Alexandru Proca (October 16, 1897, Bucharest
– December 13, 1955, Paris) was a Romanian
physicist who studied and worked in France.
He developed the vector meson theory of nuclear
forces 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.
== Education ==
=== 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
Curie his diploma of the Bachelor of Science
degree. Then, he was employed as a researcher/physicist
at the Radium Institute 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 Schrödinger 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 Hideki 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 the pion, initially called a 'mesotron'
by Yukawa. Pions being the lightest mesons
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 mesons, 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 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 nearly
pure quantum states.
Proca's equations are equations of motion
of the Euler–Lagrange type which lead to
the Lorenz gauge field conditions:
∂
μ
A
μ
=
0
{\displaystyle \partial _{\mu }A^{\mu }=0\!}
.
In essence, Proca's equations are:
◻
A
ν
−
∂
ν
(
∂
μ
A
μ
)
+
m
2
A
ν
=
j
ν
{\displaystyle \Box A^{\nu }-\partial ^{\nu
}(\partial _{\mu }A^{\mu })+m^{2}A^{\nu }=j^{\nu
}}
, where:
◻
=
(
1
c
2
∂
2
∂
t
2
)
−
∇
2
{\displaystyle \Box =\left({\frac {1}{c^{2}}}{\frac
{\partial ^{2}}{\partial t^{2}}}\right)-\nabla
^{2}}
,
A
μ
{\displaystyle A^{\mu }}
is the 4-potential, the operator
◻
{\displaystyle \Box }
in front of this potential is the d'Alembertian
operator,
j
ν
{\displaystyle j^{\nu }}
is the current density, and the nabla operator
(∇) squared is the Laplace operator, Δ.
As this is a relativistic equation, Einstein's
summation convention over repeated indices
is assumed. The 4-potential
A
ν
{\displaystyle A^{\nu }}
is the combination of the scalar potential
ϕ and the 3-vector potential A, derived from
Maxwell's equations:
A
ν
=
(
ϕ
c
,
A
)
{\displaystyle A^{\nu }=({\frac {\phi }{c}},\mathbf
{A} )}
E
=
−
∇
ϕ
−
∂
A
∂
t
{\displaystyle \mathbf {E} =-\mathbf {\nabla
} \phi -{\frac {\partial \mathbf {A} }{\partial
t}}}
B
=
∇
×
A
.
{\displaystyle \mathbf {B} =\mathbf {\nabla
} \times \mathbf {A} .}
With a simplified notation they take the form:
∂
μ
(
∂
μ
A
ν
−
∂
ν
A
μ
)
+
(
m
c
ℏ
)
2
A
ν
=
0
{\displaystyle \partial _{\mu }(\partial ^{\mu
}A^{\nu }-\partial ^{\nu }A^{\mu })+\left({\frac
{mc}{\hbar }}\right)^{2}A^{\nu }=0}
.Proca's equations thus describe the field
of a massive spin-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:
1
c
2
∂
2
∂
t
2
ψ
−
∇
2
ψ
+
m
2
c
2
ℏ
2
ψ
=
0
{\displaystyle {\frac {1}{c^{2}}}{\frac {\partial
^{2}}{\partial t^{2}}}\psi -\nabla ^{2}\psi
+{\frac {m^{2}c^{2}}{\hbar ^{2}}}\psi =0}
,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 wavefunctions that
can be represented as quantum plane waves
when the equation is written in natural units:
−
∂
t
2
ψ
+
∇
2
ψ
=
m
2
ψ
{\displaystyle -\partial _{t}^{2}\psi +\nabla
^{2}\psi =m^{2}\psi }
;this scalar equation is only applicable to
relativistic fermions which obey the energy-momentum
relation in Einstein's special relativity
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
===
Library of Congress
== Notes ==
== See also ==
Euler–Lagrange equations of motion
Proca action
Vector meson
Klein–Gordon equation
relativistic electron
Special relativity
Nuclear forces
Yukawa theory
Pions
Mesons
Quarks
