Particles and quantum symmetries

Gaetano Fiore, Peter Schupp

Joan A. Vaccaro

Symmetry plays a central role in many areas of modern physics. Here, we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry, whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by , where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus a more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.

Justin C. Pniower

This thesis analyses the ontological nature of quantum particles. In it I argue that quantum particles, despite their indistinguishability, are objects in much the same way as classical particles. This similarity provides an important point of continuity between classical and quantum physics. I consider two notions of indistinguishability, that of indiscernibility and permutation symmetry. I argue that neither sort of indistinguishability undermines the identity of quantum particles. I further argue that, when we understand in distinguishability in terms of permutation symmetry, classical particles are just as indistinguishable as quantum particles; for classical physics also possesses permutation symmetry.

Heinz Dietrich Doebner, Jörg Hennig, W. Lücke +1 more

Manuel Gadella, Ş. Kuru, M. A. del Olmo +2 more

Felix M. Lev

In our previous papers it has been shown that quantum theory based on a Galois field (GFQT) possesses a new symmetry between particles and antiparticles, and for massless particles this symmetry (called the AB one) is compatible with all representation operators of the symmetry algebra. In the present paper, it is shown that the AB symmetry is compatible with all representation operators of the symmetry algebra in the general case. As a consequence of simple arithmetical considerations, this symmetry is compatible with the vacuum condition, only for particles with half-integer spin (in usual units). If the AB symmetry is combined with the spin-statistics theorem, one arrives at the following conclusions: in quantum theory based on a Galois field i) any neutral particle can be only composite but not elementary (this property has been proved for the massless case in hep-th/0207192); ii) any interaction can involve only an even number of creation/annihilation operators.