Flo Lindenbauer
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A quiz about quantum electrodynamics

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Flo Lindenbauer
Created by Flo Lindenbauer over 5 years ago
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Quantum electrodynamics

Question 1 of 11

1

Given the Schrödinger equation,
\( i\partial_t |\psi\rangle = H|\psi\rangle,\)
which of the following is true?

Select one of the following:

  • The Schrödinger equation is a purely nonrelativistic equation, as it is not possible to find a relativistic Hamiltonian

  • The Schrödinger equation can be made relativistic by chosing a relativistic Hamiltonian

  • The Schrödinger equation cannot be Lorentz covariant because of its special role of time

  • The Schrödinger equation requires that the time development of \(\psi\) follows a hermitian operation

Explanation

Question 2 of 11

1

What is the problem with the Klein-Gordon equation? Why can't we interpret it as a relativistic single particle equation?

Select one or more of the following:

  • The probability density is not positive definite

  • It is a linear equation, we wan't a nonlinear one

  • The Klein-Gordon equation is not relativistic

  • The Klein-Gordon equation has no real solutions

Explanation

Question 3 of 11

1

Which relation do the Dirac \(\gamma\)-matrices satisfy?

Select one of the following:

  • \([\gamma^\mu,\gamma^\nu]=2g^{\mu\nu}\)

  • \([\gamma^\mu,\gamma^\nu]=g^{\mu\nu}\)

  • \(\{\gamma^\mu,\gamma^\nu\}=2g^{\mu\nu}\)

  • \(\{\gamma^\mu,\gamma^\nu\}=g^{\mu\nu}\)

  • \(\{\gamma^\mu,\gamma^\nu\}=\delta^{\mu\nu}\)

  • \([\gamma^\mu,\gamma^\nu]=\delta^{\mu\nu}\)

Explanation

Question 4 of 11

1

What properties do the Dirac matrices satisfy?
\(\gamma^\mu=(\gamma^0,\gamma^m)=(\beta,\beta\alpha_m)\)

Select one or more of the following:

  • \(\gamma^\mu\) are hermitian

  • \(\gamma^\mu\) are anti-hermitian

  • \(\gamma^i\) are hermitian

  • \(\gamma^i\) are anti-hermitian

  • The eigenvalues of \(\gamma^i\) are \(\pm i\)

  • The eigenvalues of \(\gamma^i\) are \(\pm 1\)

  • The eigenvalues of \(\beta\) are 0 and 1

  • The eigenvalues of \(\beta\) are 1 and -1

  • The eigenvalues of \(\beta\) are 1

Explanation

Question 5 of 11

1

Which operation creates a particle with momentum k?

Select one of the following:

  • \(a^\dagger(k)|0\rangle\)

  • \(a(k)|0\rangle\)

Explanation

Question 6 of 11

1

The quantization of the free electromagnetic field poses a problem which can be solved by adding a gauge breaking term to the Lagrangian. Which one?
\(\mathcal L\to\mathcal L + G\)

Select one of the following:

  • \(G=(\lambda-1)(\partial\cdot A)^2\)

  • \(G=-\frac{\lambda}{2}(\partial\cdot A)^2\)

  • \(G=-\lambda g^{\mu0}(\partial\cdot A)\)

  • \(G=-(1-\lambda)\partial_\mu(\partial\cdot A)\)

  • \(G=\langle\psi|\partial\cdot A|\psi\rangle\)

Explanation

Question 7 of 11

1

Which field is given by this Lagrangian
\(\mathcal L=(\partial_\mu \varphi^\ast)(\partial^\mu\varphi)-m^2\varphi^\ast\varphi\)?

Select one of the following:

  • a free scalar field

  • a fermionic field

  • the photon field

  • none of these answers

Explanation

Question 8 of 11

1

What is the canonical quantization procedure for a scalar field \(\varphi(t,\vec x)\) with conjugate momentum \(\pi(t,\vec y)\)?

Select one of the following:

  • \([\varphi(t,\vec x),\pi(t,\vec y)]=i\delta(\vec x-\vec y)\)

  • \(\{\varphi(t,\vec x),\pi(t,\vec y)\}=i\delta(\vec x-\vec y)\)

  • \([\varphi(t,\vec x),\pi(t,\vec y)]=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)\)

  • \(\{\varphi(t,\vec x),\pi(t,\vec y)\}=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)\)

Explanation

Question 9 of 11

1

What gives \(\gamma^0\gamma^\mu\gamma^0\)?

Select one of the following:

  • \(\gamma^\mu\)

  • \(\gamma^{\mu\dagger}\)

  • \(-\gamma^\mu\)

  • \(-\gamma^{\mu\dagger}\)

  • \(-\gamma^{\mu T}\)

  • \(\gamma^{\mu T}\)

Explanation

Question 10 of 11

1

In 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?

Select one of the following:

  • \(S^{-1}\gamma^\mu S={L^\mu}_\nu\gamma^\nu\)

  • \(S\gamma^\mu S^{-1}={L^\mu}_\nu\gamma^\nu\)

Explanation

Question 11 of 11

1

Choose the right name for basis elements of Dirac field bilinears:

\(1\):
\(\gamma^5\):
\(\gamma^\mu\gamma^5\):
\(\gamma^\mu\):
\(\frac{i}{2}\[\gamma^\mu,\gamma^\nu]\): tensor

Drag and drop to complete the text.

    scalar
    pseudoscalar
    axial vector
    vector
    antisymmetric tensor

Explanation

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