An Innovative Face Emotion Recognition-based Platform by using a Mobile Device as a Virtual Tour

Emotions are the base of human evolution. They help us to survive and to face up all problems of our life. Without emotions human evolution was not possible and we would be in caves. Nowadays, emotions are a very important aspect in different field not only in psychology. They are very important to understand human mind and decision-making process.Emotional tourism is an example of a new way to use emotions analysis. In this field emotions are used to create a most deep experience from the begin of a travel to each steps of the journey. They help tourism to make traveler the protagonist of his travel and not just a spectator.In this paper, we are going to show an app which predicts a travel destination based on user’s mood and facial expressions to specifics visual and auditory trigger to encounter his reactions. This app uses different technology linked together to make this solution versatile and dynamic. It implements different technology modules to perform facial and mood analysis, capturing the image, store image and show all trigger to the user. By adopting this solution is possible to easily upgrade the app and each module can be changed with no large problem adapting it to the current version of the app

Integrating out beyond tree level and relativistic superfluids

We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a more involved procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). As a concrete example, we study the $U(1)$ Goldstone low-energy effective theory that describes the spontaneously broken phase of a $\phi^4$ theory for a complex scalar. Working to lowest order in the derivative expansion, but to all orders in the Goldstones, we integrate out the radial mode at one loop and express the low-energy effective action in terms of the renormalized couplings of the UV completion. This yields the one-loop equation of state for the superfluid phase of (complex) $\phi^4$. We perform the same analysis for a renormalizable scalar $SO(N)$ theory at finite chemical potential, integrating out the gapped Goldstones as well, and confirm that the effective theory for the gapless Goldstone exhibits no obvious sign of the original $SO(N)$ symmetry.Comment: 25 page

An analytic approach to quasinormal modes for coupled linear systems

Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled linear differential equations of second order. We first show, under general assumptions, that such a system can be brought to a Schr\"odinger-like form. We then devise an analytic approximation scheme to compute the spectrum of quasinormal modes. We validate our approach using a toy model with a controllable mixing parameter $\varepsilon$ and showing that the analytic approximation for the fundamental mode agrees with the numerical computation when the approximation is justified. The accuracy of the analytic approximation is at the (sub-) percent level for the real part and at the level of a few percent for the imaginary part, even when $\varepsilon$ is of order one. Our approximation scheme can be seen as an extension of the approach of Schutz and Will to the case of coupled systems of equations, although our approach is not phrased in terms of a WKB analysis, and offers a new viewpoint even in the case of a single equation.Comment: 30 page

Fermions at finite density in the path integral approach

International audienceWe study relativistic fermionic systems in $3+1$ spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the $i\varepsilon$ term that projects on the finite density ground state, and compute the path integral analytically for free fermions in homogeneous external backgrounds, using complex analysis techniques. As an application, we show that the ${\rm U}(1)$ symmetry is always linearly realized for free fermions at finite charge density, differently from scalars. We study various aspects of finite density QED in a homogeneous magnetic background. We compute the free energy density, non-perturbatively in the electromagnetic coupling and the external magnetic field, obtaining the finite density generalization of classic results of Euler--Heisenberg and Schwinger. We also obtain analytically the magnetic susceptibility of a relativistic Fermi gas at finite density, reproducing the de Haas--van Alphen effect. Finally, we consider a (generalized) Gross--Neveu model for $N$ interacting fermions at finite density. We compute its non-perturbative effective potential in the large-$N$ limit, and discuss the fate of the ${\rm U}(1)$ vector and $\mathbb{Z}_2^A$ axial symmetries

Fermions at finite density in the path integral approach

International audienceWe study relativistic fermionic systems in $3+1$ spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the $i\varepsilon$ term that projects on the finite density ground state, and compute the path integral analytically for free fermions in homogeneous external backgrounds, using complex analysis techniques. As an application, we show that the ${\rm U}(1)$ symmetry is always linearly realized for free fermions at finite charge density, differently from scalars. We study various aspects of finite density QED in a homogeneous magnetic background. We compute the free energy density, non-perturbatively in the electromagnetic coupling and the external magnetic field, obtaining the finite density generalization of classic results of Euler--Heisenberg and Schwinger. We also obtain analytically the magnetic susceptibility of a relativistic Fermi gas at finite density, reproducing the de Haas--van Alphen effect. Finally, we consider a (generalized) Gross--Neveu model for $N$ interacting fermions at finite density. We compute its non-perturbative effective potential in the large-$N$ limit, and discuss the fate of the ${\rm U}(1)$ vector and $\mathbb{Z}_2^A$ axial symmetries

