Related papers: The negative q-binomial
The measurement conundrum seems to have plagued quantum mechanics for so long that impressions of an inconsistency amongst its axioms have spawned. A demonstration that such purported inconsistency is fictitious may then be in order and is…
The $q$-analogue of an integer $m$ is given by $[m]_q=(1-q^m)/(1-q)$. Let $a$ be an integer, and let $n$ be a positive odd integer. Via discrete Fourier transforms, we establish the following two identities:…
The straightforward description of q-deformed systems leads to transition amplitudes that are not numerically valued. To give physical meaning to these expressions without introducing {\it ad hoc} remedies, one may exploit an "internal"…
The classical limit of quantum q-oscillators suggests an interpretation of the deformation as a way to introduce non linearity. Guided by this idea, we considered q-fields, the partition fumction, and compute a consequence on specific heat…
Let $\lambda =\left( \lambda_{1},\lambda_{2},...,\lambda_{r}\right) $ be an integer partition, and $\left[p_{\lambda }\right] $ the $q$-analog of the symmetric power function $%p_{\lambda }$. This $q$-analogue has been defined as a special…
An equivalent formulation of the Riemann hypothesis is given. The physical interpretation of the Riemann hypothesis equivalent formulation is given in the framework of quantum theory terminology. One more power series related to the Riemann…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
We discuss the transactional interpretation of quantum mechanics, apply it to several counter-intuitive quantum optics experiments (two-slit, quantum eraser, trapped atom, ...) and describe a mathematical model that shows how transactions…
It is generally known that the energy density can be negative in quantum field theory. It is also believed that there are limits on this negative energy density. These limits are known as the quantum inequalities. In a recent paper [8] an…
Many widely different problems have a common mathematical structure wherein limited knowledge lead to ambiguity that can be captured conveniently using a concept of invisibility that requires the introduction of negative values for…
Let F be a finite extension of Q_p. We show that every Schwartz function on F, with values in an algebraic closure of Q_p, is the uniform limit of a sequence of Schwartz functions, whose Fourier transforms tend uniformly to 0. The proof…
In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.
The q-binomial coefficients were assumed to be unimodal as early as the 1850's, but it remained unproven until Sylvester's 1878 proof using invariant theory. In 1982, Proctor gave an "elementary" proof using linear algebra. Finally, in…
The fractional q-calculus is the q-extension of the ordinary fractional calculus and dates back to early 20-th century. The theory of q-calculus operators are used in various areas of science such as ordinary fractional calculus, optimal…
The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…
Negative probabilities have long been discussed in connection with the foundations of quantum mechanics. We have recently shown that, if signed measures are allowed on the hidden variables, the class of probability models which can be…
In this paper, we gave some properties of binomial coefficient.
We study examples where conformal invariance implies triviality of the underlying quantum field theory.
In this work an observation concerning a positivity property of the quantum anharmonic oscillator is made. This positivity property is suggested by the BMV conjecture.
In the space of bounded real-valued functions on the interval $(0,1)$, we study the convergent sequences of $q$-analogues of multiple zeta values which do not converge to $0$. And we obtain the derived sets of the set of some $q$-analogue…