Implementation problem for the canonical commutation relation in terms of quantum white noise derivatives

2010 ◽  
Vol 51 (12) ◽  
pp. 123507 ◽  
Author(s):  
Un Cig Ji ◽  
Nobuaki Obata
Keyword(s):  
White Noise ◽  
Commutation Relation ◽  
Canonical Commutation Relation ◽  
Implementation Problem

scholarly journals Deformation of the Wheeler–DeWitt equation

2014 ◽  
Vol 29 (20) ◽  
pp. 1450106 ◽  
Author(s):  
Mir Faizal
Keyword(s):  
Commutation Relation ◽  
Canonical Commutation Relation ◽  
Big Bang ◽  
Minimum Length ◽  
Second Quantization ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
The Big Bang ◽  
Big Bang Singularity ◽  
Modified Theory

In this paper, we will analyze the consequences of deforming the canonical commutation relations consistent with the existence of a minimum length and a maximum momentum. We first generalize the deformation of first quantized canonical commutation relation to second quantized canonical commutation relation. Thus, we arrive at a modified version of second quantization. A modified Wheeler–DeWitt equation will be constructed by using this deformed second quantized canonical commutation relation. Finally, we demonstrate that in this modified theory the big bang singularity gets naturally avoided.

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