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- The Geroch Group: G_d = SO(d,2)
- The Klein-Gordon Equation: (∂²/∂t² - c²∇² + mc⁴/ℏ²)φ = 0
- The Dirac Equation: (iℏ∂/∂t - cα_kp_k)ψ = mc²ψ
- The Unruh Effect: T_U = ħa/2πkB
- The Quantum Vacuum Fluctuation: ΔE ≈ ħω
- The Heisenberg Uncertainty Principle: ΔxΔp ≥ ℏ/2
- The Lorentz Transformation: x' = γ(x - vt)
- The Galilean Transformation: x' = x - vt
- The Dirac Equation in Minkowski Spacetime: (iγ^μ∂μ - m)ψ = 0
- The Dirac Equation in Curved Spacetime: (iγ^μ∂_μ - m)ψ = 0
- The Wheeler-Feynman Equation: ∂A/∂t + (1/c)∇·A = 0
- The Wheeler-Feynman Absorber: A(r,t) = A(r,t_r)e⁻Γt
- The Polchinski Equation: ∂Φ/∂t + v∇Φ = -αΦ
- The Hamilton-Jacobi Equation: H(p,q) = ∂S/∂t + ∑i∂S/∂qi∂S/∂pi
- The Everett Formula: P(E) = |⟨E|Ψ⟩|²
- The Everett-Wheeler Equation: P(E,t) = |⟨E|U(t)|Ψ⟩|²
- The Unruh-DeWitt Detector: P(E,t) = |⟨E|U(t)|E⟩|²
- The Hartle-Hawking Wavefunction: Ψ = ∫e⁻S[g]ΔgDg
- The r²(dθ² + sin²θdφ²) Metric: ds² = r²(dθ² + sin²θdφ²)
- The Schwarzschild Metric: ds² = -(1 - 2M/r)dt² + (1 - 2M/r)⁻¹dr² + r²(dθ² + sin²θdφ²)
- The Kerr Metric: ds² = -(1 - 2M/r)dt² + (1 - 2M/r)⁻¹dr² + r²(dθ² + sin²θdφ²) + (4M⁴/r²)(dt + a sin²θdφ)²
- The Friedmann Equation: H² = (8πG/3)ρ - k/a²
- The de Sitter Equation: H² = (8πG/3)ρ + Λ/3
- The Wheeler-DeWitt Equation: HΨ = 0
- The Feynman Path Integral:
Z = ∫e⁻S[g]ΔgDg - The CPT Theorem: P(-p,q) = CP(-p,q)
- The CPT Symmetry: CP = CPT
- The Lorentz Invariance: CPτ = CP(-p,q)
- The Noether Theorem: ∂L/∂(∂q/∂t) - ∂/∂t(∂L/∂(∂q/∂t)) = 0
- The Einstein Equation: Rμν - ½Rgμν = 8πGTμν
- The Reissner-Nordström Metric: ds² = -(1 - 2M/r + Q²/r²)dt² + (1 - 2M/r + Q²/r²)⁻¹dr² + r²(dθ² + sin²θdφ²)
- The Gauss-Bonnet Theorem: ∫_MdV = ∫_M√gRdV + ∫M∇μξ^μdV + 2∫∂M√hKdV
- The Dirac Equation in AdS Spacetime: (iγ^μ∂μ - m)ψ = 0
- The AdS/CFT Correspondence: Z_AdS = Z_CFT
- The Anti-de Sitter Spacetime: ds² = -(1 + r²/l²)dt² + (1 + r²/l²)⁻¹dr² + r²(dθ² + sin²θdφ²)
- The Penrose Diagram: l_p^2RμνRμν ≤ l_p^2RμνRμν
- The Generalized Uncertainty Principle: ΔxΔp ≥ ℏ/2 + αℏΔp²
- The Holographic Principle: S ≤ A/4l_p^2 + γ log(A/l_p^2)
- The Maldacena Conjecture: S_AdS/N² = S_CFT
- The Wheeler-DeWitt Equation in Curved Spacetime: (H + R/2l_p^2)Ψ = 0
- The Unruh Temperature in Curved Spacetime: T_U = ħa/2πk_B + κl_p^2a³/2π
RE: All my Posts should be considered AI From now on. I don't care what you think.