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The Non-Hermitian Dirac Equation and its Solutions

Tuesday October 17, 2017
2:00 pm

 Presenter:  Dr. Kate Brown (Physics Department, Hamilton College)
 Series:  Nuclear, Particle, Astroparticle and Cosmology (NUPAC) Seminars
 Abstract:  One of the fundamental assumptions of quantum mechanics is that observable quantities are represented by the eigenvalues of Hermitian matrix operators. The Dirac equation, which describes relativistic fermions, was originally constructed using a Hermitian matrix Hamiltonian, in keeping with this assumption. In recent decades it has been shown that Hermitian matrix operators are sufficient but not necessary to ensure a valid quantum mechanical theory; the parity (P) and time-reversal (T) operators can be used to ensure real eigenvalues, unitary time evolution, etc.  In this (chalk) talk we examine the consequence of allowing the matrices in the Dirac Hamiltonian to be non-Hermitian, but subject to the requirements of PT-quantum mechanics.  We find that the basic Dirac fermion is common to both the Hermitian and non-Hermitian Dirac equations, and that the non-Hermitian version hosts more complicated solutions which can be interpreted as particles with interesting properties that are not allowed within the Hermitian Standard Model. 
 Host:  Dinesh Loomba
 Location:  Room 190, Physics & Astronomy

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