Exact Foldy-Wouthuysen transformation for a Dirac theory with the complete set ofCPT-Lorentz invariance violating terms

Abstract

The exact Foldy-Wouthuysen transformation is performed in order to study the Dirac field interacting with many possible external fields associated with CPTLorentz violation. We also derived the calculation of equations of motion as well as the generalized Lorentz force corrected by the mentioned external fields. The main point is the interaction between the Dirac particle and the terms that have the multiplication of electromagnetic field and the terms that break CPT-Lorentz. Finally, with the transformed Hamiltonian we were able to write an expression for the bound state of the theory and analyze it in the atomic experiments context. This result is an analytical expression that gives the possibility of the weakness of CPT/Lorentz terms to be compensated by the presence of a strong magnetic field.

Constrains of Charge-to-Mass Ratios on Noncommutative Phase Space

“…[40] is expected to give a strong limit on the parameter c µν . The non-relativistic approximation can be obtained by using the well-known Foldy-Wouthuysen unitary transformation (FWUF) [45], and neglecting the spin degree of freedom the non-relativistic Hamiltonian is given as [59],…”

Lorentz andCPTtests with hydrogen, antihydrogen, and related systems

“…Related experiments with antihydrogen are being developed [19][20][21][22], and experiments with hydrogen molecules and molecular ions have been proposed as well [23]. In the context of the minimal SME, theoretical modifications to the spectra of hydrogen and antihydrogen have been widely studied [13,[24][25][26][27][28][29][30][31], while spectral shifts are also known to arise from specialized nonminimal SME interactions with d = 5 [32] and from d = 6 terms originating in noncommutative quantum field theory [33,34]. The minimal SME also introduces CPT-violating effects in positronium decay [35,36].…”

Effective theories and non-minimal couplings in low-dimensional systems

“…For example, it has been a useful tool to describe fundamental and excited states of atomic nuclei [3], some interactions with gravitational and torsion fields [4][5][6][7][8]. Also, it was considered in scenarios with Lorentz symmetry violation [9][10][11][12], accelerated frames [13,14], topological defects [15,16] and topological insulators [17,18].…”