This article summarizes the history of the quantum theory of the fields .

The Quantum theory of the fields is the application of the concepts of the Quantum physics to the fields. Exit of the Mechanical quantum relativist, whose interpretation as theory describing only one particle had proven to be incoherent, the quantum theory of the fields provides a conceptual framework largely used in Physique of the particles, Physique of the condensed matter, and in Physique statistics.

History

First steps

In 1925 with Göttingen, little time after the birth of the mechanics of the matrices, Jordan tries to quantify the electromagnetic field created by a particle charged while following the new rules introduced by Heisenberg for the particles. This first attempt fails, but Jordan perseveres and, one year later, tries this time to quantify the free electromagnetic field (i.e in the absence of loads). The reception of this work by its pars is rather hostile, and it is usually considered that the Théorie Quantique of the fields is born truly in 1927 when the princeps article of the British Dirac intitulé  is published;: “  The quantum theory of the emission and the absorption of the rayonnement  ”. In this paper, Dirac quantifies the system {loads completely + fields} by using the Hamiltonien formalism. The method used by Dirac will be baptized Second quantification by Fock and Jordan in 1932.

The theory of Dirac was accepted and discussed eulogistically, in particular by Bohr, during famous the Congrès Solvay of October 1927. However, it presented a defect majeur  obviously;: its formalism, based on the Hamiltonian, made play time a particular part, which was not compatible with the invariance of Lorentz claimed by the theory of the restricted Relativité of Einstein. The Heisenberg, Jordan, Pauli and Klein then decided to create their own version of the relativistic quantum electrodynamics. Since 1927, Pauli and Jordan succeeded in formulating the relations of commutations covariantes components of the tensor of Maxwell describing a free electromagnetic field quantified (of representation of Heisenberg)  :

$\backslash \; left\; \backslash ,\; naked\; F\_\; \{\backslash \; driven\; \backslash \}\; (X),\; \backslash ,\; F\_\; \{\backslash \; rho\; \backslash \; sigma\}\; (x\text{'})\; \backslash ,\; \backslash \; right\; =\; I\; \backslash ,\; \backslash \; left\; \backslash ,\; \backslash \; left\; (\backslash ,\; \backslash \; eta\_\; \{\backslash \; naked\; \backslash \; sigma\}\; \backslash ,\; \backslash \; partial\_\; \{\backslash \; rho\}\; “-\; \backslash \; eta\_\; \{\backslash \; naked\; \backslash \; rho\}\; \backslash ,\; \backslash \; partial\_\; \{\backslash \; sigma\}”\; \backslash \; \backslash \; right)\; \backslash ,\; \backslash \; partial\_\; \{\backslash \; driven\}\; \backslash \; -\; \backslash \; \backslash \; left\; (\backslash ,\; \backslash \; eta\_\; \{\backslash \; driven\; \backslash \; sigma\}\; \backslash ,\; \backslash \; partial\_\; \{\backslash \; rho\}\; \text{'}-\; \backslash \; eta\_\; \{\backslash \; driven\; \backslash \; rho\}\; \backslash ,\; \backslash \; partial\_\; \{\backslash \; sigma\}\; “\backslash ,\; \backslash \; right)\; \backslash ,\; \backslash \; partial\_\; \{\backslash \; naked\}\; \backslash ,\; \backslash \; right]\; \backslash ,\; \backslash \; Delta\; (X\; -\; X”)$

where $\backslash \; eta\_\; \{\backslash \; driven\; \backslash \; naked\}$ is the metric one of Minkowski, and where the function of Pauli-Jordan $\backslash \; Delta\; (X)$ is the relativistic generalization of the distribution of Dirac $\backslash \; delta\; (X)$ :

$$

\ Delta (X) \, = \, - \, I \, \ int \ frac {d^4 K} {(2 \ pi) ^3} \ \ delta (k^2) \ \ epsilon (k^0) \ e^ {- \, I \, K \ cdot X}

In this formula, the fonction : $\backslash \; epsilon\; (k^0)$ = sign $(k^0)$ is worth $\backslash \; pm\; 1$ according to the sign of the temporal component $k^0$ of the quadri-implusion.

In 1933, Bohr and his collaborator Rosenfeld analyzed the mesurability electromagnetic field quantified starting from the relations of commutations of the components of this one. They showed that a quantum field local in a point is a singular mathematical being, and that only a space average of the field on a small area of space is likely to be accessible to measurement. They established inequalities , similar to the Principe of uncertainty for a particle, which express the fundamental limitations on the possibility of measuring fields in point of space times separated by an interval from the time kind. This important work was published in a Danish review in the form of a somewhat hermetic article.

In addition to the authors already mentioned above, Wigner, Weisskopf, Pram, Peierls, Oppenheimer, Podolsky, and especially Fermi brought each one of the important contributions to the formalism. The method of Fermi was made profitable as of 1932 in particular by Dirac, Fock and Podolsky to entirely establish a formulation covariante quantum electrodynamics, incorporated at once by Dirac in its famous ouvrage : Principles of quantum mechanics . This final shape will be regained and synthesized in 1943 by Wentzel in a book which will be used a long time as reference.

It will be noted that all the authors quoted previously butted at one time or another against an obstacle récurrent : systematic appearance of Infinite during calculations of judicious sizes Physical S being measurable, making the theory unusable.

Quantum electrodynamics

See also: Electrodynamic quantum

The first true theoretical projection concerning the problem of infinite goes back to 1947. This year were indeed measured precisely certain variations in the fine Structure and hyperfine of the energy levels of the Atome of hydrogen, variations compared to the predictions of the equation of Dirac of a electron in the Coulomb field of the Proton.

