scholarly journals Test function spaces for direct product representations of the canonical commutation relations

1967 ◽  
Vol 4 (1) ◽  
pp. 22-31 ◽  
Author(s):  
L. Streit
Keyword(s):  
Direct Product ◽  
Function Spaces ◽  
Test Function ◽  
Canonical Commutation Relations ◽  
Commutation Relations

Direct-Product Representations of the Canonical Commutation Relations

1966 ◽  
Vol 7 (5) ◽  
pp. 822-828 ◽  
Author(s):  
J. R. Klauder ◽  
J. McKenna ◽  
E. J. Woods
Keyword(s):  
Direct Product ◽  
Canonical Commutation Relations ◽  
Commutation Relations

The Mehler-Fock-Clifford transform and pseudo-differential operator on function spaces

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2457-2469
Author(s):  
Akhilesh Prasad ◽  
S.K. Verma
Keyword(s):  
Differential Operator ◽  
Function Spaces ◽  
Pseudo Differential Operator ◽  
Test Function ◽  
Basic Properties ◽  
Cone Function ◽  
Translation Operators

In this article, weintroduce a new index transform associated with the cone function Pi ??-1/2 (2?x), named as Mehler-Fock-Clifford transform and study its some basic properties. Convolution and translation operators are defined and obtained their estimates under Lp(I, x-1/2 dx) norm. The test function spaces G? and F? are introduced and discussed the continuity of the differential operator and MFC-transform on these spaces. Moreover, the pseudo-differential operator (p.d.o.) involving MFC-transform is defined and studied its continuity between G? and F?.

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

scholarly journals Noisy effects in interferometric quantum gravity tests

2017 ◽  
Vol 15 (08) ◽  
pp. 1740014 ◽  
Author(s):  
F. Benatti ◽  
R. Floreanini ◽  
S. Olivares ◽  
E. Sindici
Keyword(s):  
Quantum Gravity ◽  
Weak Coupling ◽  
Scale Effects ◽  
External Environment ◽  
Planck Scale ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Photon Propagation ◽  
Gravity Theories ◽  
Planck Scale Effects

Quantum-enhanced metrology is boosting interferometer sensitivities to extraordinary levels, up to the point where table-top experiments have been proposed to measure Planck-scale effects predicted by quantum gravity theories. In setups involving multiple photon interferometers, as those for measuring the so-called holographic fluctuations, entanglement provides substantial improvements in sensitivity. Entanglement is however a fragile resource and may be endangered by decoherence phenomena. We analyze how noisy effects arising either from the weak coupling to an external environment or from the modification of the canonical commutation relations in photon propagation may affect this entanglement-enhanced gain in sensitivity.

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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