Action with Acceleration I: Euclidean Hamiltonian and Path Integral
arXiv:1211.7168 · doi:10.1142/S0217751X13501376
Abstract
An action having an acceleration term in addition to the usual velocity term is analyzed. The quantum mechanical system is directly defined for Euclidean time using the path integral. The Euclidean Hamiltonian is shown to yield the acceleration Lagrangian and the path integral with the correct boundary conditions. Due to the acceleration term, the state space depends on both position and velocity, and hence the Euclidean Hamiltonian depends on two degrees of freedom. The Hamiltonian for the acceleration system is non-Hermitian and can be mapped to a Hermitian Hamiltonian using a similarity transformation; the matrix elements of this unbounded transformation is explicitly evaluated. The mapping fails for a critical value of the coupling constants.
References in corpus (7)
- No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
- Exactly solvable PT-symmetric Hamiltonian having no Hermitian counterpart
- Solution to the ghost problem in fourth order derivative theories
- Comprehensive Solution to the Cosmological Constant, Zero-Point Energy, and Quantum Gravity Problems
- Tackling Higher Derivative Ghosts with the Euclidean Path Integral
- Which Green Functions Does the Path Integral for Quasi-Hermitian Hamiltonians Represent?
- Action with Acceleration II: Euclidean Hamiltonian and Jordan Blocks