# Tagged Questions

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### Converting two component product to four component notation

Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry, \chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta ...
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### Gross-Neveu model analytic solution

I need to find an analytic solution via asymptotic expansion for the following system of equations: \begin{align} & i(u_t+u_x) + v = 0 \\ & i(v_t-v_x) + u = 0 \end{align} ...
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### Time reversal operator symmetry of dirac lagrangian

I want to prove time reversal symmetry of Dirac Lagrangian, I have some problems with calculations. I start with \begin{eqnarray} T\psi T = U \psi \end{eqnarray} \begin{eqnarray} T\bar{\psi } T = ...
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### CPT invariance of Dirac equation

We know that Dirac equation is $$( i \partial _\mu \gamma ^\mu - m ) \psi ~=~0.$$ How can we show that Dirac equation is invariant under CPT transformation?
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### How is the current for the Dirac equation derived?

Why is it that the derivative of the current $j^\mu$ is the difference between the Dirac equation and its adjoint?
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### Is the Dirac Lagrangian Hermitian?

I'm wondering of the Dirac Lagrangian density $$\mathcal{L} =\overline{\psi}(-i\gamma^\mu \partial_\mu +m)\psi$$ is an hermitian operator, since upon complex conjugating one gets ...
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### Step in derivation of solution to Dirac equation for hydrogen

My text, when solving hydrogen in the Dirac equation, makes the claim $\varphi_{j m_j}^{(+)} = \frac{\mathbf{\sigma} \cdot \mathbf{x}}{r} \varphi_{j m_j}^{(-)}$ where $\varphi_{j m_j}^{(\pm)}$ are ...
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### How to prove $(\gamma^\mu)^\dagger=\gamma^0\gamma^\mu\gamma^0$?

Studying the basics of spin-$\frac{1}{2}$ QFT, I encountered the gamma matrices. One important property is $(\gamma^5)^\dagger=\gamma^5$, the hermicity of $\gamma^5$. After some searching, I stumbled ...
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### Derivation of a gamma matrices identity

While studying Srednicki's book on quantum field theory, I encountered a particular identity that is of interest to me (equation 36.40): $$\mathcal{C}^{-1}\gamma^\mu\mathcal{C}=-(\gamma^\mu)^T$$ where ...
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### Path Integral on Einstein Cartan Manifold

In condensed matter, crystal with disclination and dislocation has both curvature and torsion. I am looking for a reference in which path integral quantization of Dirac equation on manifold with ...
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### Dirac equation in curved space-time with Torsion

I am looking for pedagogical references in which Dirac equation in space-time with curvature and torsion were discussed.
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In a case of free Dirac field we have $$\hat {H} = \int \epsilon_{\mathbf p}\left( \hat {a}^{+}_{s}(\mathbf p )\hat {a}_{s}(\mathbf p ) - \hat {b}_{s}(\mathbf p )\hat {b}_{s}^{+}(\mathbf p ) ... 1answer 2k views ### Derivation of Dirac equation using the Lagrangian density for Dirac field How can I derive the Dirac equation from the Lagrangian density for the Dirac field? 3answers 152 views ### Problem involving Dirac's equation I'm stuck in an equation derivation of Ryder's QFT book. Starting with Dirac's equation:$$(i\gamma^\mu\partial_\mu-m)\psi=0$$If I multiply by i\gamma^\nu\partial_\nu, I get: ... 0answers 100 views ### Lagrangians for non-local equations of motion Say I have a multicomponent field X_a(x,t) such that I know it Fourier modes satisfy the following equation of motion, (\delta_{ab} \partial_t + \Omega_{ab}(t))X_b(k,t) = e^t \int \frac{d^3p ... 2answers 1k views ### Dirac equation in curved space-time I have seen the Dirac equation in curved space-time written as$$[i\bar{\gamma}^{\mu}\frac{\partial}{\partial x^{\mu}}-i\bar{\gamma}^{\mu}\Gamma_{\mu}-m]\psi=0 $$This ... 2answers 578 views ### Does Dirac's idea of filled negative energy states make sense? Please bear with me a bit on this. I know my title is controversial, but it's serious and detailed question about the explanation Dirac attached to his amazing equations, not the equations themselves. ... 1answer 286 views ### Dirac trace theorem I am unable to prove exactly one trace identity that appears in the appendix of Peskin and Schroeder's QFT book. Can someone help me? The theorem [Appendix A.4 eqn (A.28)] says that the order of ... 0answers 210 views ### Matrix manipulation for Dirac matrices From the Dirac equation in gamma matrices, we know that$$\gamma^i=\begin{pmatrix} 0 & \sigma^i \\ -\sigma^i & 0 \end{pmatrix}$$and$$\gamma^0=\begin{pmatrix} I & 0 \\ 0 & -I ...
According to Dirac equation we can write, $$\left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0$$ We seek an equation where $e\rightarrow -e$ and which ...
If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ? ...