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Quantum field theory

Fields of reality

 Automatic translation  Automatic translation Updated November 11, 2015

When we want to talk about matter and its behavior in the world of the infinitely small, that of particles, we approach quantum field theory.
Quantum field theory provides an understanding of particle physics. In some situations, the number of particles entering a portion of space-time fluctuates and differs from the number leaving.
The number of particles changes when, for example, an atom in an initial state gives an atom plus 1 photon in a final state. In other words, a photon suddenly came out of the vacuum and appeared in the electromagnetic field.
Quantum theory tells us that in the real world, everything is "field".
We bathe entirely to the very depths of ourselves in multiple, diverse fields with astonishing characteristics.
The field is a fundamental concept in physics, it does not consist of anything else, it is itself which constitutes the real world. Fields carry the energy of everything in the universe, from atoms to large galactic structures.
Magnetism, gravitation, nuclear force, light, matter and many other physical phenomena are carried by fields.
The most surprising thing is that matter itself, that of which we are made, is made up of a set of fields. Electrons and protons are also fields, so we are made up of fields beyond intuition. In other words, we are made of a ghostly aggregate of quantum particles bathed in fields. These fields carry the energy of the particles throughout the available space around them.


With the notion of field, the vision of the nature of things is overwhelming, reality becomes strange and escapes our 5 main senses. Reality is not explained simply by the presence of matter, but also by the exchanges and interactions between real objects and virtual objects of low-energy quantum fields.
In the quantum world all Standard Model particles, fermions and bosons, emerge from vibrations in a field. This is also the basic concept of the operation of particle accelerators such as the Large Hadron Collider (LHC).
When scientists want to see a particle, they cause collisions whose energy corresponds to the particle in question.
Quarks and electrons make up ordinary matter, but matter above absolute zero (-273.15°C) emits radiation, that is, light moving through a field.
Each type of fermion and each type of boson has its own field. The particles are considered as excited states of these fields. The wave-particle duality of light was extended to electrons in 1929 by the French mathematician and physicist Louis de Broglie (1892 − 1987) and then to all particles.
However, our mind needs an image of our world to feed its intuition and represent the concepts, but conceptualizing quantum and all the quantum fields in which we exist is not easy. Everything is a "field" and quantum fields which are bubbling and charged dynamic systems are all subsets of the gravitational field or the electromagnetic field, the only two fundamental fields in nature.

 Quantum field and function of molecular wave

Image: representation of the molecular wave function showing the boundary of atoms in a molecule.
Where does an atom begin and where does it end?
The atom is a field and it is the field lines that define its volume. No one has ever seen the fields of quantum physics, but it might look like this computer image. When the atoms bind together, their fields are deformed, it is this deformation which characterizes the bonds.
The particles of quantum theory are not "little balls" but ripples, fields that have a wavelength. This wavelength represents the size of the particle, and the field, the energy of the particle. Image credit: T.A. Keith.

note: pre-Socratics like Leucippus (5th century BC) and his disciple Democritus (460 − 370 BC), thought that reality was made of atoms and emptiness.
"He (Leucippus) held that all things are limitless and mutually transform into each other, and that the universe is both empty and filled with bodies." (Diogenes Laertius poet and biographer of the 3rd century AD).

What is a field?


In physics, a field is three related things in a system with a large number of objects.
A delimited portion of space, a measurable physical quantity and a relation that links the portion of space to the physical quantity.
In other words, a field is filled with physical quantities, measurable objects that can be quantified using an instrument where each point in the portion of space is linked to the physical quantity by a correspondence or a function.
For example (see image) atmospheric pressure, air temperature, wind speed but also rain, magnetism, gravity, radioactivity, can be represented by fields.
The fields are scalar or vectorial.
A scalar field is measurable by a simple quantity for example, the temperature or the mass defined by a physical quantity measurable entirely by a single value.
A vector field is associated with a vector quantity, that is to say a quantity for which a single value is not sufficient. It also requires an orientation, that is to say a direction and a sense as in a field of wind speed.
How to represent a field?
For a scalar field it suffices to represent the spaces where the value is identical as in a field of temperatures or pressures (1st and 3rd thumbnail).
For a vector field, it suffices to represent the field lines where each point is a tangent field vector, as in the field of the direction of the winds or in a magnetic field (2nd and 4th thumbnail).
The field energy fades into space. This is the reason why apart from the electromagnetic field generated by a broadcasting station, we no longer pick up at all. When an electromagnetic field is suddenly interrupted, a spark is produced (the field does indeed contain energy).
And the quantum field?
In quantum physics, we do not use the notion of corpuscle since quantum particles are not corpuscles but mathematical quantities represented by state vectors in the Hilbert space. This concept escapes intuition and our vision.


