Title

Time in quantum mechanics and quantum field theory

Authors

Authors

Z. Y. Wang; B. Chen;C. D. Xiong

Comments

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Abbreviated Journal Title

J. Phys. A-Math. Gen.

Keywords

UNCERTAINTY PRINCIPLE; TUNNELING TIME; ARRIVAL; ENERGY; OPERATOR; Physics, Multidisciplinary; Physics, Mathematical

Abstract

W Pauli pointed out that the existence of a self-adjoint time operator is incompatible with the semi-bounded character of the Hamiltonian spectrum. As a result, there has been much argument about the time-energy uncertainty relation and other related issues. In this paper, we show a way to overcome Pauli's argument. In order to define a time operator, by treating time and space on an equal footing and extending the usual Hamiltonian H to the generalized Hamiltonian (H) over cap (mu) (with (H) over cap (0) = (H) over cap), we reconstruct the analytical mechanics and the corresponding quantum (field) theories, which are equivalent to the traditional ones. The generalized Schrodinger equation ipartial derivative(mu)psi = (H) over cap (mu)psi and Heisenberg equation d (F) over cap /dx(mu) = partial derivativemu(F) over cap + i[(H) over cap (mu), (F) over cap] are obtained, from which we have: (1) t is to (H) over cap (0) as x(j). is to (H) over cap (j) (j = 1, 2, 3); likewise, t is to ipartial derivative(0) as x(j) is to ipartial derivative(j); (2) the proposed time operator is canonically conjugate to ipartial derivative(0) rather than to (H) over cap (0), therefore Pauli's theorem no longer applies; (3) two types of uncertainty relations, the usual Deltax(mu)Deltap(mu) greater than or equal to 1/2 and the Mandelstam-Tamm treatment Deltax(mu)DeltaH(mu) greater than or equal to 1/2, have been formulated.

Journal Title

Journal of Physics a-Mathematical and General

Volume

36

Issue/Number

18

Publication Date

1-1-2003

Document Type

Article

Language

English

First Page

5135

Last Page

5147

WOS Identifier

WOS:000183213500018

ISSN

0305-4470

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