Plane Wave in the System of N Particles with Zero Angular Momentum

Shimpei Endo, Pascal Naidon, Masahito Ueda

Toshihiro Iwai, Toru Hirose

Quantum systems of three identical particles on a plane are analyzed from the viewpoint of symmetry. Upon reduction by rotation, such systems are described in the space of sections of a line bundle over a three-dimensional shape space whose origin represents triple collision. It is shown that if the total angular momentum is nonzero, then the wave section must vanish at the origin, while if it is zero, then the wave section can be finite at the origin. Since the particles are assumed to be identical, the quantum system admits the action of the symmetric group S3 as well, which stands for the group of particle exchanges and is commutative with rotation. Hence the reduced system still admits the S3 action, so that Bose and Fermi states can be discussed in the space of sections of the line bundle. A detailed analysis of a system of three free particles on a plane is presented in the latter part of the article.

V.B. Berestetskii, А. З. Долгинов, K.A. Ter-Martirosyan

Kundeti Muralidhar

A charged elementary particle fluctuates from its mean position because of the presence of zero-point fields in vacuum. Considering the complex oscillations of the particle as two general types of rotations, an attempt has been made to explore the classical origin of spin angular momentum. The oscillations of the particle in zero-point field can be transformed as rotations on complex plane and the spin angular momentum is identified with imaginary part of rotations. The quantum value of spin angular momentum has been determined within the purview of stochastic electrodynamics. Keywords: Spin angular momentum, Zero-point energy, Stochastic Electrodynamics. 1.

Fedor I. Fedorov

David V. George