## JMI2010A-3 Self-adjoint extensions of momentum operators: application of weak Weyl relations (pp.21-25)

Author(s)： Fumio Hiroshima, Sotaro Kuribayashi and Itaru Sasaki

J. Math-for-Ind. 2A (2010) 21-25.

Abstract
By weak Weyl relations it is shown that momentum operators, $-i\partial_{x_j}$, defined on $C_0^{\infty}(\Omega)$ with some general open set $\Omega \subset\mathbb{R}^n$ are not essentially self-adjoint but have uncountably many self-adjoint extensions.

Keyword(s).　 canonical commutation relation, CCR, Weyl relation, weak Weyl relation, momentum operator