COORDINATE REPRESENTATION AND MOMENTUM REPRESENTATION IN QUANTUM MECHANICS WITH NEGATIVE METRIC
Uan T
On the basis of our previous papers~[1,2], we discuss the representations in quantum mechanics with negative metric. With the aid of the properties of the coherent state of the abnormal boson (the boson with negative metric), in addition to the properties of the normal product, we derive the ordered product form of the metric operator, and them discuss the eigenstates of the coordinate and the momentum with the imaginary eigenvalues. With the coherent-state method we prove that these eigenstates cannot be normalized, but we can find metric-like operators which can normalize the eigenstates as the δ function. We also provide the completeness condition for these eigenstates with imaginary eigenvalues and their relation to the eigenstates with real eigenvalues, as well as the physical vacuum state's new representations.
Science China Mathematics•Jan 1, 1985•0 citations