles enclosed in a box with periodic boundary conditions is determined by the scattering phases at these energies, and exact exact formulae are derived which can be used to compute the energy levels given the scattering phase.

968 citations

Journal ArticleDOI
TL;DR: The determination of the light-quark masses, the form factor, and the decay-constant ratio arising in semileptonic $$K \rightarrow \pi $$K→π transition at zero momentum transfer are reported on.
Abstract: We review lattice results related to pion, kaon, D- and B-meson physics with the aim of making them easily accessible to the particle physics community. More specifically, we report on the determination of the light-quark masses, the form factor f+(0), arising in semileptonic K -> pi transition at zero momentum transfer, as well as the decay constant ratio fK/fpi of decay constants and its consequences for the CKM matrix elements Vus and Vud. Furthermore, we describe the results obtained on the lattice for some of the low-energy constants of SU(2)LxSU(2)R and SU(3)LxSU(3)R Chiral Perturbation Theory and review the determination of the BK parameter of neutral kaon mixing. The inclusion of heavy-quark quantities significantly expands the FLAG scope with respect to the previous review. Therefore, for this review, we focus on D- and B-meson decay constants, form factors, and mixing parameters, since these are most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. In addition we review the status of lattice determinations of the strong coupling constant alpha_s.

901 citations

Journal ArticleDOI
TL;DR: In this paper, a detailed proof of this basic relation is given for all orders of perturbation theory in arbitrary massive quantum field theories, which follows from an apparently universal asymptotic formula, which relates Δm to certain forward elastic scattering amplitudes.
Abstract: Due to polarization effects, the massM of a stable particle in a quantum field theory enclosed in a large (space-like) box of sizeL and periodic boundary conditions in general differs from its infinite volume valuem. AsL increases, the finite size mass shift Δm =M−m goes to zero exponentially with a rate, which depends on the particle considered and on the spectrum of light particles in the theory. This behaviour follows from an apparently universal asymptotic formula, already presented earlier, which relates Δm to certain forward elastic scattering amplitudes. A detailed proof of this basic relation is given here to all orders of perturbation theory in arbitrary massive quantum field theories.

764 citations

References
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Journal ArticleDOI
TL;DR: In this article, the low energy representation of several Green's functions and form factors and of the na scattering amplitude are calculated in terms of a few constants, which may be identified with the coupling constants of a unique effective low energy Lagrangian.

3,277 citations


"Volume dependence of the energy spe..." refers background in this paper

  • ...The values of the scattering lengths a~ suggested by experiment [7] and chiral perturbation theory [ 8 ] are...

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Book
01 Jan 1960

2,756 citations

Journal ArticleDOI
TL;DR: In this paper, a detailed proof of this basic relation is given for all orders of perturbation theory in arbitrary massive quantum field theories, which follows from an apparently universal asymptotic formula, which relates Δm to certain forward elastic scattering amplitudes.
Abstract: Due to polarization effects, the massM of a stable particle in a quantum field theory enclosed in a large (space-like) box of sizeL and periodic boundary conditions in general differs from its infinite volume valuem. AsL increases, the finite size mass shift Δm =M−m goes to zero exponentially with a rate, which depends on the particle considered and on the spectrum of light particles in the theory. This behaviour follows from an apparently universal asymptotic formula, already presented earlier, which relates Δm to certain forward elastic scattering amplitudes. A detailed proof of this basic relation is given here to all orders of perturbation theory in arbitrary massive quantum field theories.

764 citations

Journal ArticleDOI
TL;DR: In this paper, the φ4 theory can be reduced systematically by use of lattice actions that also include suitable irrelevant terms, and the principles of such constructions are described in detail.

727 citations


"Volume dependence of the energy spe..." refers background in this paper

  • ...However, if data from different points on the same renormalization group trajectory (points of equal low energy physics in other words) are included in the analysis, one must make sure that finite size effects are not confused with O(a 2) corrections [ 13 ]....

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Journal ArticleDOI
TL;DR: In this paper, a generalization of Fermi's pseudopotential for the two-body hard-sphere problem is introduced, which leads to an expansion of the energy levels of the system in powers of $a.
Abstract: The system under consideration is an $N$-particle quantum-mechanical system enclosed in a volume $V$, in which the particles interact via two-body hard-sphere potentials, with hard-sphere diameter $a$. The two-body hard-sphere problem is first discussed by a generalization of Fermi's pseudopotential by means of which the problem is formulated entirely in terms of the scattering phase shifts. It is then shown that a pseudopotential for the $N$-body problem can be introduced, and leads to an expansion of the energy levels of the system in powers of $a$. The first order energy levels of a Bose and a Fermi system are calculated. For the Bose system, the first order energy formula exhibits an "energy gap" above the ground state, leading to properties of the system not dissimilar to that of a superfluid. The ground state energy for a Bose system is calculated to order ${a}^{3}$ and that for the Fermi system, to order ${a}^{2}$. The physical interpretation and validity of these results are discussed.

635 citations


"Volume dependence of the energy spe..." refers background in this paper

  • ...In their work on the non-ideal Bose gas almost 30 years ago, Huang and Yang [ 3 ] have already derived Eq. (1.3) in the special case of two (non-relativistic) hard spheres enclosed in a periodic box 1. More recently, the existence of the first nontrivial term in Eq. (1.3) has also been mentioned in ref....

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  • ...[ 3 ] and the values quoted here is due to an approximation made by Huang and Yang 156 M. Liischer...

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  • ...... amplitude, the requirement of periodicity leads to an (implicit) eigenvalue equation for E in which the dynamics of the system is only represented through the scattering amplitude at energy E. Except for the case of l + 1-dimensional quantum mechanics, which will be discussed later, this equation is complicated and is therefore not very useful, but it does explain why E is a function of the scattering amplitude at large L (cf. ref. [ 3 ] and ......

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