Chen Ning Yang

Thermodynamics of a One‐Dimensional System of Bosons with Repulsive Delta‐Function Interaction

The equilibrium thermodynamics of a one‐dimensional system of bosons with repulsive delta‐function interaction is shown to be derivable from the solution of a simple integral equation. The excitation spectrum at any temperature T is also found.

Dirac Monopole Without Strings: Monopole Harmonics

Abstract Using the ideas developed in a previous paper which are borrowed from the mathematics of fibre bundles, it is shown that the wave function ψ of a particle of charge Ze around a Dirac monopole of strength g should be regarded as a section . The section is without discontinuities. Thus the monopole does not possess strings of singularities in the field around it. The eigensections of the angular momentum operators are monopole harmonics which are explicitly exhibited.

Generalization of Dirac’s monopole to SU2 gauge fields

Dirac’s monopole is generalized to SU2 gauge fields in five‐dimensional flat space or four‐dimensional spherical space. The generalized fields have SO5 symmetry. The method used is related to the concept of orthogonal gauge fields which is developed in an appendix. The angular momenta operators for the SO5 symmetrical fields are given.

One-dimensional chain of anisotropic spin-spin interactions

Abstract Some properties of the lowest eigenvalue, for fixed magnetization per site, of the Hamiltonian for a one-dimensional chain of anisotropic spin-spin interactions are described.

Magnetic monopoles, fiber bundles, and gauge fields

The reports in this monograph have shown great enthusiasm and exuberance for the unification of various interactions through the concept of gauge fields. I would like to emphasize a point that has not yet been explicitly stated by any of the other authors: gauge fields are deeply related to some profoundly beautiful ideas of contemporary mathematics, ideas that are the driving forces of part of the mathematics of the last 40 years. Recalling the relationship between physics and mathematics in earlier periods, general relativity and Riemannian geometry, quantum mechanics and Hilbert space, it is all too obvious that physicists may again be zeroing in on a fundamental new secret of nature.

Binomial distribution for the charge asymmetry parameter

Abstract It is suggested that for high energy collisions the distribution with respect to the charge asymmetry z = nF − nB is binomial, where nFand nB are the forward and backward charge multiplicities.

Elastic scattering at CERN collider energy and the geometrical picture

Abstract Recent UA1 and UA4 experimental results for p p collisions at 540 GeV center of mass energy are analyzed in the geometrical picture.

Bose-Einstein condensation of atoms in a trap

We point out that the local density approximation (LDA) of Oliva is an adaptation of the Thomas-Fermi method, and is a good approximation when {epsilon}={h_bar}{omega}/{ital kT}{lt}1. For the case of scattering length {ital a}{approx_gt}0, the LDA leads to a quantitative result, Eq. (14{prime}), easily checked by experiments. Critical remarks are made about the physics of the many-body problem in terms of the scattering length {ital a}. {copyright} {ital 1996 The American Physical Society.}

SU2 monopole harmonics

For a particle of I‐spin I in an SU2 monopole field in five‐dimensional Euclidean space, the monopole harmonics are found. They belong to the irreducible representation (p,q)5 where p =q+2I. They form a complete set of wave sections.

Einstein's impact on theoretical physics

There occurred in the early years of this century three conceptual revolutions that profoundly changed Mans understanding of the physical universe: the special theory of relativity (in 1905), the general theory of relativity (1915) and quantum mechanics (1925). Einstein personally was responsible for the first two of these revolutions, and influenced and helped to shape the third. But it is not about his work in these conceptual revolutions that I shall write here. Much has been written about that work already. Instead, I shall discuss, in general terms, Einsteins insights on the structure of theoretical physics and their relevance to the development of physics in the second half of this century. I shall divide the discussion into four sections which are, of course, very much related.