One of these variations is celebrates it Décalage of Lamb ( Lamb shift ). This experimental result was intensely discussed from June 2nd to 4th 1947 at the time of the “  conference of Shelter Island  ” of theoretical physics intitulée : “  Bases of mechanics quantique  ”.

At the conclusion of this conference, in a train which took it along from New York to Schenectady, the theorist Bethe succeeds in for the first time calculating a correct order of magnitude finished of this displacement of Lamb. But this first calculation was not-relativist, therefore imperfect. Of return at the beginning of July to the Université Cornell (Ithaca) where he taught, Bethe made a conference during which he exposed his result, conclusive that an entirely relativistic calculation was necessary. In the assistance the young person Feynman appeared, who saw Bethe at the end of exposed to say to him that he thought of being able to make this relativistic calculation. What it did.

The difficulty of infinite was however entirely overcome only in 1948, with the invention of the systematic procedure of Renormalization, which had mainly with work of Japanese Tomonaga and American Schwinger (Université Harvard) and Feynman. These three authors will share the Nobel Prize of physique 1965. The equivalence of the abstract formulation developed by Schwinger and that, based on graphs, invented independently by Feynman, was shown in 1948 by Dyson (Institute for Advanced Study, Princeton).

The method of quantification of the electromagnetic field proposed by Feynman is based on its concept of Intégrale of way. The systematic use of this procedure of quantification in the place of the old canonical quantification will allow later on an easy quantification of the theories of gauge.

Theories of gauge

See also: Theory of gauge

Successes of the quantum electrodynamics, theory of gauge Abelian based on the commutative Group $U\; (1)$, led the theorists to apply the concepts of the Quantum theory of the fields to the not-Abelian theories of gauge. These theories are also called theories of Yang-Millets , according to the name of their two inventors in 1954  : Chen Yang and Robert Millets. The use of these theories gave rise to current the standard model of the Physique of the particles.

The first theory was the electro-weak unified theory of Glashow, Salam and Weinberg (1962 - 1968), built on the Groupe of gauge $SU\; (2)\; \backslash \; otimes\; U\; (1)$. These authors received the Nobel Prize of physique 1979. In this theory, material particles (electron S, Muon S, Neutrino S…) interact by exchanging one or more Boson S virtuels : Photon, W ⁺, W^- and Z ⁰. With the difference of the photon, the boson-vectors W and Z are massive, their mass being about 100 GeV /c ². This explains the very short range of the weak Interaction. The introduction of a mass for these particles required besides the invention of a new mechanism, called Mécanisme of Higgs (of the name of its inventor Peter Higgs), because the introduction of a traditional term of mass into the Lagrangian one would break the invariance of gauge. This mechanism, the spontaneous Crack of symmetry, was introduced by Higgs. It corresponds to him a new massive particle, the Boson of Higgs, not yet highlighted in experiments but whose final checking should take place with the startup nearest of LHC (2007 in theory).

Came then in the years 1970 the theory from the strong nuclear interaction, worked out by Gross, Politzer and Wilczek; these three authors obtained the Nobel Prize of physique 2004. This theory, also baptized quantum Chromodynamique (Q.C.D.), is built on the group of gauge $SU\; (3)$ of color. The material particles (Quark S) there interact by exchanging one or more virtual bosons, the Gluon S. Like the photon, gluons them are particles of null mass. But, unlike the photon, let us gluons them carry a load of color and interact between-eux : contrary to the electrodynamics of Maxwell, the theories of Yang-Millets are indeed non-linear. Another remarkable property of chromodynamic quantum was that of the asymptotic Liberté i.e. the fact for the quarks of seeing their interaction weakening when concerned energies are very large and contrary to very strongly interacting with weak energy. This particular phenomenon is at the origin of the mechanism of Confinement of the quarks which prevents from observing a quark with in an isolated state. Indeed, if one increases the distance between two quarks their energy of interaction becomes so tall that other quarks emerge from the surrounding vacuum so that the Charge of color observed by far remains always null.

A decisive stage in the validation as of these not-Abelian theories of gauge was the proof of their renormalisability, established in 1972 by 'T Hooft and Veltman, Nobel Prize of physique 1999.

Statistical physics

See also: History of thermodynamics and statistical mechanics, Physical statistics

The program of the Physique statistics is to describe the properties Macroscopique S of the bodies starting from their contents Microscopique. An important problem consists in particular describing the changes of state, also called transitions from phase. Under certain experimental conditions, certain bodies present sometimes a particular behavior which one arranges under the name of Phénomène criticizes, which is characterized by certain critical exhibitors universal. The calculation of these critical exhibitors by the old methods of statistical physics (methods of average field) gave results in dissension with the experiment.

At the end of the years 1960, Kadanoff had introduced the idea that the transitions from phase presented properties of universality and Invariance of scale. Wilson had then the idea to apply the methods of Renormalization of the quantum theory of the fields. Successes of this new approach were worth in Wilson the Nobel Prize of physique 1982; specialists - Wilson the first were surprised that Kadanoff was not associated with this prestigious recognition.

For its part, the France contributed to a significant degree to this adventure of calculations of critical exhibitors, with the work completed in the years 1970 by Jean Zinn-Justin (Service of theoretical physics of the C.E.A., Saclay), Jean-Claude Guillou (theoretical Physics laboratory and high energies, Université Paris 6) and Edouard Brézin (theoretical Physics laboratory of the E.N.S.).

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