The Conventionality of Parastatistics

Abstract

Nature seems to be such that we can describe it accurately with quantum theories of bosons and fermions alone, without resort to parastatistics. This has been seen as a deep mystery: paraparticles make perfect physical sense, so why don't we see them in nature? We consider one potential answer: every paraparticle theory is physically equivalent to some theory of bosons or fermions, making the absence of paraparticles in our theories a matter of convention rather than a mysterious empirical discovery.We argue that this equivalence thesis holds in all physically admissible quantum field theories falling under the domain of the rigorous Doplicher-Haag-Roberts approach to superselection rules. Inadmissible parastatistical theories are ruled out by a localityinspired principle we call Charge Recombination.

On a ℤ2n-Graded Version of Supersymmetry

“…Moreover, interacting field theories and their superselection rules are far less well understood than free theories -this is a current generic problem with algebraic field theory. A good discussion of the equivalence of paraparticles and particles, together with the limitations of what is mathematically established, can be found in [4]. Thus, there is still some possibility of, as of yet unseen (c.f.…”

Simulating para-Fermi oscillators

“…It was later demonstrated that this approach relates to the previous idea of parity deformed oscillators 3 , 6 – 8 characterized by a deformation parameter equivalent to the statistics order. Quantization of these parity deformed oscillators leads to interesting properties 9 – 12 but their selection rules render their natural occurrence highly unlikely 13 , 14 . Thus, a method for simulating these para-oscillators is most sought after.…”

Quantum simulation of driven para-Bose oscillators

“…Note that the standard boson algebra is recovered with order p = 1. Interestingly enough, quantum mechanics allows for the existence of paraparticles that have not been experimentally discovered as fundamental particles in nature [6,7]. On the other hand, trapped ions have proved a reliable platform for quantum simulation, offering high precision in both parameter control and measurement [8,9].…”