Inequivalent Representations of Canonical Commutation and Anti-Commutation Relations

2020 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Commutation Relations ◽  
Inequivalent Representations

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.

HAPPER'S CURIOUS DEGENERACIES AND YANGIAN

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1867-1873 ◽  
Author(s):  
CHENG-MING BAI ◽  
MO-LIN GE ◽  
KANG XUE
Keyword(s):  
Representation Theory ◽  
Algebraic Structure ◽  
Zeeman Effect ◽  
Tensor Space ◽  
Commutation Relations ◽  
Raising And Lowering Operators ◽  
Degenerate States ◽  
Lowering Operators

We find raising and lowering operators distinguishing the degenerate states for the Hamiltonian [Formula: see text] at x = ± 1 for spin 1 that was given by Happer et al.1,2 to interpret the curious degeneracies of the Zeeman effect for condensed vapor of 87 Rb . The operators obey Yangian commutation relations. We show that the curious degeneracies seem to verify the Yangian algebraic structure for quantum tensor space and are consistent with the representation theory of Y(sl(2)).

Some consequences of the isospin commutation relations for isovector form factors

1964 ◽  
Vol 29 (2) ◽  
pp. 161-174 ◽  
Author(s):  
Wolfgang Kummer ◽  
Herbert Pietschmann ◽  
A.P Balachandran
Keyword(s):  
Form Factors ◽  
Commutation Relations
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