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A not necessary rectangular Euclidean space (NoNRES) is constructed, in
which one obtains a generally Lorentz invariant scalar product for the low
energy sector (LES). This sector is defined for energies below the Planckian
limit. If the energy is zero, the NoNRES becomes rectangular and due to the Lorentz
invariance, it is applicable for the complete LES of the theory. In contrast to
the usual Minkowski space the metric of the NoNRES depends on the kinetic
energy of the observed quantum particles. It is assumed that this metric may be
useful to derive the scattering cross-section of the corresponding quantum
field theory. This assumption is related to the occurrence of divergent loop
momentum integrals caused by including the infinite energy range above the
Planckian limit (high energy sector or HES). Due to its energy dependence, the
metric in both energy sectors differs. In the HES, it depends on the effective
dimension of the NoNRES. This dependency results from fluctuations of the
space-time above the Planckian limit. Even if they are not part of the theory
(as they would be in quantum gravity), these fluctuations should not be
ignored. The effective dimension decreases if the energy of the considered
particle increases. Since this is true for the HES only, the ultraviolet
divergences of loop integrals seem to vanish without distorting the results of
the LES. The mechanism is illustrated by calculating the tadpole integral
occurring for a simple self-interacting scalar quantum field (with the Higgs
mass as example). One obtains a finite contribution for the integral and
consequently for the lifetime of the scalar particle.
As expected for years, nanotechnology has revolutionized engineering, biology, chemistry, physics and medicine of today. These disciplines are evolving thanks to the ongoing development of new materials and applications. Nanomedicine, as application of nanotechnology in the field of health care, has undergone unprecedented development. Some of these changes have real applications as, for example, the use of nanoparticles in MRI imaging, in hyperthermia, in immunotherapy, or to improve the bioavailability of drugs, among others -.
When a drug is administered to a patient, the blood distributes it throughout the body. In the case of very localized diseases (i.e. tumors), only a small fraction of the drug reaches the target. Chemotherapy is one of the most aggressive treatment options used in some types of cancer, and is usually administered intravenously. In this type of therapy, the drug circulates throughout the body, reaching and destroying healthy and cancerous tissues, producing side effects throughout the body, sometimes with serious consequences for the health of the patient (nephrotoxicity, cardiotoxicity, peripheral neuropathy, anemia, etc.). Among the many applications of nanotechnology, the fabrication of nanostructures capable of safely transporting these drugs is seen as a strategy for reducing these side effects. Nanoparticles are able to carry and release the drug in the right place and with the required dose, greatly reducing the problems associated with direct treatment with these drugs.
In recent years, there have been continuous improvements in the design and development of new tailor-made drug delivery systems , including hollow magnetic nanoparticles, liposomal structures, dendrimers, nanoporous silicon, etc. These structures can be obtained with different molecular weights (in the case of polymers), structures, shapes, and even with the appropriate functional groups for interaction at the desired positions. However, a great effort is still required to solve many of the current problems , including toxicity, aggregation, solubility and stability in the human body, physiological processes of elimination, identification of targets by highly specific receptors, controlled drug release over time, etc.