The fate of Galilean relativity in minimal-length theories

A number of arguments at the interplay of general relativity and quantum theory suggest an operational limit to spatial resolution, conventionally modelled as a generalized uncertainty principle (GUP). Recently, it has been demonstrated that the dynamics postulated as a part of these models are only loosely related to the existence of the minimal-length scale. In this paper, we intend to make a more informed choice on the Hamiltonian by demanding, among other properties, that the model be invariant under (possibly) deformed Galilean transformations in one dimension. In this vein, we study a two-particle system with general interaction potential under the condition that the composition as well as the action of Galilean boosts on wave numbers be deformed so as to comply with the cut-off. We find that the customary GUP-Hamiltonian does not allow for invariance under (any kind of) generalised Galilean transformations. Those Hamiltonians which allow for a deformed relativity principle have to be related to the ordinary Galilean ones by virtue of a momentum-space diffeomorphism, i.e. a canonical transformation. Far from being trivial, the resulting dynamics is deformed, as we show at the example of the harmonic interaction.Comment: 21 pages, 2 figures, 1 appendi

Phenomenology of DSR-relativistic in-vacuo dispersion in FLRW spacetime

Studies of in-vacuo dispersion are the most active area of quantum-gravity phenomenology. The way in which in-vacuo dispersion produces redshift-dependent corrections to the time of flight of astrophysics particles depends on the model-dependent interplay between Planck-scale effects and spacetime curvature/expansion, and we here derive the most general formula for the leading order redshift-dependent correction to the time of flight for the scenario in which relativistic symmetries are deformed at the Planck scale (DSR). We find that, contrary to the broken symmetries scenario (LIV), where in principle any arbitrary form of redshift dependence could be allowed, for the DSR scenario only linear combinations of three possible forms of redshift dependence are allowed. We also discuss some specific combinations of these three terms whose investigation might deserve priority from the quantum-gravity perspective

Quantum Euler angles and agency-dependent spacetime

Quantum gravity is expected to introduce quantum aspects into the description of reference frames. Here we set the stage for exploring how quantum gravity induced deformations of classical symmetries could modify the transformation laws among reference frames in an effective regime. We invoke the quantum group $SU_q(2)$ as a description of deformed spatial rotations and interpret states of a representation of its algebra as describing the relative orientation between two reference frames. This leads to a quantization of one of the Euler angles and to the new paradigm of agency-dependence: space is reconstructed as a collection of fuzzy points, exclusive to each agent, which depends on their choice of reference frame. Each agent can choose only one direction in which points can be sharp, while points in all other directions become fuzzy in a way that depends on this choice. Two agents making different choices will thus observe the same points with different degrees of fuzziness.Comment: 9 pages, 3 figures, 4 appendice

Standard model anomalies: Lepton flavour non-universality and lepton g-2

We critically analyze the body of results that hints to the existence of New Physics from possible violations of lepton universality observed by the LHCb experiment in the $\mu/e$ ratios $R_{K}$ and $R_{K^*}$ to the $g-2$ lepton anomalies. The analysis begins with a theoretical, in depth, study of the $\mu/e$ ratios $R_{K}$ and $R_{K^*}$ as well as the process $B_s \rightarrow \mu^+ \mu^-$. Here we consider the impact of complex Wilson coefficients and derive constraints on their imaginary and real parts. We then move to a comprehensive comparison with experimental results. We show that, by fitting a single Wilson coefficient, the deviations from the Standard Model are at the $4.7\sigma$ level when including only the hadronic insensitive observables while it increases to $6.1\sigma$ when including also the hadronic sensitive ones. When switching on all relevant Wilson coefficients and combining both hadronic sensitive and insensitive data into the fit, the deviation from the Standard Model peaks at 7.2$\sigma$ and decreases at the $4.9\sigma$ level if we assume that the central values of $R_K$ and $R_K^{\ast}$ are taken to be unity. We further estimate the non-perturbative long distance hadronic contributions and show that their inclusion still requires New Physics to fit the data. We then introduce the $g-2$ lepton anomalies results. Different theoretical models are considered that can explain the discrepancies from the Standard Model. In the final part of our work we estimate the impact of the forthcoming data from LHCb (coming from LHC Run3) and Belle II, when it will have accumulated about $5~ab^{-1}$

Entanglement entropy in conformal quantum mechanics

Abstract We consider sets of states in conformal quantum mechanics associated to generators of time evolution whose orbits cover different regions of the time domain. States labelled by a continuous global time variable define the two-point correlation functions of the theory seen as a one-dimensional conformal field theory. Such states exhibit the structure of a thermofield double built on bipartite eigenstates of generators of non-global time evolution. In terms of the correspondence between radial conformal symmetries in Minkowski space-time and time evolution in conformal quantum mechanics proposed in [1, 2] these generators coincide with conformal Killing vectors tangent to worldlines of Milne and diamond observers at constant radius. The temperature of the thermofield double states in conformal quantum mechanics reproduces the temperatures perceived by such diamond and Milne observers. We calculate the entanglement entropy associated to the thermofield double states and obtain a UV divergent logarithmic behaviour analogous to known results in two-dimensional conformal field theory in which the entangling boundary is point-like

Standard model anomalies: lepton flavour non-universality, g − 2 and W-mass

International audienceWe critically analyze the body of results that hints to the existence of New Physics from possible violations of lepton universality observed by the LHCb experiment in the μ/e ratios R$_{K}$ and ${R}_{K^{\ast }}$ to the g − 2 lepton anomalies. The analysis begins with a theoretical, in depth, study of the μ/e ratios R$_{K}$ and ${R}_{K^{\ast }}$ as well as the process B$_{s}$→ μ$^{+}$μ$^{−}$. Here we consider the impact of complex Wilson coefficients and derive constraints on their imaginary and real parts. We then move to a comprehensive comparison with experimental results. We show that, by fitting a single Wilson coefficient, the deviations from the Standard Model are at the 4.7σ level when including only the hadronic insensitive observables while it increases to 6.1σ when including also the hadronic sensitive ones. When switching on all relevant Wilson coefficients and combining both hadronic sensitive and insensitive data into the fit, the deviation from the Standard Model peaks at 7.2σ and decreases at the 4.9σ level if we assume that the central values of R$_{K}$ and ${R}_K^{\ast }$ are taken to be unity. We further estimate other unaccounted for SM contributions and show that their inclusion still requires New Physics to fit the data. We then introduce the g − 2 lepton anomalies as well as the most recent W-mass results. Different theoretical models are considered that can explain the discrepancies from the Standard Model. In the final part of our work we estimate the impact of the forthcoming data from LHCb (coming from LHC Run3) and Belle II, when it will have accumulated about 5 ab$^{−1}$