Energy expectation values of a particle in nonstationary fields

Abstract

We show that the origin of the nonequivalence of Hamiltonians in different representations is a change of the form of the time-derivative operator at a time-dependent unitary transformation. This nonequivalence does not lead to an ambiguity of the energy expectation values of a particle in nonstationary fields but assigns the basic representation. It has been explicitly or implicitly supposed in previous investigations that this representation is the Dirac one. We prove the alternative assertion about the basic role of the Foldy-Wouthuysen representation. We also derive the general equation for the energy expectation values in the Dirac representation. As an example, we consider a spin-1/2 particle with anomalous magnetic and electric dipole moments in strong time-dependent electromagnetic fields. We apply the obtained results to a spin-1/2 particle in a plane monochromatic electromagnetic wave and give an example of the exact Foldy-Wouthuysen transformation in the nonstationary case.

16 pages; final version

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Cited by in corpus (9)

• General treatment of quantum and classical spinning particles in external fields
• Position and spin in relativistic quantum mechanics
• Manipulating twisted electron beams
• General relativity effects in precision spin experimental tests of fundamental symmetries
• Relativistic spin dynamics conditioned by dark matter axions
• New symmetry properties of pointlike scalar and Dirac particles
• Dynamics of the relativistic electron spin in an electromagnetic field
• Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession
• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian