scholarly journals Quantum generalized Heisenberg algebras and their representations

2021 ◽  
pp. 1-21
Author(s):  
Samuel A. Lopes ◽  
Farrokh Razavinia
Keyword(s):  
Heisenberg Algebras

scholarly journals Clifford Algebras and Their Decomposition into Conjugate Fermionic Heisenberg Algebras

2016 ◽  
Vol 766 ◽  
pp. 012001
Author(s):  
Sultan Catto ◽  
Yasemin Gürcan ◽  
Amish Khalfan ◽  
Levent Kurt ◽  
V. Kato La
Keyword(s):  
Clifford Algebras ◽  
Heisenberg Algebras

scholarly journals KAPPA-MINKOWSKI SPACETIME, KAPPA-POINCARÉ HOPF ALGEBRA AND REALIZATIONS

2012 ◽  
Vol 09 (06) ◽  
pp. 1261009 ◽  
Author(s):  
DOMAGOJ KOVAČEVIĆ ◽  
STJEPAN MELJANAC
Keyword(s):  
Hopf Algebra ◽  
Star Product ◽  
Minkowski Spacetime ◽  
Inner Product ◽  
Translation Invariance ◽  
Dual Algebra ◽  
Lorentz Algebra ◽  
Heisenberg Algebras ◽  
The Matrix ◽  
Poincaré Algebra

The κ-Minkowski spacetime and Lorentz algebra are unified in unique Lie algebra. Introducing commutative momenta, a family of κ-deformed Heisenberg algebras and κ-deformed Poincaré algebras are defined. They are determined by the matrix depending on momenta. Realizations and star product are defined and analyzed in general. The relation among the coproduct of momenta, realization and the star product is pointed out. Hopf algebra of the Poincaré algebra, related to the covariant realization, is presented in unified covariant form. Left–right dual realizations and dual algebra are introduced and considered. The generalized involution and the star inner product are defined and analyzed. Partial integration and deformed trace property are obtained in general. The translation invariance of the star product is pointed out.

Polynomial Heisenberg algebras

2004 ◽  
Vol 37 (43) ◽  
pp. 10349-10362 ◽  
Author(s):  
Juan M Carballo ◽  
David J Fernández C ◽  
Javier Negro ◽  
Luis M Nieto
Keyword(s):  
Heisenberg Algebras

scholarly journals POSSIBLE POLARIZATION AND SPIN-DEPENDENT ASPECTS OF QUANTUM GRAVITY

2008 ◽  
Vol 17 (03n04) ◽  
pp. 495-504 ◽  
Author(s):  
D. V. AHLUWALIA ◽  
N. G. GRESNIGT ◽  
ALEX B. NIELSEN ◽  
D. SCHRITT ◽  
T. F. WATSON
Keyword(s):  
Quantum Gravity ◽  
Structure Formation ◽  
Spin Dependence ◽  
Strong Polarization ◽  
Heisenberg Algebras ◽  
Gravity Effects ◽  
Gravity Theories

We argue that quantum gravity theories that carry a Lie-algebraic modification of the Poincaré and Heisenberg algebras inevitably provide inhomogeneities that may serve as seeds for cosmological structure formation. Furthermore, in this class of theories one must expect a strong polarization and spin dependence of various quantum gravity effects.

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