Fermi Gamma-ray Space Telescope

Selfentangled Majorana Objects

Z. Arvay

Abstract:

Self entanglement In the famous article Einstein called the attention for the importance of quantum entanglement. We call the pure state ?_AB on the non interacting composite system A U B bipartitate, if it is written with respect to the partitions A, B for every ? ?|???_AB=?_(i,j)??C_ij |? i?_A ? ??|? j?_B ? (1) where exists bases {?|? j?_A ?} and {?|? j?_B ?} in HA and HB respectively. Let {?|? j?_A ?} and {?|? j?_B ?} an other appropriate two basis so that ? ?|???_AB=?_i??C_i |? i?_A ? ??|? i?_B ? is valid and i=1,..,n. (2) Let more than one Schmidt coefficients C_i are nonzero and hince the ?_AB state is entangled. Let the distance between the two bipartitate objects is vanishingly small, that is 0 than ?_AB is selfentangled. We have made a Schmidt decomposition of a bipartition at R=0. Antiparticles In case of R=0 the time dimension is free for object development. When a bipartitate object arises at R=0 and t=0 the partitions can one is antiparticle of the other __ ?_B=?_A , which means propagate in opposite directions in time according to Feynman who introduced in his remarkable diagrams the antiparticles as particles propagating backward in time. Such a quasiparticle {?_A ?_B } we call SECP (selfentangled conjugated pair) object. Majorana object When permutation symmetry holds the SECP quasiparticle is a self antiparticle which we can call SEMP, as _ ______ _ _ ?_AB={?_A ?_B }={?_A ?_B }={?_B ?_A }={?_A ?_B }=?_AB (3) which means{?_A ?_B } is a Majorana particle as Majorana proposed the possible existence of self antiparticles.