Generalized Commutation Relations for Single Mode Oscillator

秀司 渡邉

David G. Boulware, S. Deser

S. Chaturvedi, Ashok Kumar Kapoor, R. Sandhya +2 more

A generalized commutation relation of a single-mode oscillator is proposed. Bose-Einstein, Fermi-Dirac, and Greenberg's infinite statistics are shown to be special cases of this commutation relation. The Fock states, coherent states, and analogs of squeezed coherent states for this commutation relation are constructed. Finally, the quantization of a free infinite-statistics field is discussed using the Umezawa-Takahashi procedure [H. Umezawa and Y. Takahashi, Prog. Theor. Phys. 9, 14 (1953); Nucl. Phys. 51, 193 (1964)].

Bruno J. Gruber, Lochlainn O'Raifeartaigh

M. KRISHNA KUMARI, P. Shanta, S. Chaturvedi +1 more

Three generalized commutation relations for a single mode of the harmonic oscillator which contains para-bose and q oscillator commutation relations are constructed. These are shown to be inequivalent. The coherent states of the annihilation operator for these three cases are also constructed.

Hadrien Chevalier, Hyukjoon Kwon, Kiran E. Khosla +2 more

Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work, we inspect the capacity for correlated many-body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a nonstandard phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators.