Probabilistic representation and fall-off of bound states of relativistic Schrodinger operators with spin 1/2 Fumio Hiroshima Takashi Ichinose Jozsef Lorinczi 2134/21512 https://repository.lboro.ac.uk/articles/journal_contribution/Probabilistic_representation_and_fall-off_of_bound_states_of_relativistic_Schrodinger_operators_with_spin_1_2/9384743 A Feynman-Kac type formula of relativistic Schrodinger operators with unbounded vector potential and spin 1/2 is given in terms of a three-component process consisting of Brownian motion, a Poisson process and a subordinator. This formula is obtained for unbounded magnetic fields and magnetic fields with zeros. From this formula an energy comparison inequality is derived. Spatial decay of bound states is established separately for growing and decaying potentials by using martingale methods. 2016-06-07 13:55:54 Relativistic Schrodinger operators Bound states Spatial decay Feynman-Kac formulae Poisson process Subordinate Brownian motion Martingales Mathematical Sciences not elsewhere classified