توصيفگر ها :
ناظر آزاد افتان , ژئودزيك , دستگاه لخت موضعي , تحول زماني , يكاني , ضرب داخلي , هميوغ هرميتي
چكيده انگليسي :
Free falling Observer in an Asymptotically Flat Spacetime Fataneh Bakherad F Bakherad @ yahoo com June 25 2018 Department of Physics Isfahan University of Technology Isfahan 84156 83111 Iran University Code IUT 77142 Degree M S c Language Farsi Supervisor Dr Farhang Loran laran@cc iut ac ir Abstract We evaluate the path of the free falling point particle in an asymptotically at spacetime Toreview the observations of such observer we will de ne a localy at spacetime by making use of thegeodesics The coresponding time like and space like vectors should be and respectively Where is the proper time of the free falling observer and is its space with cosideration that at any timethis observer is simultaneous event Hamiltonian is the time evolution of the wave equation whichcan be obtained from the Dirac equation If Hamiltonian be hermition operator of time evolutionwould be unitary We need a de nition for inner product in Hilbert space to verify the hermition ofthe hamiltonian As this de nition should be invariant under time transformation we search for aconservative bilinear form This conservative bilinear form is also derived from the Dirac equation Finally by making use of the de nition of the inner product we will derive the hermition of theHamiltonian and we shall see that this is equal to hamiltonian so the hamiltonian is Hermitian Keywords Free falling Observer Geodesic Localy Flat Spacetime Hamiltonian Time Evolution Dirac Equation Inner Product Hermition
