The role of the observers is frequently obscured in the literature, either by writing equations in a coordinate system implicitly pertaining to some specific observer or by entangling the invariance and the observer dependence of physical quantities. Using examples in relativistic kinematics and classical electrodynamics, we clarify the confusion underlying these misconceptions.

We compute the decay constants of the lowest cc-states with quantum numbers J P C = 0 −+ (η c ), 1 −− (J/ψ), and 1 +− (h c ) by using lattice QCD and QCD sum rules. We consider the coupling of J/ψ to both the vector and tensor currents. Lattice QCD results are obtained from the unquenched (N f = 2) simulations using twisted mass QCD at four lattice spacings, allowing us to take the continuum limit. On the QCD sum rule side we use the moment sum rules. The results are then used to discuss the rate of η c → γ γ decay, and to comment on the factorization in B → X cc K decays, with X cc being either η c or J/ψ.

We numerically study free expansion of a few Lieb-Liniger bosons, which are initially in the ground state of an infinitely deep hard-wall trap. Numerical calculation is carried out by employing a standard Fourier transform, as follows from the Fermi-Bose transformation for a time-dependent Lieb-Liniger gas. We study the evolution of the momentum distribution, the real-space single-particle density, and the occupancies of natural orbitals. Our numerical calculation allows us to explore the behavior of these observables in the transient regime of the expansion, where they are non-trivially affected by the particle interactions. We derive analytically (by using the stationary phase approximation) the formula which connects the asymptotic shape of the momentum distribution and the initial state. For sufficiently large times the momentum distribution coincides (up to a simple scaling transformation) with the shape of the real-space single-particle density (the expansion is asymptotically ballistic). Our analytical and numerical results are in good agreement.Comment: small changes; references correcte

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We present a derivation of an exact high temperature expansion for a one-loop thermodynamic potential ΩðμÞ with complex chemical potentialμ. The result is given in terms of a single sum, the coefficients of which are analytical functions ofμ consisting of polynomials and polygamma functions, decoupled from the physical expansion parameter βm. The analytic structure of the coefficients permits us to explicitly calculate the thermodynamic potential for the imaginary chemical potential and analytically continue the domain to the complexμ plane. Furthermore, our representation of ΩðμÞ is particularly well suited for the Landau-Ginzburg type of phase transition analysis. This fact, along with the possibility of interpreting the imaginary chemical potential as an effective generalized-statistics phase, allows us to investigate the singular origin of the m 3 term appearing only in the bosonic thermodynamic potential.