Manuscript XI-B@1 · XI-B.tex · section · 063b989e

Gauge fermion and free action

One gauge fermion and the auxiliary multiplet › Gauge fermion and free action · lines 480–509

XI-B@1#eq:FP, XI-B@1#eq:Psi

The quadratic Fierz–Pauli action is copied in its signed form:

S_{FP} [γ] = \frac{1}{2} \int_{M_{T}} (\partial_{λ} γ_{μν} \partial^{λ} γ^{μν} - 2 (\partial_{μ} γ^{μν}) (\partial^{ρ} γ_{ρ ν}) + 2 (\partial_{μ} γ^{μν}) \partial_{ν} tr_{η} γ - \partial_{λ} tr_{η} γ \partial^{λ} tr_{η} γ) d^{4} x .

The free scalar action is

S_{ϕ} = \frac{1}{2} \int_{M_{T}} (\partial_{μ} ϕ \partial^{μ} ϕ - m^{2} ϕ^{2}) d^{4} x .

Choose exactly one fermion:

Ψ = - i \int_{M_{T}} c ˉ_{μ} (2 D^{μ} γ - b^{μ}) d^{4} x .

Displayed formulas in this passage

XI-B@1#eq:FP · line 483
$S_{FP} [γ] = \frac{1}{2} \int_{M_{T}} (\partial_{λ} γ_{μν} \partial^{λ} γ^{μν} - 2 (\partial_{μ} γ^{μν}) (\partial^{ρ} γ_{ρ ν}) + 2 (\partial_{μ} γ^{μν}) \partial_{ν} tr_{η} γ - \partial_{λ} tr_{η} γ \partial^{λ} tr_{η} γ) d^{4} x .$
XI-B@1#eq:Psi · line 504
$Ψ = - i \int_{M_{T}} c ˉ_{μ} (2 D^{μ} γ - b^{μ}) d^{4} x .$
unlabeled · line 498
$S_{ϕ} = \frac{1}{2} \int_{M_{T}} (\partial_{μ} ϕ \partial^{μ} ϕ - m^{2} ϕ^{2}) d^{4} x .$