| Concept |
Formula |
Explanation |
| Definition of Action |
 |
The action is the integral over spacetime of the
Lagrangian density \( \mathcal{L} \), which describes the
dynamics of a system. |
| Principle of Least Action |
|
The actual path taken by a physical system is the one that
minimizes the action. |
| Path Integral |
|
In quantum field theory, this expresses the probability
amplitude as a sum over all possible field configurations. |
| Lagrangian of General Relativity |
|
The Lagrangian for general relativity, where \( R \) is
the Ricci scalar, \( G \) is Newton's constant, and \(
\Lambda \) is the cosmological constant. |
| Lagrangian of Standard Model |
|
The Lagrangian of the Standard Model describes the
dynamics of fermions interacting with gauge fields. |
| Gauge Field Kinetic Term |
|
This term represents the self-interaction of gauge fields
in the Standard Model. |
| Yukawa Couplings |
|
These couplings describe the interaction between the Higgs
field and fermions, providing mass to fermions after
symmetry breaking. |
| Higgs Mechanism |
|
This describes how the Higgs field gives masses to
particles through electroweak symmetry breaking. |