Related papers: q \bar q-potential
We describe the generators and prove a number of relations for the construction of a planar algebra from the restricted quantum group $\bar{U}_{q}(\mathfrak{sl}_{2})$. This is a diagrammatic description of…
We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. We show that the birational type of the graph potential only depends on the homotopy type of the colored graph, and use this to define a…
By encoding a qudit in a harmonic oscillator and investigating the d --> infinity limit, we give an entirely new realization of continuous-variable quantum computation. The generalized Pauli group is generated by number and phase operators…
In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This "BB" system is an attractive theoretical laboratory for the…
Let Q be a non-singular quadratic form with integer coefficients. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q=0. When Q is positive definite we provide improved upper bounds…
Starting from the observation that colour charge is only well defined on gauge invariant states, we construct perturbatively gauge invariant, dynamical dressings for individual quarks. Explicit calculations show that an infra-red finite…
Let $\mathbb{F}_q[t]$ denote the ring of polynomials over $\mathbb{F}_q$, the finite field of $q$ elements. We prove an estimate for fractional parts of polynomials over $\mathbb{F}_q[t]$ satisfying a certain divisibility condition…
A factor-graph representation of quantum-mechanical probabilities (involving any number of measurements) is proposed. Unlike standard statistical models, the proposed representation uses auxiliary variables (state variables) that are not…
We present results for tetraquark potentials of two static anti-quarks $\bar b \bar b$ in the presence of two light quarks $u$ and/or $d$. We improve on existing results by computing the static potential also for off-axis separations, which…
The energy spectrum of q-deformed Schr\"odinger equation is demonstrated. This spectrum includes an exponential factor with new quantum numbers--the $q$-exciting number and the scaling index. The pattern of quark and lepton masses is…
The first lattice QCD numerical study of heavy quark-quark potentials at finite temperature is reported. Using the quenched approximation, we evaluate the color anti-symmetric and symmetric potentials.
In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. It is illustrated through the particular cases of the harmonic oscillator and the Coulomb potential. In this kind of system the…
It is shown that there is an absolute constant $C$ such that any rational $\frac bq\in]0, 1[, (b, q)=1$, admits a representation as a finite sum $\frac bq=\sum_\alpha\frac {b_\alpha}{q_\alpha}$ where $\sum_\alpha\sum_ia_i(\frac…
We gather material from many sources about the quantum potential and its geometric nature. The presentation is primarily expository but some new observations relating Q, V, and psi are indicated.
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
The spectra of some 0++ four-quark states, which are composed of \bar qq pairs, are calculated in QCD. The light four-quark states are calculated using the traditional sum rules while four-quark states containing one heavy quark are…
We examine combinatorial counting functions with two parameters, $n$ and $q$. For fixed $q$, these functions are (quasi-)polynomial in $n$. As $q$ varies, the degree of this polynomial is itself polynomial in $q$, as are the leading…
We perform a study of various anharmonic potentials using a recently developed method. We calculate both the wave functions and the energy eigenvalues for the ground and first excited states of the quartic, sextic and octic potentials with…
We propose a string theory construction for the system of two heavy quarks and two light antiquarks. The potential of the system is a function of separation between the quarks. We define a critical separation distance below which the system…
A monic polynomial in F_q[t] of degree n over a finite field F_q of odd characteristic can be written as the sum of two irreducible monic elements in F_q[t] of degrees n and n-1 if q is larger than a bound depending only on n. The main tool…