scholarly journals Causal Relations in Support of Implicit Evolution Equations

2018 ◽  
Vol 11 (3) ◽  
pp. 85-102 ◽  
Author(s):  
N. Sauer ◽  
◽  
J. Banasiak ◽  
Wha-Suck Lee ◽  
◽  
...  
Keyword(s):  
Evolution Equations ◽  
Causal Relations ◽  
Implicit Evolution Equations

scholarly journals Realistic Approach of the Relations of Uncertainty of Heisenberg

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Paul E. Sterian
Keyword(s):  
Evolution Equations ◽  
Uncertainty Relations ◽  
Theory Of Relativity ◽  
Intrinsic Nature ◽  
Nonrelativistic Case ◽  
Quantum Operators ◽  
Principle Of Causality ◽  
Generator Function ◽  
Implicit Evolution Equations ◽  
Simultaneous Measuring

Due to the requirements of the principle of causality in the theory of relativity, one cannot make a device for the simultaneous measuring of the canonical conjugate variables in the conjugate Fourier spaces. Instead of admitting that a particle’s position and its conjugate momentum cannot be accurately measured at the same time, we consider the only probabilities which can be determined when working at subatomic level to be valid. On the other hand, based on Schwinger's action principle and using the quadridimensional form of the unitary transformation generator function of the quantum operators in the paper, the general form of the evolution equation for these operators is established. In the nonrelativistic case one obtains the Heisenberg's type evolution equations which can be particularized to derive Heisenberg's uncertainty relations. The analysis of the uncertainty relations as implicit evolution equations allows us to put into evidence the intrinsic nature of the correlation expressed by these equations in straight relations with the measuring process. The independence of the quantisation postulate from the causal evolution postulate of quantum mechanics is also put into discussion.

scholarly journals A new characterization ofB-bounded semigroups with application to implicit evolution equations

2000 ◽  
Vol 5 (4) ◽  
pp. 227-244 ◽  
Author(s):  
Luisa Arlotti
Keyword(s):  
Evolution Equations ◽  
Parameter Family ◽  
Linear Operators ◽  
The One ◽  
Implicit Evolution Equations

We consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and calledB-bounded semigroups. We first determine all the properties possessed by a couple(A,B)of operators if they generate aB-bounded semigroup(Y(t))t≥0. Then we determine the simplest further property of the couple(A,B)which can assure the existence of aC0-semigroup(T(t))t≥0such that for allt≥0,f∈D(B)we can writeY(t)f=T(t)Bf. Furthermore, we compare our result with the previous ones and finally we show how our method allows to improve the theory developed by Banasiak for solving implicit evolution equations.

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