Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2003-03-02
Am.J.Phys. 71 (2003) 1095-1102
Physics
High Energy Physics
High Energy Physics - Theory
Revised version to appear in American Journal of Physics
Scientific paper
10.1119/1.1574043
A consistent physical theory of quantum mechanics can be built on a complex Hamiltonian that is not Hermitian but instead satisfies the physical condition of space-time reflection symmetry (PT symmetry). Thus, there are infinitely many new Hamiltonians that one can construct that might explain experimental data. One would think that a quantum theory based on a non-Hermitian Hamiltonian violates unitarity. However, if PT symmetry is not broken, it is possible to use a previously unnoticed physical symmetry of the Hamiltonian to construct an inner product whose associated norm is positive definite. This construction is general and works for any PT-symmetric Hamiltonian. The dynamics is governed by unitary time evolution. This formulation does not conflict with the requirements of conventional quantum mechanics. There are many possible observable and experimental consequences of extending quantum mechanics into the complex domain, both in particle physics and in solid state physics.
Bender Carl M.
Brody Dorje C.
Jones Hugh F.
No associations
LandOfFree
Must a Hamiltonian be Hermitian? does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Must a Hamiltonian be Hermitian?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Must a Hamiltonian be Hermitian? will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-381366