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Magnetic Vector Potential01:15

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...
Determining Electric Field From Electric Potential01:12

Determining Electric Field From Electric Potential

The electric field and electric potential are related to each other. If the electric field at various points in the region of interest is known, it can be used to calculate the electric potential difference between any two points. Similarly, if the electric potential is known for various points, then it is possible to calculate the electric field.
In general, regardless of whether the electric field is uniform, it points in the direction of decreasing potential because the force on a positive...
Gauss's Law01:07

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.
The Principle of Superposition and the Gravitational Field01:17

The Principle of Superposition and the Gravitational Field

The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...
Calculations of Electric Potential II01:27

Calculations of Electric Potential II

An electric dipole is a system of two equal but opposite charges, separated by a fixed distance. This system is used to model many real-world systems, including atomic and molecular interactions. One of these systems is the water molecule, but only under certain circumstances. These circumstances are met inside a microwave oven, where electric fields with alternating directions make the water molecules change orientation. This vibration is equivalent to heat at the molecular level.
Consider a...
The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...

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Related Experiment Video

Updated: May 26, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Effective potential for quantum scalar fields in a de Sitter geometry.

Julien Serreau1

  • 1Astro-Particule et Cosmologie, Université Paris 7-Denis Diderot, 10 rue Alice Domont et Léonie Duquet, 75205 Paris cedex 13, France.

Physical Review Letters
|December 21, 2011
PubMed
Summary
This summary is machine-generated.

We investigated quantum O(N) scalar fields on de Sitter geometry. Our findings show self-interactions create a positive mass, preventing broken symmetry states due to enhanced fluctuations.

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Last Updated: May 26, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
09:23

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

Published on: May 30, 2014

Area of Science:

  • Quantum Field Theory
  • Cosmology
  • String Theory

Background:

  • De Sitter geometry is crucial for understanding cosmic inflation and the early universe.
  • Scalar fields are fundamental in many cosmological models, including inflation and dark energy.
  • The O(N) scalar field model provides a simplified yet powerful framework for studying quantum field behavior in curved spacetimes.

Purpose of the Study:

  • To analyze the quantum theory of an O(N) scalar field on de Sitter geometry.
  • To investigate the effects of nonperturbative 1/N expansion on quantum field dynamics.
  • To determine the behavior of the effective potential and symmetry breaking in this context.

Main Methods:

  • Leading order analysis in a nonperturbative 1/N expansion.
  • Resummation of superdaisy loop diagrams.
  • Derivation and solution of renormalized dynamical field equations.
  • Computation of the complete effective potential.

Main Results:

  • The scalar field acquires a strictly positive square mass due to self-interactions.
  • This positive mass effectively screens potential infrared divergences.
  • Strongly enhanced ultralong-wavelength fluctuations were observed.
  • The existence of a spontaneously broken symmetry state is prevented in any dimension.

Conclusions:

  • Self-interactions in quantum O(N) scalar fields on de Sitter space lead to mass generation and infrared divergence screening.
  • Enhanced quantum fluctuations disrupt symmetry breaking mechanisms.
  • The study provides insights into the behavior of quantum fields in cosmological spacetimes, relevant for early universe physics.