2013/10/31 by Huan-Hang Chi, Hong-Jian He · 15 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Hamiltonian (control theory) #Hamiltonian mechanics #Legendre function #Legendre polynomials #Legendre transformation #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Unitary state #Unitary transformation #gr-qc #hep-ph #hep-th #quant-ph
paper · pdf · doi:10.1016/j.nuclphysb.2014.05.017
published in Nuclear Physics B 885, 448-458 (Elsevier BV) · Journal Version, 16pp. All results + conclusions un-changed, only minor refinements to clarify the importance of our new LFT method and its physics applications; references added
openalex publication_date 2014/05/23 · arxiv created 2014/06/02 · arxiv updated 2014/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Under conventional Legendre transformation, systems with a non-convex Lagrangian will result in a multi-valued Hamiltonian as a function of conjugate momentum. This causes problems such as non-unitary time evolution of quantum state and non-determined motion of classical particles, and is physically unacceptable. In this work, we propose a new construction of single-valued Hamiltonian by applying Legendre–Fenchel transformation, which is a mathematically rigorous generalization of conventional Legendre transformation, valid for non-convex Lagrangian systems, but not yet widely known to the physics community. With the new single-valued Hamiltonian, we study spontaneous breaking of time translation symmetry and derive its vacuum state. Applications to theories of cosmology and gravitation are discussed.