December 2012
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Day December 6, 2012

Correspondence between future-included and future-not-included theories

Keiichi Nagao, Holger Bech Nielsen

We briefly review the correspondence principle proposed in our previous paper, which claims that if we regard a matrix element defined in terms of the future state at time \(T_B\) and the past state at time \(T_A\) as an expectation value in the complex action theory whose path runs over not only past but also future, the expectation value at the present time \(t\) of a future-included theory for large \(T_B-t\) and large \(t- T_A\) corresponds to that of a future-not-included theory with a proper inner product for large \(t- T_A\). This correspondence principle suggests that the future-included theory is not excluded phenomenologically.

Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th)

Time-dependent q-deformed coherent states for generalized uncertainty relations

Sanjib Dey, Andreas Fring, Laure Gouba, Paulo G. Castro

We investigate properties of generalized time-dependent q-deformed coherent states for a noncommutative harmonic oscillator. The states are shown to satisfy a generalized version of Heisenberg’s uncertainty relations. For the initial value in time the states are demonstrated to be squeezed, i.e. the inequalities are saturated, whereas when time evolves the uncertainty product oscillates away from this value albeit still respecting the relations. For the canonical variables on a noncommutative space we verify explicitly that Ehrenfest’s theorem hold at all times. We conjecture that the model exhibits revival times to infinite order. Explicit sample computations for the fractional revival times and superrevival times are presented.
Mathematical Physics (math-ph); High Energy Physics – Theory (hep-th); Quantum Physics (quant-ph)