Fundamental length in quantum theories with PT-symmetric Hamiltonians
- Nuclear Physics Institute ASCR, 250 68 Rez (Czech Republic)
One-dimensional motion of a quantum point particle is usually described by its wave function {psi}(x), where the argument x is an element of R represents a (measurable) coordinate and where the integrated probability density is normalized to one, {integral}{psi}*(x){psi}(x)=1. The direct observability of x may be lost in PT-symmetric quantum mechanics where a 'smeared' metric kernel {theta}{sub (x,x{sup '})}{ne}{delta}(x-x{sup '}) may enter the double-integral normalization {integral}{integral}{psi}*(x){theta}{sub (x,x{sup '})}{psi}(x{sup '})=1. We argue that such a formalism proves particularly suitable for the introduction of a nonvanishing fundamental length {theta}>0, which would characterize the 'smearing width' of the kernel {theta}{sub (x,x{sup '})}. The technical feasibility of such a project is illustrated via a toy family of Hamiltonians H{sup (N)}({lambda}) taken from Ref. 11. For each element of this family the complete set of all the eligible metric kernels {theta}{sub (x,x{sup '})}{sup (N)}({lambda}) is constructed in closed form. We show that at any preselected non-negative fundamental length these metrics can be made to vanish unless |x-x{sup '}|{<=}{theta}. The strictly local inner product of Ref. 11 recurs at {theta}=0, while the popular CPT-symmetric option requires {theta}={infinity} in this language.
- OSTI ID:
- 21322518
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 80, Issue 4; Other Information: DOI: 10.1103/PhysRevD.80.045022; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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