Journal ArticleDOI
Volume dependence of the energy spectrum in massive quantum field theories. I. Stable particle states
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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.read more
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Journal ArticleDOI
Volume dependence of the energy spectrum in massive quantum field theories. II. Scattering states
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.
Journal ArticleDOI
Two-particle states on a torus and their relation to the scattering matrix
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.
Journal ArticleDOI
How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation
TL;DR: In this paper, a method to calculate the elastic scattering amplitude at low energies in two-dimensional quantum field theories is proposed and tested in a numerical simulation of the O(3) non-linear σ-model on a simple square lattice.
Journal ArticleDOI
FLAG Review 2019
Sinya Aoki,Yasumichi Aoki,Yasumichi Aoki,Damir Becirevic,Tom Blum,Tom Blum,Gilberto Colangelo,Sara Collins,M. Della Morte,Petros Dimopoulos,Stephan Dürr,Stephan Dürr,Hidenori Fukaya,Maarten Golterman,Steven Gottlieb,Rajan Gupta,Shoji Hashimoto,Shoji Hashimoto,Urs M. Heller,Gregorio Herdoiza,Roger Horsley,Andreas Jüttner,T. Kaneko,T. Kaneko,C.-J. D. Lin,C.-J. D. Lin,E. Lunghi,Robert D. Mawhinney,Amy Nicholson,Tetsuya Onogi,Carlos Pena,Antonin Portelli,Alberto Ramos,Stephen R. Sharpe,James N. Simone,Silvano Simula,Rainer Sommer,R. S. Van de Water,Anastassios Vladikas,Urs Wenger,H. Wittig +40 more
TL;DR: In this article, a review of lattice results related to pion, kaon, D-meson, neutral kaon mixing, B-meon, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities is presented.
Journal ArticleDOI
Ab initio determination of light hadron masses.
Stephan Dürr,Zoltan Fodor,Julien Frison,C. Hoelbling,C. Hoelbling,C. Hoelbling,R. Hoffmann,Sandor D. Katz,Stefan Krieg,Thorsten Kurth,Laurent Lellouch,Thomas Lippert,Kalman K. Szabo,G. Vulvert +13 more
TL;DR: This work presents a full ab initio calculation of the masses of protons, neutrons, and other light hadrons, using lattice quantum chromodynamics, and represents a quantitative confirmation of this aspect of the Standard Model with fully controlled uncertainties.
References
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Journal ArticleDOI
Volume dependence of the energy spectrum in massive quantum field theories. II. Scattering states
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.
Journal ArticleDOI
Finite Size Effects in Phase Transitions
Edouard Brézin,Jean Zinn-Justin +1 more
TL;DR: In this paper, an effective hamiltonian for the homogeneous modes, obtained by tracing out all other degrees of freedom, is constructed for finite size effects in phase transitions, and simple universal properties of rounding of first order transitions are derived.
Journal ArticleDOI
Some Analytic Results Concerning the Mass Spectrum of Yang-Mills Gauge Theories on a Torus
TL;DR: When nonabelian gauge fields are enclosed in a box with periodic boundary conditions, the spectrum of the hamiltonian becomes discrete and energy values can be expanded in a power series of ifλ = g 2 3 (g: renormalized coupling constant).
Journal ArticleDOI
Weak-coupling expansion of the low-lying energy values in the SU(2) gauge theory on a torus☆
Martin Lüscher,Gernot Münster +1 more
TL;DR: In this article, the SU(2) gauge theory was studied in an L × L ×L × L periodic box and the crossover from small-volume to large-volume behavior is likely to take place at z ≅ 2.