Time operators and time crystals: self-adjointness by topology change

Abstract

We investigate time operators in the context of quantum time crystals in ring systems. A generalized commutation relation called the generalized weak Weyl relation is used to derive a class of self-adjoint time operators for ring systems with a periodic time evolution: The conventional Aharonov-Bohm time operator is obtained by taking the infinite-radius limit. Then, we discuss the connection between time operators, time crystals and real-space topology. We also reveal the relationship between our time operators and a PT -symmetric time operator. These time operators are then used to derive several energy-time uncertainty relations.

The Nakano–Nishijima–Gell-Mann Formula from Discrete Galois Fields

“…The NNG formula is a phenomenological equation. By using a Galois field, the NNG Formula (24) is rewritten as (23). The new quantum number n, which includes isospin I z and hypercharge Y, arises from the multivaluedness of a linear representation of the Galois field.…”

“…Recently, with the development of quantum information, Galois fields have begun to be used to construct space-time models as error-correcting codes [33]. Further application of Galois fields is expected in the foundation of quantum physics [34] and time crystal with discrete space-time symmetry [20][21][22][23][24].…”

“…Q is the charge number of baryon and i, j, k are total isospins of quark. n is derived from Equation (23).…”

“…Fourth, the field theory of Galois field was investigated by Nambu in the context of recurrence time [6]. Recently, the discreteness of time is also discussed the context of time crystals [20][21][22][23][24]. So, if space-time is both finite and discrete, we have to re-examine the laws of physics [6].…”

“…Figure 2. Classification of hadrons with Equation(23). Our model take the n and I axis instead of Y and I z .…”