Search results for "Mathematical physics"

Off-forward Matrix Elements in Light-front Hamiltonian QCD

2002

We investigate the off-forward matrix element of the light cone vector operator for a dressed quark state in light-front Hamiltonian perturbation theory. We obtain the corresponding splitting functions in a straightforward way. We show that the end point singularity is canceled by the contribution from the normalization of state. Considering mixing with the gluon operator, we verify the helicity sum rule in perturbation theory. We show that the quark mass effects are suppressed in the plus component of the matrix element but in the transverse component, they are not suppressed. We emphasize that this is a particularity of the off-forward matrix element and is absent in the forward case.

Ratio of strange to non-strange quark condensates in QCD

2001

Laplace transform QCD sum rules for two-point functions related to the strangeness-changing scalar and pseudoscalar Green's functions $\psi(Q^2)$ and $\psi_5(Q^2)$, are used to determine the subtraction constants $\psi(0)$ and $\psi_5(0)$, which fix the ratio $R_{su}\equiv \frac{}{}$. Our results are $\psi(0)= - (1.06 \pm 0.21) \times 10^{-3} {GeV}^4$, $\psi_5(0)= (3.35 \pm 0.25) \times 10^{-3} {GeV}^4$, and $R_{su}\equiv \frac{}{} = 0.5 \pm 0.1$. This implies corrections to kaon-PCAC at the level of 50%, which although large, are not inconsistent with the size of the corrections to Goldberger-Treiman relations in $SU(3)\otimes SU(3)$.

Improving the kinetic couplings in lattice nonrelativistic QCD

2019

We improve the non-relativistic QCD (NRQCD) action by comparing the dispersion relation to that of the continuum through $\mathcal{O}(p^6)$ in perturbation theory. The one-loop matching coefficients of the $\mathcal{O}(p^4)$ kinetic operators are determined, as well as the scale at which to evaluate $\alpha_s$ in the $V$-scheme for each quantity. We utilise automated lattice perturbation theory using twisted boundary conditions as an infrared regulator. The one-loop radiative corrections to the mass renormalisation, zero-point energy and overall energy-shift of an NRQCD $b$-quark are also found. We also explore how a Fat$3$-smeared NRQCD action and changes of the stability parameter $n$ aff…

Practical scheme from QCD to phenomena via Dyson-Schwinger equations

2019

We deliver a new scheme to compute the quark propagator and the quark-gluon interaction vertex through the coupled Dyson-Schwinger equations (DSEs) of QCD. We take the three-gluon vertex into account in our calculations, and implement the gluon propagator and the running coupling function fitted by the solutions of their respective DSEs. We obtain the momentum and current mass dependence of the quark propagator and the quark-gluon vertex, and the chiral quark condensate which agrees with previous results excellently. We also compute the quark-photon vertex within this scheme and give the anomalous chromo- and electro-magnetic moment of quark. The obtained results also agree with previous on…

QCD generates the ϱ-resonance

1991

Abstract The question whether the asymptotic QCD amplitude contains potentially hadronic resonances is examined by a mathematically rigorous method, based on the theory of maximally converging sequences of polynomials and conformal mappings. It is shown that the extrapolated amplitude to the physical cut exhibits indeed a bump structure which corresponds to the ϱ-resonance.

Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states

2006

We present a novel, detailed study on the usefulness of three-mode Gaussian states states for realistic processing of continuous-variable quantum information, with a particular emphasis on the possibilities opened up by their genuine tripartite entanglement. We describe practical schemes to engineer several classes of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\em arbitrary} entanglement structure (upon availability of an initial two-mode squeezed state). We analyze in depth the properties of dist…

Multipartite entanglement in three-mode Gaussian states of continuous variable systems: Quantification, sharing structure and decoherence

2005

We present a complete analysis of multipartite entanglement of three-mode Gaussian states of continuous variable systems. We derive standard forms which characterize the covariance matrix of pure and mixed three-mode Gaussian states up to local unitary operations, showing that the local entropies of pure Gaussian states are bound to fulfill a relationship which is stricter than the general Araki-Lieb inequality. Quantum correlations will be quantified by a proper convex roof extension of the squared logarithmic negativity (the contangle), satisfying a monogamy relation for multimode Gaussian states, whose proof will be reviewed and elucidated. The residual contangle, emerging from the monog…

Non-Markovianity of Gaussian Channels

2015

We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated to arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.

Path Integrals in Noncommutative Geometry

2006

Non-Equilibrium Thermodynamics of Unsteady Superfluid Turbulence in Counterflow and Rotating Situations

2005

The methods of nonequilibrium thermodynamics are used in this paper to relate an evolution equation for the vortex line density $L$, describing superfluid turbulence in the simultaneous presence of counterflow and rotation, to an evolution equation for the superfluid velocity ${\mathbf{v}}_{s}$, in order to be able to describe the full evolution of ${\mathbf{v}}_{s}$ and $L$, instead of only $L$. Two alternative possibilities are analyzed, related to two possible alternative interpretations of a term coupling the effects of the counterflow and rotation on the vortex tangle, and which imply some differences between situations where counterflow and rotation vectors are parallel or orthogonal …