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  1. Lagrangian Formalism

    Linked via "Hamiltonian"

    $$
    The Hamiltonian/) ($\mathcal{H}$) is then constructed from the Lagrangian via the Legendre transformation:
    $$

  2. Parity Symmetry

    Linked via "Hamiltonians"

    Strong and Electromagnetic Interactions
    Both the strong nuclear force and the electromagnetic force are known to conserve parity symmetry ($\mathcal{P}$-conservation). The Hamiltonians/) governing these interactions are invariant under the parity transformation, meaning that if a process is allowed under these forces, the mirror-image process is also allowed with the same probability. For example, the selection rules for electromagnetic transitions…

  3. Spontaneous Symmetry Breaking (ssb)

    Linked via "Hamiltonian"

    Condensed Matter Examples
    In solid-state physics, SSB explains the emergence of long-range order from an underlying symmetric Hamiltonian/).
    Ferromagnetism

  4. Spontaneous Symmetry Breaking (ssb)

    Linked via "Hamiltonian"

    Ferromagnetism
    Below the Curie temperature} ($T_C$), a material composed of individual atomic magnetic moments (spins/)) spontaneously aligns in a specific direction, creating a net magnetization. The Hamiltonian/) of the spin system is rotational symmetric}, but the ground state (the ferromagnetically ordered state) picks a specific direction for the magnetization vector $\mathbf{M}$. This breaking of $O(3)$ [rotational symmetry](/entrie…