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Concept# Classical field theory

Résumé

A classical field theory is a physical theory that predicts how one or more physical fields interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically intended to describe electromagnetism and gravitation, two of the fundamental forces of nature.
A physical field can be thought of as the assignment of a physical quantity at each point of space and time. For example, in a weather forecast, the wind velocity during a day over a country is described by assigning a vector to each point in space. Each vector represents the direction of the movement of air at that point, so the set of all wind vectors in an area at a given point in time constitutes a vector field. As the day progresses, the directions in which the vectors point change as the directions of the wind change.
The first field theories, Newtonian gravitation an

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Lagrangien (théorie des champs)

La théorie lagrangienne des champs est un formalisme de la théorie classique des champs.
C'est l'analogue de la théorie des champs de la mécanique lagrangienne. La mécanique lagrangienne est utilisé

Théorie de jauge

En physique théorique, une théorie de jauge est une théorie des champs basée sur un groupe de symétrie locale, appelé groupe de jauge, définissant une « invariance de jauge ». Le prototype le plus si

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Simone Padoan, Stefano Rizzelli

The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated data, such as maxima of a random number of observations, are considered. We derive a limit theorem concerning the attractors for the distributions of the aggregated data, which boil down to a new family of max-stable distributions. We also connect the extremal dependence structure of classical max-stable distributions and that of our new family of max-stable distributions. Using an inversion method, we derive a semiparametric composite-estimator for the extremal dependence of the unobservable data, starting from a preliminary estimator of the extremal dependence of the aggregated data. Furthermore, we develop the large-sample theory of the composite-estimator and illustrate its finite-sample performance via a simulation study.

Cours associés (19)

PHYS-431: Quantum field theory I

The goal of the course is to introduce relativistic quantum field theory as the conceptual and mathematical framework describing fundamental interactions.

PHYS-313: Quantum physics I

The objective of this course is to familiarize the student with the concepts, methods and consequences of quantum physics.

PHYS-202: Analytical mechanics (for SPH)

Présentation des méthodes de la mécanique analytique (équations de Lagrange et de Hamilton) et introduction aux notions de modes normaux et de stabilité.

Why are classical theories often sufficient to describe the physics of our world even though everything around us is entirely composed of microscopic quantum systems? The boundary between these two fundamentally dissimilar theories remains an unsolved problem in modern physics. Position measurements of small objects allow us to probe the area where the classical approximation breaks down. In quantum mechanics, Heisenbergâs uncertainty principle dictates that any measurement of the position must be accompanied by measurement induced back-action---in this case manifested as an uncertainty in the momentum. In recent years, cavity optomechanics has become a powerful tool to perform precise position measurements and investigate their fundamental limitations. The utilization of optical micro-cavities greatly enhances the interaction between light and state-of-the-art nanomechanical oscillators. Therefore, quantum mechanical phenomena have been successfully observed in systems far beyond the microscopic world. In such a cavity optomechanical system, the fluctuations in the position of the oscillator are transduced onto the phase of the light, while fluctuations in the amplitude of the light disturb the momentum of the oscillator during the measurement. As a consequence, correlations are established between the amplitude and phase quadrature of the probe light. However, so far, observation of quantum effects has been limited exclusively to cryogenic experiments, and access to the quantum regime at room temperature has remained an elusive goal because the overwhelming amount of thermal motion masks the weak quantum effects. This thesis describes the engineering of a high-performance cavity optomechanical device and presents experimental results showing, for the first time, the broadband effects of quantum back-action at room temperature. The device strongly couples mechanical and optical modes of exceptionally high quality factors to provide a measurement sensitivity $\sim\!10^4$ times below the requirement to resolve the zero-point fluctuations of the mechanical oscillator. The quantum back-action is then observed through the correlations created between the probe light and the motion of the nanomechanical oscillator. A so-called âvariational measurementâ, which detects the transmitted light in a homodyne detector tuned close to the amplitude quadrature, resolves the quantum noise due to these correlations at the level of 10% of the thermal noise over more than an octave of Fourier frequencies around mechanical resonance. Moreover, building on this result, an additional experiment demonstrates the ability to achieve quantum enhanced metrology. In this case, the generated quantum correlations are used to cancel quantum noise in the measurement record, which then leads to an improved relative signal-to-noise ratio in measurements of an external force. In conclusion, the successful observation of broadband quantum behavior on a macroscopic object at room temperature is an important milestone in the field of cavity optomechanics. Specifically, this result heralds the rise of optomechanical systems as a platform for quantum physics at room temperature and shows promise for generation of ponderomotive squeezing in room-temperature interferometers.

This thesis presents a general discussion of the Composite Higgs scenario of Electro-Weak Symmetry Breaking (EWSB). We start by reviewing the Standard Model of Electro-Weak interaction, discussing its experimental tests and conceptual pitfalls. Emphasis is given to the effective field theory point of view. In particular, the inherent tension related to the stability of the Electro-Weak scale motivates us to explore the possibility of having the Higgs field emerging as a Nambu-Goldstone boson from a new strongly coupled sector. Our construction is to a large extent inspired by the picture of the long range dynamics of QCD. The main ingredients are the symmetry of the UV theory, the pattern of its spontaneous breakdown and the sources of explicit breaking. In QCD, the latter are provided by the light quark masses and by the electromagnetic interaction. In Composite Higgs models, the most relevant symmetry breaking couplings are those related to the generation of the third family quark Yukawas through partial compositeness. They generate a potential for the Higgs and thus trigger EWSB. The constraints on the scenario are exposed, with a particular emphasis on the composite Two Higgs Doublet Model (THDM). While a residual SO(4) symmetry is sufficient to ensure a realistic phenomenology in presence of a single composite Higgs doublet, an extended Higgs sector needs more symmetries. For two doublets we show how either CP or a ℤ2 symmetry can play this role and construct a model for each realisation relying on the SO(6)/SO(4) × SO(2) coset. Finally, we discuss the phenomenology of this scenario. In particular, we present de differences between an elementary and a composite THDM. We also conclude that composite fermions associated to the third family quarks seem to be the most promising experimental handles for these models. We discuss their discovery range at the LHC, and the possibility of measuring the structure of their couplings. This knowledge would allow important insight into the strong dynamics.

Séances de cours associées (18)