Time Operator in Relativistic Quantum Mechanics. (July 2017)

• Record Type: Journal Article
• Authors: Khorasani, Sina
• Is Part Of: Communications in theoretical physics. Volume 68:Number 1(2017:Jul.)
• Publication Date: 2017-07
• Subjects: quantum mechanics -- special relativity -- foundations of quantum mechanics -- operator theory; 03.65.-w -- 03.30.+p -- 03.65.Ta -- 02.30.Tb; Physics -- Periodicals; 530.105
• DOI: 10.1088/0253-6102/68/1/35
• Languages: English
• ISSNs: 0253-6102

Abstract

Abstract: It is first shown that the Dirac's equation in a relativistic frame could be modified to allow discrete time, in agreement to a recently published upper bound. Next, an exact self-adjoint 4 × 4 relativistic time operator for spin-1/2 particles is found and the time eigenstates for the non-relativistic case are obtained and discussed. Results confirm the quantum mechanical speculation that particles can indeed occupy negative energy levels with vanishingly small but non-zero probablity, contrary to the general expectation from classical physics. Hence, Wolfgang Pauli's objection regarding the existence of a self-adjoint time operator is fully resolved. It is shown that using the time operator, a bosonic field referred here to as energons may be created, whose number state representations in non-relativistic momentum space can be explicitly found .