Studies On The Velocities Of Relativistic Particles In Commutative And Noncommutative Space

Spatial noncommutativity is one of the foci of the theoretical research today.It has been proven that the Lorentz invariance will be violated in noncommutative space since the electromagnetic wave propagates with different speed in the noncommutative space in the presence of a magnetic field.It can exceed the speed of light in the vacuum if it propagates along the magnetic field.However,such studies are only concern the massless particles—photons.It is still interesting to know whether the Lorentz invariance can also be broken for massive particles.In this thesis,we will study this problem.We show that the Lorentz invariance can be violated by massive particles because of spatial noncommutativity.One of the effective ways to study whether the Lorentz invariance is violated is to investigate the speed of a particle.We study massive charged spin-1/2,spin-0 and spin-1 particles interacting with the uniform magnetic fields both in the commutative and noncommutative space.We show that the speed of these particles cannot exceed the speed of light in vacuum regardless the intensities of the magnetic fields.However,in noncommutative space,it is possible for these particles travel faster than the speed of light in vacuum because of spatial noncommutativity.It is a clear signal of breaking the Lorentz invariance.Thus,our conclusions are that the Lorentz invariance in the noncommutative space will be broken even for massive particles.Therefore,our research not only widens the field of the violation of Lorentz invariance in the noncommutative space,but also provides the methods for analogous research.