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Gauss's Law

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.

Poisson's And Laplace's Equation

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.

Force and Potential Energy in Three Dimensions

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Consider a particle moving under the action of a conservative force that has components along each coordinate axis. Each component of force is a function of the coordinates. The potential energy function U is also a function of all three spatial coordinates. Force in one dimension can be written as the negative ratio of potential energy change to the displacement along that coordinate. For minimal displacement, the ratios become derivatives. If a function has many variables, the derivative only...

Magnetic Vector Potential

Magnetic Vector Potential

In electrostatics, the electric field can be written as the negative gradient of the potential. In magnetostatics, the zero divergence of the magnetic field ensures that the magnetic field can be expressed as the curl of a vector potential. This potential is known as the magnetic vector potential.
Consider an ideal solenoid with n turns per unit length and radius R. If I is the current through the solenoid, the magnetic field inside the solenoid is expressed as the product of vacuum...

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Consider a ring of radius R with a uniform charge density λ. What will the electric potential be at point M, which is located on the axis of the ring at a distance x from the center of the ring?
The ring is divided into infinitesimal small arcs such that point M is equidistant from all the arcs. Here, the cylindrical coordinate system is used to calculate the electric potential at point M. A general element of the arc between angles θ and θ + dθ is of the length Rdθ and has a charge of...

Symmetry in Maxwell's Equations

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Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...

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Related Experiment Video

Updated: Dec 15, 2025

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Generating a Higgs Potential Quartic Term.

Csaba Csáki¹, Cong-Sen Guan^1,2,3, Teng Ma^2,4

¹Department of Physics, LEPP, Cornell University, Ithaca, New York 14853, USA.

Physical Review Letters

|July 9, 2020

Summary

This summary is machine-generated.

We propose a new mechanism to generate a Higgs quartic term in composite Higgs models. This method utilizes Higgs-dependent kinetic mixing, naturally embedding into maximal symmetry and twin Higgs models for a realistic Higgs potential.

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Area of Science:

High Energy Physics
Theoretical Physics
Particle Physics

Background:

Composite Higgs models offer an alternative to the Standard Model Higgs.
Generating realistic Higgs potentials in these models presents theoretical challenges.
Existing models often require fine-tuning or additional complex mechanisms.

Purpose of the Study:

To present a novel mechanism for generating a Higgs quartic term.
To explore its implications for composite Higgs models, particularly twin Higgs models.
To achieve a natural and realistic Higgs potential without a quadratic term.

Main Methods:

Introducing Higgs-dependent kinetic mixing between additional fermionic states.
Embedding the mechanism into models with maximal symmetry.
Analyzing the generation of the Higgs quartic and Z_{2} symmetry breaking.

Main Results:

A simple mechanism for generating a Higgs quartic term is demonstrated.
The quartic term arises from Higgs-dependent kinetic mixing.
This mechanism naturally fits into maximal symmetry and twin Higgs models.

Conclusions:

The proposed mechanism provides a natural source for the Higgs quartic in composite Higgs models.
It leads to realistic Higgs potentials in twin Higgs models.
The top and gauge sectors can remain exactly Z_{2} invariant, simplifying model construction.