Lagrangian (field theory)

Summary

Lagrangian field theory is a formalism in classical field theory. It is the field-theoretic analogue of Lagrangian mechanics. Lagrangian mechanics is used to analyze the motion of a system of discrete particles each with a finite number of degrees of freedom. Lagrangian field theory applies to continua and fields, which have an infinite number of degrees of freedom. One motivation for the development of the Lagrangian formalism on fields, and more generally, for classical field theory, is to provide a clean mathematical foundation for quantum field theory, which is infamously beset by formal difficulties that make it unacceptable as a mathematical theory. The Lagrangians presented here are identical to their quantum equivalents, but, in treating the fields as classical fields, instead of being quantized, one can provide definitions and obtain solutions with properties compatible with the conventional formal approach to the mathematics of partial differential equations. This enables t

Official source

https://en.wikipedia.org/wiki/Lagrangian_(field_theory)

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (12)

Related publications

Related people

Related units

Related concepts (98)

Related concepts

Related courses (15)

Related courses

Related lectures (22)

Related lectures

Nonperturbative Quantum Field Theory in Curved Spacetime

Kamran Salehi Vaziri

Quantum Field Theory(QFT) as one of the most promising frameworks to study high energy and condensed matter physics, has been mostly developed by perturbative methods. However, perturbative methods can only capture a small island of the space of QFTs.QFT in hyperbolic space can be used to link the conformal bootstrap and massive QFT. Conformal boundary correlators also can be studied by their general properties such as unitarity, crossing symmetry and analicity. On the other hand, by sending the curvature radius to infinity we reach to the flat-space limit in hyperbolic space. This allows us to use conformal bootstrap methods to study massive QFT in one higher dimension and calculate observables like scattering amplitudes or finding bounds on the couplings of theory. The main goal of my research during my Ph.D. would be to study QFTs in hyperbolic space to better understand strongly coupled QFTs.Hamiltonian truncation is a numerical method to study strongly coupled QFTs by imposing a UV cutoff. We use this method to study strongly coupled QFT in hyperbolic space background. For simplicity, we start with scalar field theory in 2-dimensional AdS. We expect to extract the spectrum of our theory as a function of AdS curvature and find the boundary correlation functions.

EPFL2022

Thermal and quantum phase transitions of some rare earth compounds (LiErF4, LiYbF4, LiGdF4 and LiTmF4) are established using the mean field theory. These preliminary calculations allowed evidencing the existence of a novel high-field antiferromagnetic phase in LiErF4, and a still unexplained symmetry breaking in LiGdF4. But the discrepancies with experimental results impel a more sophisticated method. We then present analytical and numerical evidence for the validity of an effective approach to the description of the dipolar coupled antiferromagnet LiErF4. We show that the approach, when implemented in mean field calculations, is able to capture both the qualitative and quantitative aspects of the physics of LiErF4 at small external field and low temperature, yielding results that agree with those obtained in the full Hilbert space using mean field theory. This model nevertheless still fails to describe the LiHoF4 system and needs to be improved. We finally use this toy model as a basis for classical Monte Carlo simulations of LiErF4, which allows the calculation of thermodynamical quantities of the system, as well as the evolution of the order parameters as a function of field H and temperature T. These calculations yield results that are much closer to the experiments than those based on the mean field approximation. Although the theoretical critical temperature is still overestimated by 34%, the critical exponents computed from this effective model correspond to those found experimentally.

2012

Motion of gas bubbles, considered as massless bodies, affording deformations within a prescribed family of shapes, in an incompressible fluid under the action of gravitation and surface tension

A model allowing to describe motion and coalescence of gas bubbles in a liquid under the action of gravitation and surface tension is proposed. The shape of the bubbles is described by a pre-defined family of mappings, for example ellipsoids with a fixed volume and the effects of the gas motions inside the bubbles are neglected. The motion of a bubble is obtained in a Lagrangian form using the D'Alembert principle of virtual works. The set of equations is numerically solved with the help of the fictitious domain technique in which the Navier-Stokes equations in the domain formed by both fluid and gas are considered. The equations governing the bubbles motion are imposed by introducing Lagrange multipliers on the bubbles boundaries. Numerical results in 2D and 3D are presented.

2007