Classical and Quantum Dynamics of Higher-Derivative Systems

Abstract

A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however: ghosts are benign. We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe represents then a classical solution in this theory, having the form of a 3-brane embedded in the bulk.

29 pages, 6 figures. Final version published in IJMPA

References in corpus (5)

• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
• Supersymmetry vs ghosts
• Pais-Uhlenbeck Oscillator and Negative Energies
• Exceptional points of infinite order give a continuous spectrum

Cited by in corpus (3)

• Massive poles in Lee-Wick quantum field theory
• Stable interactions between the extended Chern-Simons theory and a charged scalar field with higher derivatives: Hamiltonian formalism
• Conservation Laws and Stability of Field Theories of Derived Type