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.
The Exact Foldy-Wouthuysen transformation (EFWT) method is generalized here. In principle, it is not possible to construct the EFWT to any Hamiltonian. The transformation conditions are the same but the involution operator has a new form. We took a particular example and constructed explicitly the new involution operator that allows one to perform the transformation. We treat the case of the Hamiltonian with 160 possible CPT-Lorentz breaking terms, using this new technique. The transformation was performed and physics analysis of the equations of motion is shown.Another possible phenomenological approach to this problem can be constructed step by step by searching for new terms in the Hamiltonian that describes this situation. Thinking this way, it makes sense the appearance of some terms in the equations of motion that could give a mix between an external known field with sufficient enough big amplitude to compensate the fact that the CPT-Lorentz terms have small amplitudes.The idea is the same shown in [15], where the strong magnetic field could, in principle, change the trajectory of the Dirac particle that interacts with gravitational waves. It is important to take into account the corrections, made with canonical FW, to these results that were shown in [16]. In [17], the massive linearized gravity was studied and some possible experiments that could measure indirect effects of gravitational waves on Dirac fermions were indicated. However, solving the Dirac equation for the general case is not a simple procedure [18]. It is well known in literature that working with the EFWT is a more prominent approach to interpret a Dirac Hamiltonian than the canonical transformation [19]. But this is true not only for the fact that it can give us new terms, but it is a faster and more economic (in terms of algebraic calculation) procedure [15,20,21,22]. One can see this transformation as a generalization of the usual FWT.Let us perform a comparison on the two procedures. It is possible to see that in the usual FWT the multiplication on each step (on each order on 1/m) by the term that makes the Hamiltonian even, generates a maximum of 1 + 2n even terms, where n represents the number of terms of the previous Hamiltonian (see, for example, pages 48-51 in [23]). The maximum number of terms in the nth-Hamiltonian is straightforward obtained by the fact that this is an expansion in power series of an operator. The factor 2 on 1 + 2n expression is obtained in case when it does not commute with all original terms.On the other hand, the EFWT impose the multiplication of all terms of the Hamiltonian by themselves. Analogous arguments give us the maximum of 1+2n 2 on the expanded Hamiltonian. If the parameter of expansion here is also taken to be 1/m, one can see that the possibility of having new terms in comparison with the usual method is greater. In many particular known cases [21,24,25], the anti-commutators on both cases are such that the results are the same! But it is not the general case. This was explicitly shown on [19]. ...
Nova metodologia para aferição da temperatura final de hastes metálicas em um experimento de dilatação térmica linear Para realizar o estudo da expansão térmica em diversos materiaisé necessário conhecer o seu coeficiente de dilatação linear, mas em alguns casosé difícil medir a temperatura final do corpo em estudo. Descrevemos uma atividade experimental de baixo custo com o objetivo de mostrar uma metodologia de medição e ensino que resolva o problema da aferição desta temperatura final. A metodologia desenvolvida utiliza materiais de fácil acesso e o resultado encontrado, bastante satisfatório,é descrito ao longo deste trabalho. O valor do coeficiente de dilatação medido experimentalmente para o cobre foi igual a (1,70 ± 0,32)x10−5 • C −1 . Palavras-chave: expansão térmica, coeficiente de dilatação térmica, materiais de baixo custo.For the study of thermal expansion in various materials it is necessary to know the coefficient of linear expansion, but in some cases it is difficult to measure the final temperature of the sample under consideration. We present a low-cost experimental setup in order to show a teaching methodology to address the problem of measuring this final temperature. The methodology uses materials that are easy to find, and the positive result are described in this paper. The value of the experimentally measured thermal expansion coefficient for copper of was (1.70 ± 0.32) x10−5 • C −1 .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.