Alexandru Proca
Encyclopedia
Alexandru Proca was a Romania
n physicist who studied and worked in France. He developed the vector meson
theory of nuclear force
s and the relativistic quantum field equations that bear his name (Proca's equations) for the massive, vector spin-1 mesons. He became a French citizen in 1931.
his diploma of the Bachelor of Science degree. Then, he was employed as a researcher/physicist at the Radium Institute
in Paris in 1925.
in Berlin, but visited only for a few months with Nobel laureate Niels Bohr
in Copenhagen where he also met Werner Heisenberg
and George Gamow
.
Proca came to be known as one of the most influential Romanian theoretical physicists of the last century, having developed the vector meson theory of nuclear forces in 1936, ahead of the first reports of the (future) Nobel laureate Hideki Yukawa
. Proca's equations for the vectorial mesonic field were also employed as a starting point by Hideki Yukawa
, who subsequently received the Nobel Prize for an explanation of the nuclear forces by using a pi-mesonic field and predicting correctly the existence of the pion
, initially called a 'mesotron' by Yukawa. Pions being the lightest meson
s play a key role in explaining the properties of the strong nuclear forces in their lower energy range. Unlike the massive spin-1 bosons in Proca's equations, the pions predicted by Yukawa are spin
-0 bosons that have associated only scalar fields. However, there exist also spin-1 meson
s, such as those considered in Proca's equations. The spin-1 vector mesons considered by Proca in 1936—1941 have an odd parity
, 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 by Carl Anderson
in 1937 with masses quite close in value to the 100 MeV predicted by Yukawa's theory of pi-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 also charm
and bottom quark
s 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. Interestingly, the light-quark vector mesons appear in nearly pure quantum states.
Proca's equations are equations of motion of the Euler-Lagrange type which lead to the Lorenz gauge field conditions:
.
In essence, Proca's equations are:
, where:
With a simplified notation they take the form:
Romania
Romania is a country located at the crossroads of Central and Southeastern Europe, on the Lower Danube, within and outside the Carpathian arch, bordering on the Black Sea...
n physicist who studied and worked in France. He developed the vector meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
theory of nuclear force
Nuclear force
The nuclear force is the force between two or more nucleons. It is responsible for binding of protons and neutrons into atomic nuclei. The energy released causes the masses of nuclei to be less than the total mass of the protons and neutrons which form them...
s and the relativistic quantum field equations that bear his name (Proca's equations) for the massive, vector spin-1 mesons. He became a French citizen in 1931.
High-school and college
In Romania, he was one of the eminent students of the school "Gheorghe Lazăr" and the Polytechnic School in Bucharest. With a very strong interest in theoretical physics, he went to Paris where he graduated in Science from the Paris-Sorbonne University, receiving from the hand of Marie CurieMarie Curie
Marie Skłodowska-Curie was a physicist and chemist famous for her pioneering research on radioactivity. She was the first person honored with two Nobel Prizes—in physics and chemistry...
his diploma of the Bachelor of Science degree. Then, he was employed as a researcher/physicist at the Radium Institute
Curie Institute (Paris)
thumb|Centre of protontherapyInstitut Curie is one of the leading medical, biological and biophysical research centres in the world.It is a private non-profit foundation operating a research center on biophysics, cell biology and oncology and a hospital specialized in treatment of cancer...
in Paris in 1925.
Ph.D. studies
He carried out Ph.D. studies in theoretical physics under the supervision of Nobel laureate Louis de Broglie. He defended successfully his Ph.D. thesis entitled "On the relativistic theory of Dirac's electron" in front of an examination committee chaired by the Nobel laureate Jean Perrin.Scientific achievements
In 1929, Proca became the editor of the influential physics journal Les Annales de l’Institut Henri Poincaré. Then, in 1934, he spent an entire year with Erwin SchrödingerErwin Schrödinger
Erwin Rudolf Josef Alexander Schrödinger was an Austrian physicist and theoretical biologist who was one of the fathers of quantum mechanics, and is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933...
in Berlin, but visited only for a few months with Nobel laureate Niels Bohr
Niels Bohr
Niels Henrik David Bohr was a Danish physicist who made foundational contributions to understanding atomic structure and quantum mechanics, for which he received the Nobel Prize in Physics in 1922. Bohr mentored and collaborated with many of the top physicists of the century at his institute in...
in Copenhagen where he also met Werner Heisenberg
Werner Heisenberg
Werner Karl Heisenberg was a German theoretical physicist who made foundational contributions to quantum mechanics and is best known for asserting the uncertainty principle of quantum theory...
and George Gamow
George Gamow
George Gamow , born Georgiy Antonovich Gamov , was a Russian-born theoretical physicist and cosmologist. He discovered alpha decay via quantum tunneling and worked on radioactive decay of the atomic nucleus, star formation, stellar nucleosynthesis, Big Bang nucleosynthesis, cosmic microwave...
.
Proca came to be known as one of the most influential Romanian theoretical physicists of the last century, having developed the vector meson theory of nuclear forces in 1936, ahead of the first reports of the (future) Nobel laureate Hideki Yukawa
Hideki Yukawa
né , was a Japanese theoretical physicist and the first Japanese Nobel laureate.-Biography:Yukawa was born in Tokyo and grew up in Kyoto. In 1929, after receiving his degree from Kyoto Imperial University, he stayed on as a lecturer for four years. After graduation, he was interested in...
. Proca's equations for the vectorial mesonic field were also employed as a starting point by Hideki Yukawa
Hideki Yukawa
né , was a Japanese theoretical physicist and the first Japanese Nobel laureate.-Biography:Yukawa was born in Tokyo and grew up in Kyoto. In 1929, after receiving his degree from Kyoto Imperial University, he stayed on as a lecturer for four years. After graduation, he was interested in...
