Time in quantum mechanics and quantum field theory
Abbreviated Journal Title
J. Phys. A-Math. Gen.
UNCERTAINTY PRINCIPLE; TUNNELING TIME; ARRIVAL; ENERGY; OPERATOR; Physics, Multidisciplinary; Physics, Mathematical
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 of Physics a-Mathematical and General
"Time in quantum mechanics and quantum field theory" (2003). Faculty Bibliography 2000s. 4116.