scholarly journals Analytic Dependence is an Unnecessary Requirement in Renormalization of Locally Covariant QFT

2016 ◽  
Vol 344 (2) ◽  
pp. 581-620 ◽  
Author(s):  
Igor Khavkine ◽  
Valter Moretti
Keyword(s):  
Author(s):  
Matteo Dalla Riva ◽  
Riccardo Molinarolo ◽  
Paolo Musolino

In this paper we study the existence and the analytic dependence upon domain perturbation of the solutions of a nonlinear nonautonomous transmission problem for the Laplace equation. The problem is defined in a pair of sets consisting of a perforated domain and an inclusion whose shape is determined by a suitable diffeomorphism $\phi$ . First we analyse the case in which the inclusion is a fixed domain. Then we will perturb the inclusion and study the arising boundary value problem and the dependence of a specific family of solutions upon the perturbation parameter $\phi$ .


1996 ◽  
Vol 10 (13n14) ◽  
pp. 1685-1693
Author(s):  
HUZIHIRO ARAKI

We study soliton sectors of the XY model by using known results and methods about its ground states. In the regions of parameters for which ground states are not unique, we show that (1) there are two soliton sectors depending on parameters of the model analytically in a well-defined sense, (2) the only sectors with “finite energy” are ground state and soliton sectors, and (3) the sudden appearance of additional ground states at a pair of specific values of parameters (despite analytic dependence of other ground states on parameters at those specific values), which were found in earlier study of ground states, can be understood as the degeneracy of one particle energy in the soliton sector (which has a continuous spectrum at other values of parameters) to a single point spectrum with infinite multiplicity at the specific values of parameters.


2021 ◽  
Vol 922 (2) ◽  
pp. 224
Author(s):  
Hongbo li ◽  
Hengqiang Feng ◽  
Yuandeng Shen ◽  
Zhanjun Tian ◽  
Guoqing Zhao ◽  
...  

Abstract Although the fast kink oscillation, as one of a few fundamental modes in coronal seismology, has received a lot of attention over the past two decades, observations of its frequency drift remain elusive. There is evidence that this phenomenon is related to the quasi-static evolution of loop density. We therefore consider analytically the effects of a quasi-static density evolution on the fast kink oscillation of coronal loops. From the analyses, we determine explicitly the analytic dependence of the oscillation period/frequency and amplitude on the evolving density of the oscillatory loop. The findings can well reconcile several key characters in some frequency drift observations, which are not understood. Models of fast kink oscillation in the thermal dynamic loop are also established to investigate the present effects in more detail. Our findings not only show us a possible explanation for the frequency drift of the coronal loop’s fast kink oscillation, but also a full new energy transformation mechanism where the internal energy and the kinetic energy of an oscillating coronal loop can be interchanged directly by the interaction of the loop’s oscillation and its density evolution, which we suggest may provide a new clue for the energy processes associated with a thermodynamic resonator in the space magnetic plasma.


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