Steven Weinberg

Nuclear forces from chiral Lagrangians

The method of phenomenological lagrangians is used to derive the consequences of spontaneously broken chiral symmetry for the forces among two or more nucleons.

Effective chiral Lagrangians for nucleon - pion interactions and nuclear forces

The general chiral invariant effective lagrangians is used to study the leading terms in powers of momenta in the S-matrix for a process involving arbitrary numbers of low-momentum pions and nucleons. This work extends and in part corrects an earlier report [S. Weinberg, Phys. Lett. B251 (1990) 288].

The Quantum Theory of Fields, Vol. 1: Foundations

Cambridge University Press) Available for the first time in paperback, The Quantum Theory of Fields is a self-contained, comprehensive, and up-to-date introduction to quantum field theory from Nobel Laureate Steven Weinberg. Volume I introduces the foundations of quantum field theory. The development is fresh and logical throughout, with each step carefully motivated by what has gone before. After a brief historical outline, the book begins with the principles of relativity and quantum mechanics, and the properties of particles that follow. Quantum field theory emerges from this as a natural consequence. The classic calculations of quantum electrodynamics are presented in a thoroughly modern way, showing the use of path integrals and dimensional regularization. It contains much original material, and is peppered with examples and insights drawn from the authors experience as a leader of elementary particle research. Exercises are included at the end of each chapter. Keyword(s): INSPIRE: book | quantum mechanics: relativistic | scattering | antiparticle | Feynman graph | quantum electrodynamics | path integral | field theory: nonperturbative | radiative correction | renormalization | infrared problem | bound state | external field | bibliography Record added 1996-05-19, last modified 2015-07-27 Export BibTeX, EndNote, LaTeX(US), LaTeX(EU), Harvmac, MARC, MARCXML, NLM, DC Information References (45) Citations (301) Files Plots The quantum theory of fields. Vol. 1: Foundations

Limits on massless particles

Abstract We show that in all theories with a Lorentz-covariant energy-momentum tensor, such as all known renormalizable quantum field theories, composite as well as elementary massless particles with j > 1 are forbidden. Also, in all theories with a Lorentz-covariant conserved current, such as renormalizable theories with a symmetry that commutes with all local symmetries, there cannot exist composite or elementary particles with nonvanishing values of the corresponding charge and j > 1/2.

Effective gauge theories

A method is described for dealing with gauge field theories that contain very heavy particles, by constructing a gauge-invariant effective field theory, in which the heavy particles do not appear. For theories in which a simple group is spontaneously broken to the strong and electroweak gauge groups, the running strong and electroweak effective couplings become equal to the original gauge coupling at different renormalization scales, given as weighted geometric averages of the super-heavy particle masses. The method is also applied to quantum chromodynamics with heavy quarks.

Testing Quantum Mechanics

Abstract This paper presents a general framework for introducing nonlinear corrections into ordinary quantum mechanics, that can serve as a guide to experiments that would be sensitive to such corrections. In the class of generalized theories described here, the equations that determine the time-dependence of the wave function are no longer linear, but are of Hamiltonian type. Also, wave functions that differ by a constant factor represent the same physical state and satisfy the same time-dependence equations. As a result, there is no difficulty in combining separated subsystems. Prescriptions are given for determining the states in which observables have definite values and for calculating the expectation values of observables for general states, but the calculation of probabilities requires detailed analysis of the method of measurement. A study is presented of various experimental possibilities, including the precession of spinning particles in external fields, experiments of Stern-Gerlach type, and the broadening and de-tuning of absorption lines.

Calculation of gauge couplings and compact circumferences from self-consistent dimensional reduction

Abstract We consider a system of gravity plus free massless matter fields in 4 + N dimensions, and look for solutions in which N dimensions form a compact curved manifold, with the energy-momentum tensor responsible for the curvature produced by quantum fluctuations in the matter fields. For manifolds of sufficient symmetry (including spheres, CP N , and manifolds of simple Lie groups) the metric depends on only a single multiplicative parameter ϱ 2 , and the field equations reduce to an algebraic equation for ϱ, involving the potential of the matter fields in the metric of the manifold. With a large number of species of matter fields, the manifold will be larger than the Planck length, and the potential can be calculated using just one-loop graphs. In odd dimensions these are finite, and give a potential of form C N /ϱ 4 . Also there are induced Yang-Mills and Einstein-Hilbert terms in the effective 4-dimensional action, proportional to additional numerical coefficients, D N and E N . General formulas are given for the gauge coupling g 2 in terms of C N and D N , and the ratio ϱ 2 /8π G in terms of C N and E N . Numerical values for C N , D N , and E N are obtained for scalar and spinor fields on spheres of odd dimensionality N . It is found that the potential, g 2 and ϱ 2 /8π G can all be positive but only when the compact manifold has N = 3 + 4 k dimensions. (The positivity of the potential is needed for stability of the sphere against uniform dilations or contractions). In this case, solutions exist either for spinor fields alone or for suitable mixes of spinor and scalar fields provided the ratio of the number of scalar fields to the number of fermion fields is not too large. Numerical values of the O( N + 1) gauge couplings and 8φ G /ϱ 2 are calculated for illustrative values of the numbers of spinor fields. It turns out that large numbers of matter fields are needed to make these parameters reasonably small.

Three-body interactions among nucleons and pions

Abstract A chiral invariant effective lagrangian may be used to calculate the three-body interactions among low-energy pions and nucleons in terms of known parameters. This method is illustrated by the calculation of the pion-nucleus scattering length.

The Cosmological Constant Problems

The old cosmological constant problem is to understand why the vacuum energy is so small; the new problem is to understand why it is comparable to the present mass density. Several approaches to these problems are reviewed. Quintessence does not help with either; anthropic considerations offer a possibility of solving both. In theories with a scalar field that takes random initial values, the anthropic principle may apply to the cosmological constant, but probably to nothing else.

Adiabatic modes in cosmology

We show that the field equations for cosmological perturbations in the Newtonian gauge always have an adiabatic solution, for which a quantity