Alexandru Proca
Born	(1897-10-16)16 October 1897 Bucharest,Kingdom of Romania
Died	13 December 1955(1955-12-13) (aged 58) Paris,France
Citizenship	Romania France
Alma mater	Politehnica University of Bucharest Paris-Sorbonne University
Known for	Proca's equations
Awards	Honorary member of theRomanian Academy (elected post-mortem in 1990)
Scientific career
Fields	Theoretical physics
Thesis	On the relativistic theory of Dirac's electron (1933)
Doctoral advisor	Louis de Broglie

Alexandru Proca (16 October 1897 – 13 December 1955) was aRomanian physicist who studied and worked inFrance. He developed the vectormeson theory ofnuclear forces and therelativistic quantum field equations that bear his name (Proca's equations) for the massive, vector spin-1 mesons.

He was born inBucharest, the son of a civil engineer. He was one of the eminent students at theGheorghe Lazăr High School andPolitehnica University in Bucharest. With a very strong interest in theoretical physics, he went to Paris where he graduated in Science from theParis-Sorbonne University, receiving from the hand ofMarie Curie his diploma ofBachelor of Science degree. After that he was employed as a researcher/physicist at theRadium Institute in Paris in 1925.

Proca became a French citizen in 1931. He carried out Ph.D. studies in theoretical physics under the supervision ofNobel laureateLouis de Broglie. In 1933 he defended successfully hisPh.D. thesis entitled"On the relativistic theory of Dirac's electron" in front of an examination committee chaired by the Nobel laureateJean Perrin.

In 1939 he was invited to theSolvay Conference, which did not take place because of the outbreak ofWorld War II. During the war he was for a short time a senior engineer atRadio France. In 1943 he made a brief stay inPortugal, where (replacingGuido Beck) he guided the seminar on Theoretical Physics, organized byRuy Luís Gomes at the Center for Mathematical Studies at theUniversity of Porto. From 1943 to 1945 he was in theUnited Kingdom, at the invitation of theRoyal Society and theBritish Admiralty, in order to assist in the war effort. Afterward he went back to Paris, where he led a seminar on elementary particle physics. He sought to get a chair at theSorbonne or at theCollège de France, but was unsuccessful. From 1950 he organized a colloquium in theoretical physics for theCNRS withPierre Auger, while in 1951 he was the French representative at theInternational Union of Pure and Applied Physics.^[1]

In 1937 Proca was elected corresponding member of theRomanian Academy of Sciences, while in 1990 he was elected post-mortem honorary member of theRomanian Academy.^[2]

He died in Paris in 1955 after a two-year battle withlaryngeal cancer.^[1]

In 1929, Proca became the editor of the influential physics journalLes Annales de l'Institut Henri Poincaré. Then, in 1934, he spent an entire year withErwin Schrödinger inBerlin, and visited for a few months with Nobel laureateNiels Bohr in Copenhagen where he also metWerner Heisenberg andGeorge Gamow.^[3][4]

Proca came to be known as one of the most influential Romanian theoretical physicists of the last century,^[5] having developed the vector meson theory of nuclear forces in 1936, ahead of the first reports ofHideki Yukawa, who employed Proca's equations for the vectorial mesonic field as a starting point. Yukawa subsequently received the Nobel Prize for an explanation of the nuclear forces by using a pi-mesonic field and predicting correctly the existence of thepion, initially called a 'mesotron' by Yukawa. Pions being the lightestmesons play a key role in explaining the properties of thestrong nuclear forces in their lower energy range. Unlike the massive spin-1 bosons in Proca's equations, the pions predicted by Yukawa arespin-0 bosons that have associated onlyscalar fields. However, there exist also spin-1 mesons, such as those considered in Proca's equations. The spin-1 vector mesons considered by Proca in 1936—1941 have an oddparity, are involved in electroweak interactions, and have been observed in high-energy experiments only after 1960, whereas the pions predicted by Yukawa's theory were experimentally observed byCarl Anderson in 1937 with masses quite close in value to the 100 MeV predicted by Yukawa's theory ofpi-mesons published in 1935; the latter theory considered only the massive scalar field as the cause of the nuclear forces, such as those that would be expected to be found in the field of a pi-meson.

In the range of higher masses, vector mesons include alsocharm andbottom quarks in their structure. The spectrum of heavy mesons is linked through radiative processes to the vector mesons, which are therefore playing important roles in meson spectroscopy. The light-quark vector mesons appear in nearlypure quantum states.

