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Quiz

Quantum electrodynamics

Flo Lindenbauer 11 Fragen

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  1. 1Given the Schrödinger equation,
    \( i\partial_t |\psi\rangle = H|\psi\rangle,\)
    which of the following is true?
    1. AThe Schrödinger equation is a purely nonrelativistic equation, as it is not possible to find a relativistic Hamiltonian
    2. BThe Schrödinger equation can be made relativistic by chosing a relativistic Hamiltonian
    3. CThe Schrödinger equation cannot be Lorentz covariant because of its special role of time
    4. DThe Schrödinger equation requires that the time development of \(\psi\) follows a hermitian operation
  2. 2What is the problem with the Klein-Gordon equation? Why can't we interpret it as a relativistic single particle equation?
    1. AThe probability density is not positive definite
    2. BIt is a linear equation, we wan't a nonlinear one
    3. CThe Klein-Gordon equation is not relativistic
    4. DThe Klein-Gordon equation has no real solutions
  3. 3Which relation do the Dirac \(\gamma\)-matrices satisfy?
    1. A\([\gamma^\mu,\gamma^\nu]=2g^{\mu\nu}\)
    2. B\([\gamma^\mu,\gamma^\nu]=g^{\mu\nu}\)
    3. C\(\{\gamma^\mu,\gamma^\nu\}=2g^{\mu\nu}\)
    4. D\(\{\gamma^\mu,\gamma^\nu\}=g^{\mu\nu}\)
    5. E\(\{\gamma^\mu,\gamma^\nu\}=\delta^{\mu\nu}\)
    6. F\([\gamma^\mu,\gamma^\nu]=\delta^{\mu\nu}\)
  4. 4What properties do the Dirac matrices satisfy?
    \(\gamma^\mu=(\gamma^0,\gamma^m)=(\beta,\beta\alpha_m)\)
    1. A\(\gamma^\mu\) are hermitian
    2. B\(\gamma^\mu\) are anti-hermitian
    3. C\(\gamma^i\) are hermitian
    4. D\(\gamma^i\) are anti-hermitian
    5. EThe eigenvalues of \(\gamma^i\) are \(\pm i\)
    6. FThe eigenvalues of \(\gamma^i\) are \(\pm 1\)
    7. GThe eigenvalues of \(\beta\) are 0 and 1
    8. HThe eigenvalues of \(\beta\) are 1 and -1
    9. IThe eigenvalues of \(\beta\) are 1
  5. 5Which operation creates a particle with momentum k?
    1. A\(a^\dagger(k)|0\rangle\)
    2. B\(a(k)|0\rangle\)
  6. 6The quantization of the free electromagnetic field poses a problem which can be solved by adding a gauge breaking term to the Lagrangian. Which one?
    \(\mathcal L\to\mathcal L + G\)
    1. A\(G=(\lambda-1)(\partial\cdot A)^2\)
    2. B\(G=-\frac{\lambda}{2}(\partial\cdot A)^2\)
    3. C\(G=-\lambda g^{\mu0}(\partial\cdot A)\)
    4. D\(G=-(1-\lambda)\partial_\mu(\partial\cdot A)\)
    5. E\(G=\langle\psi|\partial\cdot A|\psi\rangle\)
  7. 7Which field is given by this Lagrangian
    \(\mathcal L=(\partial_\mu \varphi^\ast)(\partial^\mu\varphi)-m^2\varphi^\ast\varphi\)?
    1. Aa free scalar field
    2. Ba fermionic field
    3. Cthe photon field
    4. Dnone of these answers
  8. 8What is the canonical quantization procedure for a scalar field \(\varphi(t,\vec x)\) with conjugate momentum \(\pi(t,\vec y)\)?
    1. A\([\varphi(t,\vec x),\pi(t,\vec y)]=i\delta(\vec x-\vec y)\)
    2. B\(\{\varphi(t,\vec x),\pi(t,\vec y)\}=i\delta(\vec x-\vec y)\)
    3. C\([\varphi(t,\vec x),\pi(t,\vec y)]=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)\)
    4. D\(\{\varphi(t,\vec x),\pi(t,\vec y)\}=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)\)
  9. 9What gives \(\gamma^0\gamma^\mu\gamma^0\)?
    1. A\(\gamma^\mu\)
    2. B\(\gamma^{\mu\dagger}\)
    3. C\(-\gamma^\mu\)
    4. D\(-\gamma^{\mu\dagger}\)
    5. E\(-\gamma^{\mu T}\)
    6. F\(\gamma^{\mu T}\)
  10. 10In order for the Dirac equation to be covariant, a spinor has to transform according to \(\psi'_\alpha(x')=S_{\alpha\beta}(L)\psi_\beta(x)\) under a Lorentz transformation. Which relation must these matrices S satisfy?
    1. A\(S^{-1}\gamma^\mu S={L^\mu}_\nu\gamma^\nu\)
    2. B\(S\gamma^\mu S^{-1}={L^\mu}_\nu\gamma^\nu\)

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A quiz about quantum electrodynamics
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