# Exchange particles

In quantum mechanics and quantum field theory , exchange particles are understood to be particles that mediate an interaction between two systems by being given off by one system and being absorbed by the other. The interaction caused in this way is also referred to as an exchange interaction , and its exchange particles as messenger particles, carrier particles, interaction particles or force particles.

It is characteristic that the exchange particles as such remain invisible to the outside world. You are in an indefinite number of virtual states , but you may call. a. the known effects of a classical force field . Proof of their existence are the measurable properties of the physical processes, which are explained with the help of this theoretical concept with an accuracy that would otherwise not be achieved. This also includes experiments in which the exchange particles change into real states through the addition of energy and can then be detected individually.

Note: The article Exchange interaction deals with a different meaning of the same word (see also development of the term and the name below ).

## Examples

Three of the four fundamental interactions on which all physical processes are based are exchange interactions; their exchange particles belong to the fundamental elementary particles of the boson type :

It is not yet known whether gravitation is also an exchange interaction.

Sometimes only those bosons are meant by exchange particles that transmit the elementary interactions. In a broader sense, one also refers to others, e.g. T. non-elemental particles as exchange particles, which can be viewed in the same sense as causing a binding force, e.g. B.

## Calibration bosons

The exchange particles of the fundamental interactions are also known as gauge bosons . The name comes from the fact that these particles belong to the bosons because of their integral spin and are justified by the principle of gauge invariance: the fundamental interactions can be formulated in the form of a gauge theory with the help of the requirement for local gauge invariance of the Lagrangian .

In the context of the quantum field theoretical treatment ( which could not yet be developed only for gravity ) it follows that fields are caused by field quanta . The field quanta of the force fields are the exchange particles of the respective interaction.

In the context of classical field theory, this results in the existence of the respective classical force field with its field equations, e.g. B. the electromagnetic field with the Maxwell equations of electromagnetism or the gravitational field with Einstein's field equations of general relativity .

## illustration

### Model presentation from classical physics

If you take two handball players as the two systems and a heavy ball as an exchange particle, which they toss and catch each other, then throwing and catching the players causes the players to change their impulses in opposite directions. This is - at least in the time average - indistinguishable from the effect of a repulsive force field between them. This illustration, taken from classical physics, is also correct for quantum mechanical systems - for example, when an excited atom emits a photon, which is then absorbed by another atom. This process is the basis of radiation pressure . The illustration does not do justice to the role of the exchange particles in the quantum-physical occurrence of an interaction, e.g. B. it cannot explain any attraction.

### Difference between classical analogy and exchange particles

The ball in the classical model, but also the photon that is actually generated and flies from one atom to another, has certain values ​​for energy and momentum at every moment during its flight , which (with its mass , for the photon ) is the energy momentum -Relationship (classic) or ( relativistic ) fulfill. This does not apply to exchange particles that produce the effect of a force field. ${\ displaystyle E}$ ${\ displaystyle p}$${\ displaystyle m}$${\ displaystyle m = 0}$ ${\ displaystyle E = p ^ {2} / (2m)}$${\ displaystyle E ^ {2} = p ^ {2} c ^ {2} + m ^ {2} c ^ {4}}$

Consider, for example, that two bodies charged with the same name collide elastically against each other , whereby they bounce off each other due to electrostatic repulsion according to Coulomb's law . In order to interpret this through an exchange interaction, one assumes a photon that flies from one body to another. The quantum theoretical equations ensure that this photon does not cause any other interaction, i.e. that it remains unobservable. Since the bodies only change their flight direction during an elastic collision ( viewed in their center of gravity system), but retain their energy, the photon only transfers momentum, but no energy from one to the other. In doing so, it violates the energy-momentum relationship of “normal” photons. ${\ displaystyle E = pc}$

Particles in states that are unobservable and violate the otherwise valid energy-momentum relationship are called virtual particles . In contrast, the “normal” particles or the states in which they can be found during a measurement or observation according to classical physics and quantum physics are called real .

