Selected Papers of Chen Ning Yang II

With Commentaries

Chen Ning Yang

• Publisher: WSPC
• Year: 2013
• eBook ISBN: 9789814449038
• Topic: History
• Subtopic: Science History
• Index: History

Professor Chen Ning Yang, an eminent contemporary physicist, was Professor at the Institute for Advanced Study, Princeton, New Jersey, from 1955 to 1966, and Albert Einstein Professor of Physics at the State University of New York at Stony Brook until his retirement in 1999. He has been Distinguished Professor-at-Large at the Chinese University of Hong Kong since 1986 and Professor at Tsinghua University, Beijing, since 1998.

Since receiving his PhD from the University of Chicago in 1948, Prof Yang has made great impacts in both abstract theory and phenomenological analysis in modern physics. In 1983, he published “Selected Papers (1945–1980), With Commentary”. It has been considered by Freeman Dyson as one of his favorite books. The present book is a sequel to that earlier volume. It is a collection of his personally selected papers (1971–2012) supplemented by his insightful commentaries. Its contents reflect Professor Yang's changing interests after he reached age sixty. It also includes commentaries written by him in 2011 when he is 89 years old.

The papers and commentaries in this unique collection comprise a remarkable personal and professional chronicle, shedding light on both the intellectual development of a great physicist and on the nature of scientific inquiry.

Contents:

• Speech About the Great Wall
• C N Yang Discusses Physics in People's Republic of China
• A de Gaulle-Like Trip
• Condition of Self-Duality for SU(2) Gauge Fields on Euclidean Four-Dimensional Space
• Generalization of Dirac's Monopole to SU 2 Gauge Fields
• Einstein and the Physics of the Future
• Does Violation of Microscopic Time-Reversal Invariance Lead to the Possibility of Entropy Decrease?
• Joseph Mayer and Statistical Mechanics
• Flux Quantization, A Personal Reminiscence
• The Discrete Symmetries P, T and C
• Gauge Fields, Electromagnetism and the Bohm-Aharonov Effect
• Spin of Electrons, Hadrons and Nuclei
• Hermann Weyl's Contribution to Physics
• Square Root of Minus One, Complex Phases and Erwin Schrödinger
• Generalization of Sturm-Liouville Theory to a System of Ordinary Differential Equations with Dirac Type Spectrum
• C Y Chao, Pair Creation and Pair Annihilation
• A One-Dimensional N Fermion Problem with Factorized S Matrix
• Journey Through Statistical Mechanics
• Modern Physics and Warm Friendship
• SO 4 Symmetry in a Hubbard Model
• Symmetry and Physics
• S S Chern and I
• Reflections on the Development of Theoretical Physics
• Deng Jiaxian
• Julian Schwinger
• Path Crossings with Lars Onsager
• Exact Solution of the Vibration Problem for the Carbon-60 Molecule
• Father and I
• Speech After Banquet
• Writeup Upon Hearing of Mills' Death
• Enrico Fermi
• Werner Heisenberg (1901–1976)
• Banquet Speech, June 2002
• Thematic Melodies of Twentieth Century Theoretical Physics: Quantization, Symmetry and Phase Factor
• Gauge Invariance and Interactions
• Albert Einstein: Opportunity and Perception
• The Klein-Nishina Formula & Quantum Electrodynamics
• Pseudopotential Method and Dilute Hard “Sphere” Bose Gas in Dimensions 2, 4 and 5
• Ground State of Fermions in a 1D Trap with δ Function Interaction
• Banquet Speech at the Singapore Conference in Honour of Murray Gell-Mann on His 80th Birthday
• Spin 1/2 Fermions in 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction
• One-Dimensional ω-Component Fermions and Bosons with Repulsive Delta Function Interaction
• Quantum Numbers, Chern Classes, and a Bodhisattva
• My Experience as a Student and Researcher
• Fermi's β-Decay Theory
• Topology and Gauge Theory in Physics
• On Reaching Age Ninety

Readership: Graduate students and researchers in particle physics and statistical physics.

10e

Spin 1/2 Fermions in 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction ^*

MA Zhong-Qi

¹, C. N. Yang

^{2, 3**}

¹ Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049

² Center for Advanced Study, Tsinghua University, Beijing 100084

³ Institute of Theoretical Physics, Chinese University of Hong Kong, Hong Kong

(Received 19 March 2010)

Following the general theory developed in our earlier papers I [Chin. Phys. Lett. 26 (2009) 120506] and II [Chin. Phys. Lett. 27 (2010) 020506] for Bosons, we extend the investigation to trapped spin 1/2 Fermions.

