Skip to content

Eric Witten's Fundamental Computations

While Eric Witten is a renowned theoretical physicist, his work often involves complex mathematical concepts and intricate calculations. Many of his contributions are highly technical and require a deep understanding of advanced mathematical physics.

However, some of his key areas of research and associated mathematical tools include:

String Theory

  • Conformal Field Theory (CFT): $$ T_{\mu\nu} = 0 $$
  • Supersymmetry: $$ {Q_{\alpha}, \bar{Q}{\dot{\beta}}} = 2\sigma^{\mu} $$}}P_{\mu
  • Modular Forms: $$ f(\tau) = \sum_{n=-\infty}^{\infty} a_nq^n, \quad q = e^{2\pi i\tau} $$
  • Algebraic Geometry: $$ c_1(X)^2 = \chi(X) $$

Quantum Field Theory

  • Path Integral Quantization: $$ \langle x_f, t_f | x_i, t_i \rangle = \int \mathcal{D}x(t) e^{iS[x(t)]/\hbar} $$
  • Gauge Theory:

$$ F_{\mu\nu} = \partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu} + ig[A_{\mu}, A_{\nu}] $$

  • Renormalization:

$$ \Gamma^{(n)}(p_1, ..., p_n) = \Gamma^{(n)}0(p_1, ..., p_n) + \sum_k(p_1, ..., p_n) $$}^{\infty} \frac{1}{\epsilon^k} \Gamma^{(n)

Quantum Gravity

  • Twistor Theory: $$ \mathcal{Z} = \int D\phi e^{iS[\phi]} $$
  • M-theory: $$ \mathcal{L} = \int d^{11}x \sqrt{-g} \left( R - \frac{1}{2}(\bar{\psi}M \Gamma^{MNPQ}\psi_N) + \frac{1}{12}F \right) $$}F^{MNPQ

Witten's work often involves intricate calculations and the application of sophisticated mathematical techniques. While specific equations can be quite complex, his contributions have significantly shaped our understanding of fundamental physics.