### Simplified quantum mechanical interpretation

For a methodically strict elaboration of the concept of exchange interaction, one must use quantum mechanical perturbation calculations , for example with the technique of Feynman diagrams . For some aspects of the results there are comparatively simpler interpretations, but they do not meet the requirement of a conclusive derivation. The virtual character of the exchange particles means that their relationship between energy and momentum does not have to follow the equation , but the deviation does not last much longer than it does. ${\ displaystyle E ^ {2} = p ^ {2} c ^ {2} + m ^ {2} c ^ {4}}$${\ displaystyle t = {\ tfrac {\ hbar} {E}}}$

• Electrostatic Coulomb force between two electrons : A photon with the energy and the momentum can move a distance from the source during this time . If it is absorbed there after the time , it delivers its impulse and thus creates a force . This estimate correctly shows the quadratic dependence of the force on the distance. In order to obtain the Coulomb's law also quantitatively, only the dimensionless factor , which is known as the fine structure constant and which generally indicates the strength of the electromagnetic interaction , is missing .${\ displaystyle F (r) = {\ tfrac {e ^ {2}} {4 \ pi \ varepsilon _ {0} r ^ {2}}}}$${\ displaystyle E}$${\ displaystyle p = {\ tfrac {E} {c}}}$${\ displaystyle r = ct = {\ tfrac {\ hbar c} {E}} = {\ tfrac {\ hbar} {p}}}$${\ displaystyle t}$${\ displaystyle F = {\ tfrac {p} {t}} = {\ tfrac {\ hbar c} {r ^ {2}}}}$${\ displaystyle {\ tfrac {e ^ {2}} {4 \ pi \ varepsilon _ {0} \ hbar c}} \ approx 0 {,} 0035 \ dotso}$
• Force with finite range ( Yukawa potential ): For an exchange particle with mass to be generated from nothing, the energy-momentum relationship must be violated by at least . The maximum "allowed" time for this is the maximum flight distance . This length is also called the Compton wavelength of the particle. It appears here as if it were an absolute upper limit of every possible effect of the particle. The correct quantum mechanical calculation, however, gives the corresponding exponential attenuation factor as a range parameter.${\ displaystyle V (r) = {\ tfrac {g} {r}} e ^ {- r / \ lambda}}$${\ displaystyle m}$${\ displaystyle E = mc ^ {2}}$${\ displaystyle t = {\ tfrac {\ hbar} {mc ^ {2}}}}$${\ displaystyle ct = {\ tfrac {\ hbar} {mc}}}$${\ displaystyle \ lambda = ct = {\ tfrac {\ hbar} {mc}}}$

## Development of the term and the naming

Werner Heisenberg and Wolfgang Pauli treated the quantum dynamics of wave fields in 1929 . They were able to derive the correct expression for the electrostatic Coulomb energy of two electrons from the generation and destruction of photons alone. The classical Coulomb field was thus explained by a quantum field theoretical model.

At about the same time, the short-range attraction on which the chemical bond is based was explained by Linus Pauling , John C. Slater , Friedrich Hund and Robert Mulliken by the fact that an electron exchanged its place in one atom for a place in the other atom due to the quantum mechanical tunnel effect can. In 1932 Heisenberg published the approach to formulate the attraction between proton and neutron by transferring an electron , analogous to the attraction between H atom and H + ion . Accordingly, he suggested that the associated mathematical expression should be referred to as the "change of place integral". In the end, the proton and neutron (or H-atom and H + -ion) would appear as if they had just swapped their places. Because of the mathematical similarity to the exchange integral (or exchange interaction ) in multi-electron systems, in which, however, two particles exchange their places with each other, the latter designation has prevailed.

In 1934 Hideki Yukawa developed the hypothesis that the proton-neutron interaction is based on a new field . Its field strength should indicate the presence of novel field quanta, just as the electromagnetic field should indicate the presence of photons. Yukawa assumed a mass of about 200 electron masses for the field quantum  and was able to show that the field then has the required short range and that the field quanta only appear as real particles when energy is supplied. After the experimental confirmation of this hypothesis, the expression “exchange of a particle” - which was not entirely happy in terms of language - spread to the term “exchange interaction”.

The formulation of Maxwell's electrodynamics and Einstein's theory of gravity in the form of gauge theories was found in 1919 by Hermann Weyl .

## Individual evidence

1. Werner Heisenberg, Wolfgang Pauli: For quantum dynamics of the wave fields I . In: magazine f. Physics . tape 56 , 1929, pp. 1-61 .
2. ^ Silvan S. Schweber: QED and the men who made it . Princeton Univ. Press, Princeton 1994.
3. Werner Heisenberg: construction of atomic nuclei I . In: magazine f. Physics . tape 77 , 1932, pp. 1-11 .
4. ^ Hideki Yukawa: On the Interaction of Elementary Particles . In: Proc. Phys.-Math. Soc. of Japan . tape 17 , 1935, pp. 48 .
5. Hermann Weyl: A new extension of the theory of relativity . In: Annals of Physics . tape 364 , no. 10 , 1919, pp. 101-133 .