The Master Ward Identity

In the framework of perturbative quantum field theory (QFT) we propose a new, universal (re)normalization condition (called 'master Ward identity') which expresses the symmetries of the underlying classical theory. It implies for example the field equations, energy-momentum, charge- and ghost-number conservation, renormalized equal-time commutation relations and BRST-symmetry. It seems that the master Ward identity can nearly always be satisfied, the only exceptions we know are the usual anomalies. We prove the compatibility of the master Ward identity with the other (re)normalization conditions of causal perturbation theory, and for pure massive theories we show that the 'central solution' of Epstein and Glaser fulfills the master Ward identity, if the UV-scaling behavior of its individual terms is not relatively lowered. Application of the master Ward identity to the BRST-current of non-Abelian gauge theories generates an identity (called 'master BRST-identity') which contains the information which is needed for a local construction of the algebra of observables, i.e. the elimination of the unphysical fields and the construction of physical states in the presence of an adiabatically switched off interaction.Comment: 73 pages, version to appear in Rev. Math. Phy

Effective polar potential in the central force Schrodinger equation

The angular part of the Schrodinger equation for a central potential is brought to the one-dimensional 'Schrodinger form' where one has a kinetic energy plus potential energy terms. The resulting polar potential is seen to be a family of potentials characterized by the square of the magnetic quantum number m. It is demonstrated that this potential can be viewed as a confining potential that attempts to confine the particle to the xy-plane, with a strength that increases with increasing m. Linking the solutions of the equation to the conventional solutions of the angular equation, i.e. the associated Legendre functions, we show that the variation in the spatial distribution of the latter for different values of the orbital angular quantum number l can be viewed as being a result of 'squeezing' with different strengths by the introduced 'polar potential'.Comment: This is an author-created, un-copyedited version of an article accepted for publication in European Journal of Physic

Current and Future White Dwarf Mass-radius Constraints on Varying Fundamental Couplings and Unification Scenarios

We discuss the feasibility of using astrophysical observations of white dwarfs as probes of fundamental physics. We quantify the effects of varying fundamental couplings on the white dwarf mass-radius relation in a broad class of unification scenarios, both for the simple case of a polytropic stellar structure model and for more general models. Independent measurements of the mass and radius, together with direct spectroscopic measurements of the fine-structure constant in white dwarf atmospheres lead to constraints on combinations of the two phenomenological parameters describing the underlying unification scenario (one of which is related to the strong sector of the theory while the other is related to the electroweak sector). While currently available measurements do not yet provide stringent constraints, we show that forthcoming improvements, expected for example from the Gaia satellite, can break parameter degeneracies and lead to constraints that ideally complement those obtained from local laboratory tests using atomic clocks.Comment: 11 pages, 8 figure

Honey volatiles as a fingerprint for botanical origin: a review on their occurrence on monofloral honeys

Honeys have specific organoleptic characteristics, with nutritional and health benefits, being highly appreciated by consumers, not only in food but also in the pharmaceutical and cosmetic industries. Honey composition varies between regions according to the surrounding flora, enabling its characterization by source or type. Monofloral honeys may reach higher market values than multifloral ones. Honey's aroma is very specific, resulting from the combination of volatile compounds present in low concentrations. The authentication of honey's complex matrix, according to its botanical and/or geographical origin, represents a challenge nowadays, due to the different sorts of adulteration that may occur, leading to the search for reliable marker compounds for the different monofloral honeys. The existing information on the volatiles of monofloral honeys is scarce and disperse. In this review, twenty monofloral honeys and honeydews, from acacia, buckwheat, chestnut, clover, cotton, dandelion, eucalyptus, fir tree, heather, lavender, lime tree, orange, pine, rape, raspberry, rhododendron, rosemary, strawberry tree, sunflower and thyme, were selected for volatile comparison purposes. Taking into consideration the country of origin, the technique of isolation and analysis, the five main volatiles from each of the honeys are compared. Whereas some compounds were found in several types of monofloral honey, and thus not considered good volatile markers, some monofloral honeys revealed characteristic volatile compounds independently of their provenance.Funding: SFRH/BD/117013/2016, UID/AGR/00690/2019, UID/AMB/50017/2019, MED (UIDB/05183/2020), FEDER, PT2020 PACompete 2020info:eu-repo/semantics/publishedVersio

Absence of reflection as a function of the coupling constant

We consider solutions of the one-dimensional equation $-u'' +(Q+ \lambda V) u = 0$ where $Q: \mathbb{R} \to \mathbb{R}$ is locally integrable, $V : \mathbb{R} \to \mathbb{R}$ is integrable with supp$(V) \subset [0,1]$, and $\lambda \in \mathbb{R}$ is a coupling constant. Given a family of solutions $\{u_{\lambda} \}_{\lambda \in \mathbb{R}}$ which satisfy $u_{\lambda}(x) = u_0(x)$ for all $x<0$, we prove that the zeros of $b(\lambda) := W[u_0, u_{\lambda}]$, the Wronskian of $u_0$ and $u_{\lambda}$, form a discrete set unless $V \equiv 0$. Setting $Q(x) := -E$, one sees that a particular consequence of this result may be stated as: if the fixed energy scattering experiment $-u'' + \lambda V u = Eu$ gives rise to a reflection coefficient which vanishes on a set of couplings with an accumulation point, then $V \equiv 0$.Comment: To appear in Journal of Mathematical Physic