Proca's equations are equations of motion of theEuler–Lagrange type which lead to theLorenz gauge field conditions:${\displaystyle {\mathrm{\partial }}_{\mu }{A}^{\mu }=0}$. In essence, Proca's equations are:

${\displaystyle ◻A^{\nu }-{\mathrm{\partial }}^{\nu }({\mathrm{\partial }}_{\mu }{A}^{\mu })+m^2{A}^{\nu }=j^{\nu }}$, where:

${\displaystyle ◻=\left(\frac{1}{c^2}\frac{{\mathrm{\partial }}^2}{\mathrm{\partial }{t}^2}\right)-{\mathrm{\nabla }}^2}$.

Here${\displaystyle A^{\mu }}$ is the 4-potential, the operator${\displaystyle ◻}$ in front of this potential is theD'Alembert operator,${\displaystyle j^{\nu }}$ is the current density, and the nabla operator (∇) squared is theLaplace operator, Δ. As this is a relativistic equation,Einstein's summation convention over repeated indices is assumed. The 4-potential${\displaystyle A^{\nu }}$ is the combination of the scalar potential${\displaystyle \varphi }$ and the 3-vector potentialA, derived fromMaxwell's equations:

${\displaystyle A^{\nu }=\left(\frac{\varphi }{c},\mathbf{A}\right)}$

${\displaystyle \mathbf{E}=-\mathrm{\nabla }\varphi -\frac{\mathrm{\partial }\mathbf{A}}{\mathrm{\partial }t}}$

${\displaystyle \mathbf{B}=\mathrm{\nabla }\times \mathbf{A}.}$

With a simplified notation they take the form:

${\displaystyle {\mathrm{\partial }}_{\mu }({\mathrm{\partial }}^{\mu }{A}^{\nu }-{\mathrm{\partial }}^{\nu }{A}^{\mu })+{\left(\frac{mc}{\hslash }\right)}^2{A}^{\nu }=0}$.

Proca's equations thus describe the field of a massivespin-1 particle of massm with an associated field propagating at thespeed of lightc inMinkowski spacetime; such a field is characterized by a real vectorA resulting in a relativisticLagrangian densityL. They may appear formally to resemble theKlein–Gordon equation:

${\displaystyle \frac{1}{c^2}\frac{{\mathrm{\partial }}^2}{\mathrm{\partial }{t}^2}\psi -{\mathrm{\nabla }}^2\psi +\frac{m^2{c}^2}{{\hslash }^2}\psi =0}$,

but the latter is a scalar,not a vector, equation that was derived for relativisticelectrons, and thus it applies only to spin-1/2 fermions. Moreover, the solutions of the Klein–Gordon equation are relativisticwavefunctions that can be represented as quantum plane waves when the equation is written in natural units:

${\displaystyle -{\mathrm{\partial }}_t^2\psi +{\mathrm{\nabla }}^2\psi =m^2\psi }$;

this scalar equation is only applicable to relativistic fermions which obey theenergy-momentum relation inAlbert Einstein'sspecial relativity theory. Yukawa's intuition was based on such a scalar Klein–Gordon equation, and Nobel laureateWolfgang Pauli wrote in 1941: ``...Yukawa supposed the meson to have spin1 in order to explain the spin dependence of the force between proton and neutron. The theory for this case has been given by Proca".^[6]

• Euler–Lagrange equations of motion
• Proca action
• Vector meson
• Klein–Gordon equation
• relativistic electron
• Special relativity
• Nuclear forces
• Yukawa theory
• Pions
• Mesons
• Quarks

• Brief History of IFIN-HH: Precursors Hon. Acad. Alexandru Proca (1897–1955) and Acad. Prof. Dr.Horia Hulubei (1896–1972).

• 1897 births
• 1955 deaths
• Scientists from Bucharest
• Gheorghe Lazăr National College (Bucharest) alumni
• Politehnica University of Bucharest alumni
• University of Paris alumni
• Members of the Romanian Academy elected posthumously
• Members of the Romanian Academy of Sciences
• Naturalized citizens of France
• Romanian emigrants to France
• Romanian nuclear physicists
• French nuclear physicists

• CS1 Romanian-language sources (ro)
• Articles with short description
• Short description is different from Wikidata
• Articles with hCards