The quantum field fills all of space. It is a vector field of subatomic particles, whose magnitude is quantized (taken from a finite set of values) and the relation is a wave function ( state vector). This makes it possible to know all the information of the system and gives to any particle the typical interference properties of a wave.
In the quantum world all particles in the ground state (unexcited) are waves.
A field of hadrons are virtual particles, partons (gluons and quarks) that move about, appearing and disappearing in the space empty.
A field carried by the weak nuclear force is traversed by bosons W and Z.
An electromagnetic field is traversed by photons. A gravitational field is traversed by "gravitons" (not yet discovered) because gravitation is a very weak force.
Thus, the virtual and real particles of matter bathe in these bubbling fields transferring their energy from time to time. This is what scientists do in a collider. In a collider, when an electron and a positron meet, they annihilate and transfer their energy to the swarming vacuum. This energy creates real material particles that come out of the vacuum and appear for a few "moments" on computer screens.
A field is therefore a bubbling system, an undulation, a vibration, an oscillation, a wave which has a wavelength and therefore a frequency. Thanks to the formula e=hν  According to Max Planck (1858 − 1947), a field also has an energy (e is the energy of something that moves, h is Planck's constant and ν, the Greek letter nu, the frequency). This pair of values, energy and frequency, characterizes the field at each point in space. Each point of space allows the emergence or the annihilation of particles.

nota: When we want to make a fundamental or deep concept understood, we are confronted with a problem of interpretation that is often contrary to our intuition.
It is very difficult to say precisely in everyday language, something true knowing that whatever the explanation, it will be wrong?
 definition of a field

Image: A field can not be represented by an image, however, can be mapped on.

Video: The nucleon field. No optical device allows us to see the bustle of small particles inside a proton or a neutron, but the image layout, same false, is fundamental to understanding the concepts. So in this video, a simulation of the mathematical concept of the nucleon was conducted to allow us to make an intuition of what happens inside protons and neutrons. Credit: 1996 - Jean-François Colonna (Centre de Mathématiques appliquées de l'Ecole Polytechnique et France Télécom).

The wave function is one of the fundamental concepts of quantum mechanics.
It corresponds to the representation of the quantum state of a system in an infinite-dimensional basis.
The wave function gives every particle, typical interference properties of a wave.
In classical mechanics we represent the movement by particles which move in space, in quantum mechanics we represent the real and imaginary particles by wavefunctions.
These wave functions corresponding to stationary or non-stationary states (time-dependent) of energy.
In the standard model of particle physics, a hadron is composed of quarks and/or anti-quarks and gluons.
Subatomic particles constituting a hadron are called partons.
Quarks or antiquarks present in the hadron are called valence quarks while the quark-antiquark pairs and gluons that appear and disappear permanently in the hadron, are called virtual particles.
Gluons are the vectors of the strong force that holds quarks together.
Bosons are subatomic particles that transmit information different forces or interactions. Bosons are social particles, they like to mix, like light which mixes with the light, the photons are bosons.
The photon is the particle mediator the electromagnetic interaction.
The gluon is the messenger of the strong nuclear force, it confines quarks binding together very strongly.
Bosons Z 0 and W ± are the gauge bosons of the weak interaction.
The two categories of the nature of the particles are fermions and bosons.
In particle physics, the model of partons was proposed by Richard Feynman in 1969 to describe the structure of hadrons (protons, neutrons) and model the interactions with hadrons of high energy.
Partons are quarks, antiquarks and gluons that make up hadrons.
Quarks present in the hadron throughout its existence are called valence quarks, the opposite of virtual particles (quark-antiquark pairs and gluons) that appear and disappear permanently in the hadron. Gluons are the vectors of the strong force that holds quarks together.
A hadron is a compound of partons, subatomic particles governed by the strong interaction.
Fermions are subatomic particles (electrons, neutrinos and quarks) of the matter.
All matter that makes up the objects around us are made of fermions. Fermions are asocial particles, in other words they refuse to reduce their living space, this is why the matter is not compressible and that we can walk on the floor.
The two categories of nature particles are fermions and bosons.
The Hilbert space, David Hilbert (1862 - 1943), is a vector space equipped with a scalar product for measuring lengths and angles.
Hilbert space generalizes the notion of classical Euclidean space (two-dimensional plane and three-dimensional space) to spaces of any dimension, finite or infinite.
The Hilbert space is an abstract mathematical concept which allows to apply the techniques of mathematical analysis to all spaces. These techniques are used in theories of equations partial derivative, in quantum mechanics, Fourier analysis, thermodynamics.

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