Martin Lüscher

Bio: Martin Lüscher is an academic researcher from CERN. The author has contributed to research in topics: Lattice QCD & Lattice field theory. The author has an hindex of 32, co-authored 59 publications receiving 7832 citations. Previous affiliations of Martin Lüscher include University of Bern.

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

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)

Volume dependence of the energy spectrum in massive quantum field theories. I. Stable particle states

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.

Properties and uses of the Wilson flow in lattice QCD

Abstract: Theoretical and numerical studies of the Wilson flow in lattice QCD suggest that the gauge field obtained at flow time t > 0 is a smooth renormalized field. The expectation values of local gauge-invariant expressions in this field are thus well-defined physical quantities that probe the theory at length scales on the order of \( \sqrt {t} \). Moreover, by transforming the QCD functional integral to an integral over the gauge field at a specified flow time, the emergence of the topological (instanton) sectors in the continuum limit becomes transparent and is seen to be caused by a dynamical effect that rapidly separates the sectors when the lattice spacing is reduced from 0.1fm to smaller values.

Perturbative analysis of the gradient flow in non-abelian gauge theories

Abstract: The gradient flow in non-abelian gauge theories on \( {\mathbb{R}^4} \) is defined by a local diffusion equation that evolves the gauge field as a function of the flow time in a gauge-covariant manner. Similarly to the case of the Langevin equation, the correlation functions of the time-dependent field can be expanded in perturbation theory, the Feynman rules being those of a renormalizable field theory on \( {\mathbb{R}^4} \times \left[ {0,\infty } \right) \). For any matter multiplet and to all loop orders, we show that the correlation functions are finite, i.e. do not require additional renormalization, once the theory in four dimensions is renormalized in the usual way. The flow thus maps the gauge field to a one-parameter family of smooth renormalized fields.

Modern theory of nuclear forces

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.

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

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)

Hadronic molecules

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