Relativistic wave equations

In physics, specifically relativistic quantum mechanics (RQM) and its applications to particle physics, relativistic wave equations predict the behavior of particles at high energies and velocities comparable to the speed of light. In the context of quantum field theory (QFT), the equations determine the dynamics of quantum fields. The solutions to the equations, universally denoted as ψ or Ψ (Greek psi), are referred to as "wave functions" in the context of RQM, and "fields" in the context of QFT. The equations themselves are called "wave equations" or "field equations", because they have the mathematical form of a wave equation or are generated from a Lagrangian density and the field-theoretic Euler–Lagrange equations (see classical field theory for background). In the Schrödinger picture, the wave function or field is the solution to the Schrödinger equation; i\hbar\frac{\partial}{\partial t}\psi = \hat{H} \psi one of the postulates of quantum mechan

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

Related people

Related units

Related concepts

Related courses

Related lectures

Summary

Official source

About this result

Related publications (5)

Related publications

Related people (1)

Related people

Related units

No results

Related units

Related concepts (39)

Related concepts

Related courses (5)

Related courses

Related lectures (9)

Related lectures

Higgs-Dilaton cosmology: Are there extra relativistic species?

Javier Rubio

Recent analyses of cosmological data suggest the presence of an extra relativistic component beyond the Standard Model content. The Higgs-Dilaton cosmological model predicts the existence of a massless particle - the dilaton - associated with the spontaneous symmetry breaking of scale invariance and undetectable by any accelerator experiment. Its ultrarelativistic character makes it a suitable candidate for contributing to the effective number of light degrees of freedom in the Universe. In this Letter we analyze the dilaton production at the (p)reheating stage right after inflation and conclude that no extra relativistic degrees of freedom beyond those already present in the Standard Model are expected within the simplest Higgs-Dilaton scenario. The elusive dilaton remains thus essentially undetectable by any particle physics experiment or cosmological observation. (C) 2012 Elsevier B.V. All rights reserved.

Elsevier Science Bv2012

Approximation of high order homogenized wave equations for long time wave propagation

Assyr Abdulle, Timothée Noé Pouchon

EMS publishing house2019

Finite element heterogeneous multiscale method for the wave equation

Assyr Abdulle

A finite element heterogeneous multiscale method is proposed for the wave equation with highly oscillatory coefficients. It is based on a finite element discretization of an effective wave equation at the macro scale, whose a priori unknown effective coefficients are computed on sampling domains at the micro scale within each macro finite element. Hence the computational work involved is independent of the highly heterogeneous nature of the medium at the smallest scale. Optimal error estimates in the energy norm and the L-2 norm and convergence to the homogenized solution are proved, when both the macro and the micro scales are refined simultaneously. Numerical experiments corroborate the theoretical convergence rates and illustrate the behavior of the numerical method for periodic and heterogeneous media.

2011

Relativistic quantum mechanics

In physics, relativistic quantum mechanics (RQM) is any Poincaré covariant formulation of quantum mechanics (QM). This theory is applicable to massive particles propagating at all velocities up to t

Dirac equation

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all s

Klein–Gordon equation

The Klein–Gordon equation (Klein–Fock–Gordon equation or sometimes Klein–Gordon–Fock equation) is a relativistic wave equation, related to the Schrödinger equation. It is second-order in space and ti

EE-575: Wave propagation along transmission lines

In this lecture, we will describe the theoretical models and computational methods for the analysis of wave propagation along transmission lines.

PHYS-702: Advanced Quantum Field Theory

The course builds on the two previous courses on the subject. The main subject is the study of quantum field theories at the loop level. The course introduces the concept of loop divergences and renormalization. Non abelian gauge theories are also discussed in depth.

PHYS-432: Quantum field theory II

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