PACS: 05.30. Fk, 67.85. –d, 03. 75. Hh DOI: 10.1088/0256-307X/27/8/080501

In this paper we study 1D spin 1/2 Fermions in a harmonic trap, with the following Hamiltonian which was already studied in Refs. [1,2] for Bosons:

We adopt the labelling system (III.xx) for the formulas in this paper to facilitate future references.

We concentrate on the ground state space wave functions belonging to representation [2^M l ^{N – 2M}] of the permutation group S_N. We shall adopt the simplified notation

Our aim and method are the same as those for Bosons in Refs. [1,2]: We use the Thomas-Fermi method for the problem in the trap by first treating the local problem in each interval dx. Then we find the best values of the local thermodynamic variables at each x, to reach the minimum total energy for the whole system in the trap. The result gives the limit when the total number of particles N → ∞ for fixed

.

Local Thermodynamics

Because of the more complicated symmetry of wave functions for the Fermion case, the thermodynamic formula (I.9) for Bosons now assumes for trapless Fermions in length

a more complex form with 2

There are therefore two chemical potentials, μ₁ and μ₂. As a consequence there is now the very interesting new feature of the existence of kin...

Table of contents

• Cover
• Halftitle
• Title
• Copyright Page
• Preface
• Contents
• [[71d]] Speech About the Great Wall
• [[A71d]] C. N. Yang Discusses Physics in People’s Republic of China
• [[72d]] A de Gaulle-Like Trip
• [[77g]] Condition of Self-Duality for SU(2) Gauge Fields on Euclidean Four-Dimensional Space
• [[78a]] Generalization of Dirac’s Monopole to SU2 Gauge Fields
• [[79d]] Einstein and the Physics of the Future Panel Discussion
• [[80d]] Does Violation of Microscopic Time-Reversal Invariance Lead to the Possibility of Entropy Decrease? (with C. P. Yang)
• [[82c]] Joseph Mayer and Statistical Mechanics
• [[82e]] Flux Quantization, A Personal Reminiscence
• [[82g]] The Discrete Symmetries P, T and C
• [[83g]] Gauge Fields, Electromagnetism and the Bohm-Aharonov Effect
• [[85g]] Spin of Electrons, Hadrons and Nuclei (with T. T. Chou)
• [[85j]] Hermann Weyl’s Contribution to Physics
• [[86c]] Square Root of Minus One, Complex Phases and Erwin Schrödinger
• [[87a]] Generalization of Sturm-Liouville Theory to a System of Ordinary Differential Equations with Dirac Type Spectrum
• [[87b]] C. Y Chao, Pair Creation and Pair Annihilation (with B. A. Li)
• [[88b]] A One-Dimensional N Fermion Problem with Factorized S Matrix (with C. H. Gu)
• [[88d]] Journey Through Statistical Mechanics
• [[89c]] Modern Physics and Warm Friendship
• [[90b]] SO4 Symmetry in a Hubbard Model (with S. C. Zhang)
• [[90e]] Symmetry and Physics
• [[91e]] S. S. Chern and I
• [[92c]] Reflections on the Development of Theoretical Physics
• [[93b]] Deng Jiaxian
• [[95b]] Julian Schwinger
• [[95d]] Path Crossings with Lars Onsager
• [[97d]] Exact Solution of the Vibration Problem for the Carbon-60 Molecule (with T. T. Chou)
• [[97f]] Father and I
• [[99c]] Speech After Banquet
• [[A99j]] Writeup Upon Hearing of Mills’ Death
• [[01f]] Enrico Fermi
• [[01g]] Werner Heisenberg (1901–1976)
• [[02c]] Banquet Speech, June 2002
• [[02i]] Thematic Melodies of Twentieth Century Theoretical Physics: Quantization, Symmetry and Phase Factor
• [[04c]] Gauge Invariance and Interactions
• [[05b]] Albert Einstein: Opportunity and Perception
• [[06b]] The Klein-Nishina Formula & Quantum Electrodynamics
• [[08d]] Pseudopotential Method and Dilute Hard “Sphere” Bose Gas in Dimensions 2, 4 and 5
• [[09f]] Ground State of Fermions in a 1D Trap with δ Function Interaction
• [[10a]] Banquet Speech at the Singapore Conference in Honour of Murray Gell-Mann on His 80th Birthday
• [[10e]] Spin 1/2 Fermions in 1D Harmonic Trap with Repulsive Delta Function Interparticle Interaction (with Z.-Q. Ma)
• [[10h]] One-Dimensional w-Component Fermions and Bosons with Repulsive Delta Function Interaction (with Y. Z. You)
• [[11a]] Quantum Numbers, Chern Classes, and a Bodhisattva
• [[11b]] My Experience as a Student and Researcher
• [[12a]] Fermi’s β-Decay Theory
• [[12d]] Topology and Gauge Theory in Physics
• [[12f]] On Reaching Age Ninety
• Postscript
• Index of Names in the Commentaries