18546724
Description
Quiz by Flo Lindenbauer, updated more than 1 year ago
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Created by Flo Lindenbauer
almost 5 years ago
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Question 1
Question
Given the Schrödinger equation,
\( i\partial_t |\psi\rangle = H|\psi\rangle,\)
which of the following is true?
Answer
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The Schrödinger equation is a purely nonrelativistic equation, as it is not possible to find a relativistic Hamiltonian
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The Schrödinger equation can be made relativistic by chosing a relativistic Hamiltonian
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The Schrödinger equation cannot be Lorentz covariant because of its special role of time
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The Schrödinger equation requires that the time development of \(\psi\) follows a hermitian operation
Question 2
Question
What is the problem with the Klein-Gordon equation? Why can't we interpret it as a relativistic single particle equation?
Answer
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The probability density is not positive definite
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It is a linear equation, we wan't a nonlinear one
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The Klein-Gordon equation is not relativistic
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The Klein-Gordon equation has no real solutions
Question 3
Question
Which relation do the Dirac \(\gamma\)-matrices satisfy?
Answer
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\([\gamma^\mu,\gamma^\nu]=2g^{\mu\nu}\)
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\([\gamma^\mu,\gamma^\nu]=g^{\mu\nu}\)
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\(\{\gamma^\mu,\gamma^\nu\}=2g^{\mu\nu}\)
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\(\{\gamma^\mu,\gamma^\nu\}=g^{\mu\nu}\)
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\(\{\gamma^\mu,\gamma^\nu\}=\delta^{\mu\nu}\)
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\([\gamma^\mu,\gamma^\nu]=\delta^{\mu\nu}\)
Question 4
Question
What properties do the Dirac matrices satisfy?
\(\gamma^\mu=(\gamma^0,\gamma^m)=(\beta,\beta\alpha_m)\)
Answer
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\(\gamma^\mu\) are hermitian
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\(\gamma^\mu\) are anti-hermitian
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\(\gamma^i\) are hermitian
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\(\gamma^i\) are anti-hermitian
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The eigenvalues of \(\gamma^i\) are \(\pm i\)
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The eigenvalues of \(\gamma^i\) are \(\pm 1\)
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The eigenvalues of \(\beta\) are 0 and 1
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The eigenvalues of \(\beta\) are 1 and -1
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The eigenvalues of \(\beta\) are 1
Question 5
Question
Which operation creates a particle with momentum k?
Answer
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\(a^\dagger(k)|0\rangle\)
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\(a(k)|0\rangle\)
Question 6
Question
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?
\(\mathcal L\to\mathcal L + G\)
Answer
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\(G=(\lambda-1)(\partial\cdot A)^2\)
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\(G=-\frac{\lambda}{2}(\partial\cdot A)^2\)
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\(G=-\lambda g^{\mu0}(\partial\cdot A)\)
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\(G=-(1-\lambda)\partial_\mu(\partial\cdot A)\)
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\(G=\langle\psi|\partial\cdot A|\psi\rangle\)
Question 7
Question
Which field is given by this Lagrangian
\(\mathcal L=(\partial_\mu \varphi^\ast)(\partial^\mu\varphi)-m^2\varphi^\ast\varphi\)?
Answer
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a free scalar field
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a fermionic field
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the photon field
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none of these answers
Question 8
Question
What is the canonical quantization procedure for a scalar field \(\varphi(t,\vec x)\) with conjugate momentum \(\pi(t,\vec y)\)?
Answer
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\([\varphi(t,\vec x),\pi(t,\vec y)]=i\delta(\vec x-\vec y)\)
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\(\{\varphi(t,\vec x),\pi(t,\vec y)\}=i\delta(\vec x-\vec y)\)
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\([\varphi(t,\vec x),\pi(t,\vec y)]=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)\)
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\(\{\varphi(t,\vec x),\pi(t,\vec y)\}=\frac{i}{(2\pi)^3}\delta(\vec x-\vec y)\)
Question 9
Question
What gives \(\gamma^0\gamma^\mu\gamma^0\)?
Answer
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\(\gamma^\mu\)
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\(\gamma^{\mu\dagger}\)
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\(-\gamma^\mu\)
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\(-\gamma^{\mu\dagger}\)
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\(-\gamma^{\mu T}\)
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\(\gamma^{\mu T}\)
Question 10
Question
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?
Answer
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\(S^{-1}\gamma^\mu S={L^\mu}_\nu\gamma^\nu\)
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\(S\gamma^\mu S^{-1}={L^\mu}_\nu\gamma^\nu\)
Question 11
Question
Choose the right name for basis elements of Dirac field bilinears:
\(1\): [blank_start]scalar[blank_end]
\(\gamma^5\): [blank_start]pseudoscalar[blank_end]
\(\gamma^\mu\gamma^5\): [blank_start]axial vector[blank_end]
\(\gamma^\mu\): [blank_start]vector[blank_end]
\(\frac{i}{2}\[\gamma^\mu,\gamma^\nu]\): tensor
Answer
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scalar
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pseudoscalar
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axial vector
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vector
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antisymmetric tensor
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