We investigate the algebraic structure of the most general neutrino mass Hamiltonian and place the see-saw mechanism in an algebraic framework. We show that this Hamiltonian can be written in terms of the generators of an Sp(4) algebra. The Pauli-Gürsey transformation is an SU(2) rotation which is embedded in this Sp(4) group. This SU(2) also generates the see-saw mechanism. Typeset using REVTE...

Unitary evolution under a time dependent Hamiltonian is key component of simulation on quantum hardware. Synthesizing the corresponding circuit typically done by breaking into small steps, also known as Trotterization, which leads to circuits whose depth scales with number steps. When elements are limited subset SU(4) -- or equivalently, when may be mapped onto free fermionic models several ide...

This is an example of application Ziglin-Morales-Ramis algebraic studies in Hamiltonian integrability, more specifically the result by Morales, Ramis and Sim\'o on higher-order variational equations, to well-known Friedmann-Robertson-Walker cosmological model. A previous paper author formalises said systems such a way allowing simple expression notable elements differential Galois group needed ...

We discuss a procedure to determine finite sets $\mathcal{M}$ within the commutant of an algebraic Hamiltonian in enveloping algebra Lie $\mathfrak{g}$ such that their generators define quadratic algebra. Although independent from any realization algebras by differential operators, method is partially based on analytical approach, and uses coadjoint representation $\mathfrak{g}$. The procedure,...

The Hamiltonian description of the self-consistent interaction between an electromagnetic plane wave and a copropagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson brackets. The reduction to this paradigmatic Hamiltonian model is performed using a Lie algebraic for...

Abstract. In this letter, we analyse the following apparent paradox: As has been recently proved by Hastings [1], under a general set of conditions, if a local Hamiltonian has a spectral gap above its (unique) ground state (GS), all connected equal-time correlation functions of local operators decay exponentially with distance. On the other hand, statistical mechanics provides us with examples ...