相关论文: [p,q] does not equal (i h-bar)

In this letter, the (q,h)-analogue of Newton's binomial formula is obtained in the (q,h)-deformed quantum plane which reduces for h=0 to the q-analogue. For (q=1,h=0), this is just the usual one as it should be. Moreover, the h-analogue is…

Dirac's hole theory and quantum field theory are usually considered equivalent to each other. For models of a certain type, however, the equivalence may not hold as we discuss in this Letter. This problem is closely related to the validity…

With an explicit example, we show that Jordan frame and the conformally transformed Einstein frames clearly lead to different physics for a non-minimally coupled theory of gravity, namely Brans-Dicke theory, at least at the quantum level.…

Dirac's hole theory and quantum field theory are generally considered to be equivalent to each other. However, it has recently been shown that this is not necessarily the case. In this article we will discuss the reason for this lack of…

The Gibbs paradox has frequently been interpreted as a sign that particles of the same kind are fundamentally indistinguishable; and that quantum mechanics, with its identical fermions and bosons, is indispensable for making sense of this.…

The suggestion that particles of the same kind may be indistinguishable in a fundamental sense, even so that challenges to traditional notions of individuality and identity may arise, has first come up in the context of classical…

It is shown that the Jordan frame and its conformally transformed version, the Einstein frame of nonminimally coupled theories of gravity, are actually equivalent at the quantum level. The example of the theory taken up is the Brans-Dicke…

This paper is devoted to the study of fractional (q,p)-Sobolev-Poincare inequalities in irregular domains. In particular, we establish (essentially) sharp fractional (q,p)-Sobolev-Poincare inequality in s-John domains and in domains…

The EPR paradox and the meaning of the Bell inequality are discussed. It is shown that considering the quantum objects as carrying with them ''instruction kits'' telling them what to do when meeting a measurement apparatus any paradox…

We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…

Quantum theory revolutionised physics by introducing a new fundamental constant and a new mathematical framework to describe the observed phenomena at the atomic scale. These new concepts run counter to our familiar notions of classical…

Let $\mathbb K$ be a field and suppose $p, q\in\mathbb K^*$ are not roots of unity. We prove that the two quantum groups $U_q(\mathfrak {sl}_{n+1})$ and $U_p(\mathfrak{sl}_{n+1})$ are isomorphic as $\mathbb K$-algebras implies that $p=\pm…

We analyze the experiment recently realized by S. Afshar et al. [1] in order to refute the principle of complementarity. We discuss the general meaning of this principle and show that contrarily to the claim of the authors Bohr's…

A new interpretation offers a consistent conceptual basis for nonrelativistic quantum mechanics. The Einstein-Podolsky-Rosen (EPR) paradox is solved and the violation of Bell's inequality is explained by maintaining realism, inductive…

We show that fractional (p,p)-Poincar\'e inequalities and even fractional Sobolev-Poincar\'e inequalities hold for bounded John domains, and especially for bounded Lipschitz domains. We also prove sharp fractional (1,p)-Poincar\'e…

In this paper, we define k-equivalence, a relation on graphs that relies on their associated cellular algebras. We show that a k-Boson quantum walk cannot distinguish pairs of graphs that are k- equivalent. The existence of pairs of…

In 2008 Br\"and\'en proved a $(p,q)$-analogue of the $\gamma$-expansion formula for Eulerian polynomials and conjectured the divisibility of the $\gamma$-coefficient $\gamma_{n,k}(p,q)$ by $(p+q)^k$. As a follow-up, in 2012 Shin and Zeng…

Dirac's hole theory and quantum field theory are generally thought to be equivalent. In fact field theory can be derived from hole theory through the process of second quantization. However, it can be shown that problems worked in both…

Integral representations of two $q$-difference operators are provided in terms of special functions arising in the theory of asymptotic solutions to $q$-difference equations in the complex domain. Both representations are unified through…

In this paper, we first present simple proofs of Choi's results [4], then we give a short alternative proof for Fiedler and Markham's inequality [6]. We also obtain additional matrix inequalities related to partial determinants.