Introducing the general condition for an operator in curved space to be unitary

doi:10.1088/1674-1056/abe300

Abstract We investigate the general condition for an operator to be unitary. This condition is introduced according to the definition of the position operator in curved space. In a particular case, we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator. Also we introduce a universal formula for adjoint of an arbitrary linear operator. Our procedure in this paper is totally different from others, as we explore a general approach based only on the algebra of the operators. Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.

Keywords: operator theory algebraic methods unitary operator translation operator

Received: 25 December 2020
Revised: 19 January 2021
Accepted manuscript online: 04 February 2021

PACS:	03.65.-w	(Quantum mechanics)
	03.65.Fd	(Algebraic methods)
	02.30.Tb	(Operator theory)

Corresponding Authors: Jafari Matehkolaee Mehdi
E-mail: jafarimatehkolaee@semnan.ac.ir

Cite this article:

Jafari Matehkolaee Mehdi Introducing the general condition for an operator in curved space to be unitary 2021 Chin. Phys. B 30 080301

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Introducing the general condition for an operator in curved space to be unitary

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