A Class of Simple Hamiltonians with Degenerate Ground State. II A Model of Nuclear Rotation : Spontaneous Breakdown of Rotation Symmetry and Goldstone Theorem for Finite Dimensional System

概要

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As a direct generalization of our previous work, we construct a manifestly rotation invariant Hamiltonian describing a system composed of a tensor boson with spin I=2 - such as, for example, phonon of nuclear quadrupole surface vibration- in which special cubic and quartic self-interactions are taken into account. All the ground state solutions are obtained. It is shown that these solutions can be classified into three classes : The first is the normal vacuum of boson, which is manifestly rotation symmetry. The second class of solutions can be viewed as generated from a single chosen state by rotating it into an arbitrary direction. The third one is Goldstone modes built on this chosen ground state. This chosen state- an exact ground state solution of our rotation invariant Hamiltonian- is not an eigenstate of angular momentum, but contains infinitely many different angular momentum states in it ; thus, typifying "spontaneous breakdown" of "rotation symmetry". It is further shown that this state can be naturally identified to an "intrinsic" deformed state in nuclear collective model of Bohr and Mottelson. The results are examined from the standpoint of Goldstone theorem and detailed discussions are given to explore how Goldstone theorem is modified in our finite dimensional system.
理論物理学刊行会の論文
1983-07-25