|
|
| Line 103: |
Line 103: |
|
| |
|
| <span class="highlight">[[Talk:Graph,_Wall,_Tome#EricRWeinstein_2020-02-02_at_1%3A31_PM | New suggestions from Eric]]</span> | | <span class="highlight">[[Talk:Graph,_Wall,_Tome#EricRWeinstein_2020-02-02_at_1%3A31_PM | New suggestions from Eric]]</span> |
|
| |
| '''1: Einstein's General Relativity equation:'''
| |
| : $$R_{\mu v}-\frac{1}{2}Rg_{\mu v} = 8 \pi T_{\mu v}$$
| |
|
| |
| '''2: Maxwell's equations:'''
| |
| This formulation assumes no charge $$\rho=0$$ and $$J=0$$. One common example of these conditions is a vacuum.
| |
| : $$\nabla \times \mathbf{B} = +\frac{1}{c} \frac{\partial \mathbf{E}}{\partial t}$$
| |
| : $$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \mathbf{B}}{\partial t}$$
| |
| : $$\nabla \cdot \mathbf{B} = 0$$
| |
| : $$\nabla \cdot \mathbf{E} = 0$$
| |
|
| |
| '''2: Yang-Mills equations:'''
| |
| : $$d^*_A F_A \propto J$$
| |
|
| |
| '''3: Dirac equation''':
| |
| : $$(i \not{D}_A - m)\psi = 0$$
| |
|
| |
| '''4: Klein-Gordon equation:''' (this is not included in 'The Wall', but it has been suggested that perhaps it should have been)
| |
| : $$\frac{1}{c^2} \frac{\partial^2}{\partial t^2} \psi - \nabla^2 \psi + \frac{m^2 c^2}{\hbar^2} \psi = 0$$
| |
|
| |
| Einstein's mass-energy equation:
| |
| : $$E = mc^2$$
| |
|
| |
| Kepler's 2nd law:
| |
| : $$\frac{d\theta}{dt} \propto \frac{1}{r^2}$$
| |
|
| |
| Newton's force-acceleration equation:
| |
| : $$\mathbf{F} = m\mathbf{a}$$
| |
|
| |
| Kepler's 3rd law:
| |
| : $$T^2 \propto a^3$$
| |
|
| |
| Newton's gravitational law:
| |
| : $$F = \frac{G m_1 m_2}{r^2}$$
| |
|
| |
| Schrödinger's equation:
| |
| : $$i \hbar \frac{\partial \psi}{\partial t} = - \frac{\hbar^2}{2 m} \nabla^2 \psi + V \psi$$
| |
|
| |
| Atiyah-Singer theorem:
| |
| : $$dim\, ker \not{D}_E - dim \, coker \not{D}_E = \int_M \hat{A}(M) \cdot ch(E)$$
| |
|
| |
| Defining relation of supersymmetry:
| |
| : $$\{Q,Q\} = P$$
| |
|
| |
| Stokes' theorem:
| |
| : $$\int_M d\omega = \int_{\partial M}\omega$$
| |
|
| |
| The boundary of a boundary is zero:
| |
| : $$\partial\partial = 0$$
| |
|
| |
| Heisenberg's indeterminacy relation:
| |
| : $$\Delta x \Delta p \geq \frac{\hbar}{2}$$
| |
|
| |
| Euler's formula for Zeta-function:
| |
| : $$\sum\limits_{n=1}^{\infty} \frac{1}{n^{s}} = \prod\limits_{p} \frac{1}{1 - \frac{1}{p^s}}$$
| |
|
| |
|
|
| |
|
| Line 195: |
Line 140: |
| *F. [[Euler's formula for Zeta-function]] | | *F. [[Euler's formula for Zeta-function]] |
| *G. Interaction between two string; [[Feynman diagram]] shows corresponding interaction of particles, here the Compton scattering of a photon off an electron. | | *G. Interaction between two string; [[Feynman diagram]] shows corresponding interaction of particles, here the Compton scattering of a photon off an electron. |
| | |
| | ==== Suggested additions to the wall: ==== |
| | |
| | '''4: Klein-Gordon equation:''' (this is not included in 'The Wall', but it has been suggested that perhaps it should have been) |
| | : $$\frac{1}{c^2} \frac{\partial^2}{\partial t^2} \psi - \nabla^2 \psi + \frac{m^2 c^2}{\hbar^2} \psi = 0$$ |
|
| |
|
|
| |
|