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Acta Physica Sinica

THE JANOSSI WAVE EQUATIONS AS A NUCLEAR THEORY OR AS A THEORY OF ELEMENTARY PARTICLES

C. Khunyuan

Published Jan 1, 1956• 0 citations
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Abstract

It is shown that the modified Schroedirger equation, proposed by Janossi (Acta Phys. Acad. Sci. Hung. 1, electron. However, this equation can be considered as a model of a possible phenomenological theory of elementary particles. The posslbility of quantizing this equation is considered.

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JANOSSY'S WAVE EQUATION AS A THEORY OF NUCLEI OR AS A THEORY OF ELEMENTARY PARTICLES

TZU HUNG-YUAN

摘要 本文指出杨诺赛波动方程作为电子的个体理论的困难;指出这一类型波动方程可以作为原子核系综理论的数学形式,也可以作为元粒子系综理论的数学形式。本文并讨论了这一类型波动方程的第二级量子化问题。 Abstract It is shown that the modified Schr?dinger equation proposed by Janossy cannot describe the behavior of the electron correctly. However, it is further shown that the equation can be regarded as a model of a possible phenomenalogical theory of nuclei or as a model of a possible theory of elementary particles. The quantization of the equation is discussed. 作者及机构信息 朱洪元 1. 中国科学院物理研究所 Authors and contacts TZU HUNG-YUAN 1. 中国科学院物理研究所 参考文献 [1] 施引文献

Acta Physica Sinica•Jan 1, 1956•0 citations

SPINOR THEORY OF ELEMENTARY PARTICLES. II. MATHEMATICAL DERIVATION OF THE POSTULATES DESCRIBING REAL WAVE FUNCTIONS WITH 2(2s + 1) OR 4(2s + 1)

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THE BASIC EQUATIONS OF NON-RELATIVISTIC WAVE MECHANICS

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The Schroedinger wave equation is examined to determine if it can be formulated in a more rigorous and at the same time more general form to synthesize the ideas of wave and corpuscular motions. The various possibilities which are contained in non-relativistic wave mechanics and which seem to be the prerogative of relativistic theories are examined. The cases of spin and isotopic space are considered. (J.S.R.)

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The relativistic quantum mechanics of the elementary particles

H. S. Green

The search for a theory of the elementary particles which is founded on the well-established principles of quantum mechanics and conforms at the same time with the requirements of the principle of relativity has, in recent years, taken several divergent directions. On the one hand, the second quantization of wave fields derived from a Lagrangian by a variational procedure(1) has succeeded in accounting for the existence and most of the properties of the electron, the photon, and the meson. On the other hand, many generalizations of the Dirac wave equation of the electron(2) have been attempted, with applications to the meson(3) and the proton(4). Heisenberg(5) has considered the much more difficult problem of the interaction between different particles, and has found that the key to the situation is the so-called ‘scattering matrix’, which is nothing other than a limiting form of the relativistic density matrix, as defined in § 2 of this paper. It seems probable that the relativistic density matrix ρ; or statistical operator, as it may be called without reference to representation, will play an important part in relativistic quantum mechanics in the future. It satisfies the same equation as the wave function, but differs from it in being a real linear operator, or a dynamical variable, in the terminology of Dirac.

Mathematical Proceedings of the Cambridge Philosophical Society•Apr 1, 1949•5 citations

WHAT IS AN ELEMENTARY PARTICLE?

INDIVIDUALAtomism in its latest form is called quantum mechanics.It has extended its range to comprise, besides ordinary matter, all kinds of radiation, including light-in brief, all forms of energy, ordinary matter being one of them.In the present form of the theoiy the "atoms" are electrons, jorotons, photons, mesons, etc.The generic name is elementary particle, or merely particle.The term "atom" has very wisely been retained for chemical atoms, though it has become a misnomer.This essay deals with the elementary particle, more particularly with a certain feature that this concept has acquired-or rather lost in quantum mechanics.I menn this : That the elementary particle is not an individual; it cannot be identified, it lacks "sameness."The fact is known to every physicist, but is rarely given any prominence in surveys readable by nonspccialists.In technical language it is covered by saying that the particles "obey" new-fangled statistics, either Einstein-Bose or Fermi-Dirac statistics.The implication, far from obvious, is that the unsuspected epithet "this" is not quite prop- erly applicable to, say, an electron, except with caution, in a restricted sense, and sometimes not at all.My objective here is to explain this point and to give it the thought it deserves.In order to create a foil for the discussion, let me summarize in sections 2-5 what we are usually told about particles and waves in the new physics.2. CURRENT VIEWS: THE AMALGAMATION OF PARTICLES AND WAVES Our image of the material world had been made up of two kinds of "fittings"-waves and particles.The former were instanced mainly, if not exclusively, by Maxwell's waves of electromagnetic energy, comprising such as are used in radio, light, X-rays, and gamma-rays.Material bodies were said to consist of particles.One

