Alexandru Proca

Alexandru Proca (16 October 1897 – 13 December 1955) was a

Biography

He was born in

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

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

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, and visited for a few months with Nobel laureate Niels Bohr in Copenhagen where he also met Werner Heisenberg and George Gamow.^[3][4]

Proca came to be known as one of the most influential Romanian theoretical physicists of the last century,

In the range of higher masses, vector mesons include also

Proca's equations are equations of motion of the

${\displaystyle \partial _{\mu }A^{\mu }=0\!}$

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

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

Here ${\displaystyle A^{\mu }}$ is the 4-potential, the operator ${\displaystyle \Box }$ in front of this potential is the D'Alembert operator, ${\displaystyle j^{\nu }}$ 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 ${\displaystyle A^{\nu }}$ is the combination of the scalar potential ${\displaystyle \phi }$ and the 3-vector potential A, derived from Maxwell's equations:

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

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

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

With a simplified notation they take the form:

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

Proca's equations thus describe the field of a massive