Fermions at finite density in the path integral approach

International audienceWe study relativistic fermionic systems in $3+1$ spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the $i\varepsilon$ term that projects on the finite density ground state, and compute the path integral analytically for free fermions in homogeneous external backgrounds, using complex analysis techniques. As an application, we show that the ${\rm U}(1)$ symmetry is always linearly realized for free fermions at finite charge density, differently from scalars. We study various aspects of finite density QED in a homogeneous magnetic background. We compute the free energy density, non-perturbatively in the electromagnetic coupling and the external magnetic field, obtaining the finite density generalization of classic results of Euler--Heisenberg and Schwinger. We also obtain analytically the magnetic susceptibility of a relativistic Fermi gas at finite density, reproducing the de Haas--van Alphen effect. Finally, we consider a (generalized) Gross--Neveu model for $N$ interacting fermions at finite density. We compute its non-perturbative effective potential in the large-$N$ limit, and discuss the fate of the ${\rm U}(1)$ vector and $\mathbb{Z}_2^A$ axial symmetries

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

Abstract We consider U(1)-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in d > 2 spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of μ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an O(N) theory with quartic interactions in d = 3 and 4, at leading order in the 1/N expansion. We derive these results by computing analytically the zero-temperature, finite-μ one-loop effective potential, paying special attention to subtle points related to the iε terms. We check our results against the one-loop low-energy effective action for the superfluid phonons in λϕ 4 theory in d = 4 previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-n operator for the λϕ 6 conformal superfluid in d = 3, at leading order in 1/n, reproducing a numerical result of Badel et al. For a λϕ 4 superfluid in d = 4, we also reproduce the Lee-Huang-Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

International audienceWe consider ${\rm U}(1)$-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in $d>2$ spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of $\mu$ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an ${\rm O}(N)$ theory with quartic interactions in $d=3$ and $4$, at leading order in the $1/N$ expansion. We derive these results by computing analytically the zero-temperature, finite-$\mu$ one-loop effective potential. We check our results against the one-loop low-energy effective action for the superfluid phonons in $\lambda \phi^4$ theory in $d=4$ previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-$n$ operator for the $\lambda \phi^6$ conformal superfluid in $d=3$, at leading order in $1/n$, reproducing a numerical result of Badel et al. For a $\lambda \phi^4$ superfluid in $d=4$, we also reproduce the Lee--Huang--Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

International audienceWe consider ${\rm U}(1)$-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in $d>2$ spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of $\mu$ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an ${\rm O}(N)$ theory with quartic interactions in $d=3$ and $4$, at leading order in the $1/N$ expansion. We derive these results by computing analytically the zero-temperature, finite-$\mu$ one-loop effective potential. We check our results against the one-loop low-energy effective action for the superfluid phonons in $\lambda \phi^4$ theory in $d=4$ previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-$n$ operator for the $\lambda \phi^6$ conformal superfluid in $d=3$, at leading order in $1/n$, reproducing a numerical result of Badel et al. For a $\lambda \phi^4$ superfluid in $d=4$, we also reproduce the Lee--Huang--Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory

The connection between nonzero density and spontaneous symmetry breaking for interacting scalars

International audienceWe consider ${\rm U}(1)$-symmetric scalar quantum field theories at zero temperature. At nonzero charge densities, the ground state of these systems is usually assumed to be a superfluid phase, in which the global symmetry is spontaneously broken along with Lorentz boosts and time translations. We show that, in $d>2$ spacetime dimensions, this expectation is always realized at one loop for arbitrary non-derivative interactions, confirming that the physically distinct phenomena of nonzero charge density and spontaneous symmetry breaking occur simultaneously in these systems. We quantify this result by deriving universal scaling relations for the symmetry breaking scale as a function of the charge density, at low and high density. Moreover, we show that the critical value of $\mu$ above which a nonzero density develops coincides with the pole mass in the unbroken, Poincaré invariant vacuum of the theory. The same conclusions hold non-perturbatively for an ${\rm O}(N)$ theory with quartic interactions in $d=3$ and $4$, at leading order in the $1/N$ expansion. We derive these results by computing analytically the zero-temperature, finite-$\mu$ one-loop effective potential. We check our results against the one-loop low-energy effective action for the superfluid phonons in $\lambda \phi^4$ theory in $d=4$ previously derived by Joyce and ourselves, which we further generalize to arbitrary potential interactions and arbitrary dimensions. As a byproduct, we find analytically the one-loop scaling dimension of the lightest charge-$n$ operator for the $\lambda \phi^6$ conformal superfluid in $d=3$, at leading order in $1/n$, reproducing a numerical result of Badel et al. For a $\lambda \phi^4$ superfluid in $d=4$, we also reproduce the Lee--Huang--Yang relation and compute relativistic corrections to it. Finally, we discuss possible extensions of our results beyond perturbation theory