WORLD SCIENTIFIC eBooks•May 1, 1985•13 citations

RELATIVISTIC QUANTUM THEORY AS A GROUP PROBLEM. II. WORLD GEOMETRY AND THE ELEMENTARY PARTICLES

Yrjö Ahmavaara

The world geometry underlying the theory of elementary particles is investigated. The elementary, non-relativistic geometry of the physical space is given a general formulation, sufficient to yield the quanta of momentum and energy when the group quantization process is applied to the physical space. The elementary geometry is represented by a commutative (finite or continuous) group of translations to which Pontrjagin's theorem concerning the duality between a commutative group and its character group applies. The principle of uncertainty is given a group theoretical formulation in terms of the Pontrjaginian duality. This formulation allows a consequent and meaningful extension of quantum theory to a finite geometry. The role of the relativistic (finite or continuous) geometry of space-time in the theory of elementary particles is investigated. A formulation of the problem of elementary particles is given, and an eventual connection between the observed elementary particles and a geometry of the Lorentz group space is suggested. (auth)

•Jan 1, 1962•1 citation
摘要 本文指出杨诺赛波动方程作为电子的个体理论的困难;指出这一类型波动方程可以作为原子核系综理论的数学形式,也可以作为元粒子系综理论的数学形式。本文并讨论了这一类型波动方程的第二级量子化问题。 Abstract It is shown that the modified Schr?dinger equation proposed by Janossy cannot describe the behavior of the electron correctly. However, it is further shown that the equation can be regarded as a model of a possible phenomenalogical theory of nuclei or as a model of a possible theory of elementary particles. The quantization of the equation is discussed. 作者及机构信息 朱洪元 1. 中国科学院物理研究所 Authors and contacts TZU HUNG-YUAN 1. 中国科学院物理研究所 参考文献 [1] 施引文献
The search for a theory of the elementary particles which is founded on the well-established principles of quantum mechanics and conforms at the same time with the requirements of the principle of relativity has, in recent years, taken several divergent directions. On the one hand, the second quantization of wave fields derived from a Lagrangian by a variational procedure(1) has succeeded in accounting for the existence and most of the properties of the electron, the photon, and the meson. On the other hand, many generalizations of the Dirac wave equation of the electron(2) have been attempted, with applications to the meson(3) and the proton(4). Heisenberg(5) has considered the much more difficult problem of the interaction between different particles, and has found that the key to the situation is the so-called ‘scattering matrix’, which is nothing other than a limiting form of the relativistic density matrix, as defined in § 2 of this paper. It seems probable that the relativistic density matrix ρ; or statistical operator, as it may be called without reference to representation, will play an important part in relativistic quantum mechanics in the future. It satisfies the same equation as the wave function, but differs from it in being a real linear operator, or a dynamical variable, in the terminology of Dirac.
INDIVIDUALAtomism in its latest form is called quantum mechanics.It has extended its range to comprise, besides ordinary matter, all kinds of radiation, including light-in brief, all forms of energy, ordinary matter being one of them.In the present form of the theoiy the "atoms" are electrons, jorotons, photons, mesons, etc.The generic name is elementary particle, or merely particle.The term "atom" has very wisely been retained for chemical atoms, though it has become a misnomer.This essay deals with the elementary particle, more particularly with a certain feature that this concept has acquired-or rather lost in quantum mechanics.I menn this : That the elementary particle is not an individual; it cannot be identified, it lacks "sameness."The fact is known to every physicist, but is rarely given any prominence in surveys readable by nonspccialists.In technical language it is covered by saying that the particles "obey" new-fangled statistics, either Einstein-Bose or Fermi-Dirac statistics.The implication, far from obvious, is that the unsuspected epithet "this" is not quite prop- erly applicable to, say, an electron, except with caution, in a restricted sense, and sometimes not at all.My objective here is to explain this point and to give it the thought it deserves.In order to create a foil for the discussion, let me summarize in sections 2-5 what we are usually told about particles and waves in the new physics.2. CURRENT VIEWS: THE AMALGAMATION OF PARTICLES AND WAVES Our image of the material world had been made up of two kinds of "fittings"-waves and particles.The former were instanced mainly, if not exclusively, by Maxwell's waves of electromagnetic energy, comprising such as are used in radio, light, X-rays, and gamma-rays.Material bodies were said to consist of particles.One
The world geometry underlying the theory of elementary particles is investigated. The elementary, non-relativistic geometry of the physical space is given a general formulation, sufficient to yield the quanta of momentum and energy when the group quantization process is applied to the physical space. The elementary geometry is represented by a commutative (finite or continuous) group of translations to which Pontrjagin's theorem concerning the duality between a commutative group and its character group applies. The principle of uncertainty is given a group theoretical formulation in terms of the Pontrjaginian duality. This formulation allows a consequent and meaningful extension of quantum theory to a finite geometry. The role of the relativistic (finite or continuous) geometry of space-time in the theory of elementary particles is investigated. A formulation of the problem of elementary particles is given, and an eventual connection between the observed elementary particles and a geometry of the Lorentz group space is suggested. (auth)