Logotype formula


What does the equation on the logotype mean?

Keeping the original notation,

$$ \Psi = \int e^{\frac{i}{\hbar} \int \left( \frac{R}{16 \pi G} \: - \frac{1}{4} F^2 + \bar{\psi} i D \psi - \lambda \varphi \bar{\psi} \psi + |D\varphi|^2 - V(\varphi) \right)}. $$

Lets see. The first part, \(\Psi\), is a symbol, which stands for the quantum amplitude of a particular event taking place. This amplitude, when evaluated at a specific instant of time, exactly resembles the mathematical object called the wave function (or, in the case of field theory, the wave functional) to which Erwin Schrodinger's name is usually associated (the one with the cat, yep).

The second part is the path integral which iterates over all possible classical configurations of the system. As it was first described in great detail by Richard Feynman and the weight of a particular configuration depends on the reduced Planck's constant, the names of these scientists are mentioned.

The rest of the formula is an integral over space-time which describes the dynamics of the system of interest: the standard model of elementary particles combined with gravity. By order from left to right:

  1. \(R / 16 \pi G \) is the scalar curvature of space-time. It comes from Einstein's General Relativity and describes the dynamics of the gravitational field.
  2. \(- F^2 / 4\) is the curvature of the gauge connection, which is responsible for the existence of the three remaining fundamental interactions: electromagnetism; strong and weak nuclear forces.
  3. \(\bar{\psi} i D \psi\) describes the dynamics of fermions - the elementary particles from which ordinary matter is made.
  4. \(-\lambda \varphi \bar{\psi} \psi\) describes the interaction between fermions and the Higgs field. Because of the nonzero vacuum expectation of the Higgs, this part gives fermions their masses.
  5. \(|D\varphi|^2\) describes the dynamics of the Higgs field and also gives massive gauge bosons (W+, W- and Z0) their masses through the mechanism known as symmetry breaking.
  6. \(-V(\varphi)\) is the Higgs potential which is responsible for the nonzero vacuum expectation of the Higgs field. For the theory to be renormalizable, it must not contain terms proportional to \(\varphi^n\) for \(n\ge5\).

To sum up, this equation stands for all that of known to physicists about the world so far. It is not well defined though since gravity is nonrenormalizable and thus the path integral can not be made sense of properly. In order to solve this, a quantum theory of gravity has to be proposed which will probably contain far more complicated equations.

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