Physical Models on Discrete Space and Time

Alexey L. Krugly

Ricardo O. de Alba Alvarez, Nick Sims, Christian Servín +2 more

Traditional physics assumes that space and time are continuous. However, this reasonable model leads to some serious problems. One the approaches that physicists follow to solve these problems is to assume that the space-time is actually discrete. In this paper, we analyze possible computational consequences of this discreteness. It turns out that in a discrete space-time, we may be able to solve NP-hard problems in polynomial time.

Andrei Yu. Khrennikov

Leonid O. Baliev

Our representations about space and time, even considering their «a priori» status according to Kant, change over time. Their evolution necessarily accompa-nies the development of our knowledge of physical reality. The article describes the representations of space and time that allows not only to unambiguously inter-pret the effects of quantum mechanics, but also to build a model of the bases of physical reality, the development of which, according to the author, can lead to the creation of a unified physical theory of the microworld. Within the framework of this model, the discreteness of space and time is asserted, from which the proba-bilistic nature of elementary motion follows with necessity; geometry is distin-guished into the inextricably linked continual geometry of Being and the discrete geometry of Existing, and time becomes the absolute invariant of Existing.

Iégor Reznikoff

Terry Farrelly, Anthony J. Short

In this paper, we consider fermionic systems in discrete space-time evolving with a strict notion of causality, meaning they evolve unitarily and with a bounded propagation speed. First, we show that the evolution of these systems has a natural decomposition into a product of local unitaries, which also holds if we include bosons. Next, we show that causal evolution of fermions in discrete space-time can also be viewed as the causal evolution of a lattice of qubits, meaning these systems can be viewed as quantum cellular automata. Following this, we discuss some examples of causal fermionic models in discrete space-time that become interesting physical systems in the continuum limit: Dirac fermions in one and three spatial dimensions, Dirac fields, and briefly the Thirring model. Finally, we show that the dynamics of causal fermions in discrete space-time can be efficiently simulated on a quantum computer.