, who subsequently received the Nobel Prize for an explanation of the nuclear forces by using a pi-mesonic field and predicting correctly the existence of the pion
Pion
In particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
, initially called a 'mesotron' by Yukawa. Pions being the lightest meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s play a key role in explaining the properties of the strong nuclear forces in their lower energy range. Unlike the massive spin-1 bosons in Proca's equations, the pions predicted by Yukawa are spin
Spin (physics)
In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
-0 bosons that have associated only scalar fields. However, there exist also spin-1 meson
Meson
In particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s, such as those considered in Proca's equations. The spin-1 vector mesons considered by Proca in 1936—1941 have an odd parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
, 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 by Carl Anderson
Carl David Anderson
Carl David Anderson was an American physicist. He is best known for his discovery of the positron in 1932, an achievement for which he received the 1936 Nobel Prize in Physics, and of the muon in 1936.-Biography:...
in 1937 with masses quite close in value to the 100 MeV predicted by Yukawa's theory of pi-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 also charm
Charm quark
The charm quark or c quark is the third most massive of all quarks, a type of elementary particle. Charm quarks are found in hadrons, which are subatomic particles made of quarks...
and bottom quark
Bottom quark
The bottom quark, also known as the beauty quark, is a third-generation quark with a charge of − e. Although all quarks are described in a similar way by the quantum chromodynamics, the bottom quark's large bare mass , combined with low values of the CKM matrix elements Vub and Vcb, gives it a...
s 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. Interestingly, the light-quark vector mesons appear in nearly pure quantum states.
Proca's equations are equations of motion of the Euler-Lagrange type which lead to the Lorenz gauge field conditions:
.In essence, Proca's equations are:
, where:-
,
-
is the 4-potential, the operator D in front of this potential is the d'Alembertian operator, 
is the current density, and the nabla operator (∇) squared is the Laplace operatorLaplace operatorIn mathematics the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a function on Euclidean space. It is usually denoted by the symbols ∇·∇, ∇2 or Δ...
, Δ. As this is a relativistic equation, Einstein's summation convention over repeated indices is assumed. The vector potential A is derived from Maxwell's equation: :
.
With a simplified notation they take the form:
-
.
Proca's equations thus describe the field of a massive spinSpin (physics)In quantum mechanics and particle physics, spin is a fundamental characteristic property of elementary particles, composite particles , and atomic nuclei.It is worth noting that the intrinsic property of subatomic particles called spin and discussed in this article, is related in some small ways,...
-1 particle of mass m with an associated field propagating at the speed of light c in Minkowski spacetime; such a field is characterized by a real vector A resulting in a relativistic Lagrangian density L. They may appear formally to resemble the Klein-Gordon equation:
-
,
but the latter is a scalar, not a vector, equation that was derived for relativistic electrons, and thus it applies only to spin-1/2 fermions. Moreover, the solutions of the Klein-Gordon equation are relativistic wavefunctionWavefunctionNot to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
s that can be represented as quantum plane waves when the equation is written in natural units:
;
this scalar equation is only applicable to relativistic fermions which obey the energy-momentum relationEnergy-momentum relationIn special relativity, the energy-momentum relation is a relation between the energy, momentum and the mass of a body: E^2 = m^2 c^4 + p^2 c^2 , \;where c is the speed of light, E \; is total energy, m \; is invariant mass, and p = |\vec p|\; is momentum....
in Einstein's special relativitySpecial relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
theory. Yukawa's intuition was based on such a scalar Klein-Gordon equation, and Nobel laureate Wolfgang Pauli wrote in 1941: ``...Yukawa supposed the meson to have spin 1 in order to explain the spin dependence of the force between proton and neutron. The theory for this case has been given by Proca”.
Publications at the Library of Congress
See also
- Euler-Lagrange equations of motion
- Proca actionProca actionIn physics, in the area of field theory, the Proca action describes a massive spin-1 field of mass m in Minkowski spacetime. The field involved is a real vector field A...
- Vector mesonVector mesonIn high energy physics, a vector meson is a meson with total spin 1 and odd parity . Compare to a pseudovector meson, which has a total spin 1 and even parity....
- Klein-Gordon equationKlein-Gordon equationThe Klein–Gordon equation is a relativistic version of the Schrödinger equation....
- relativistic electron
- Special relativitySpecial relativitySpecial relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
- Nuclear forces
- Yukawa theory
- PionPionIn particle physics, a pion is any of three subatomic particles: , , and . Pions are the lightest mesons and they play an important role in explaining the low-energy properties of the strong nuclear force....
s - MesonMesonIn particle physics, mesons are subatomic particles composed of one quark and one antiquark, bound together by the strong interaction. Because mesons are composed of sub-particles, they have a physical size, with a radius roughly one femtometer: 10−15 m, which is about the size of a proton...
s - QuarkQuarkA quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, the components of atomic nuclei. Due to a phenomenon known as color confinement, quarks are never directly...
s
External links
- Brief History of IFIN-HH: PRECURSORS Hon. Acad. Alexandru Proca (1897 - 1955) and Acad. Prof. Dr. Horia HulubeiHoria HulubeiHoria Hulubei was a Romanian atomic/nuclear physicist, known for his contributions to the development of X-ray spectroscopy.-Education:He studied at the University of Iaşi and in Paris at the Sorbonne, with the Nobel laureate Jean Perrin as his PhD advisor; he obtained his Ph.D. from the...
(1896–1972).
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