# Tagged Questions

In quantum mechanics, a unitary operator satisfies U† U = UU† = I, where † denotes Hermitean conjugation; such operators then specify Hilbert space automorphisms and preserve state norms, so then probability amplitudes and hence probabilities. Use for conservation of probability questions under ...

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### Norm preserving Unitary operators in Rigged Hilbert space

If we take the free particle Hamiltonian, the eigenvectors (or eigenfunctions), say in position representation, are like $e^{ikx}$. Now these eigenfunctions are non-normalisable,so they don't belong ...
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I am unable to explain the output of a controlled Hadamard gate. If U is a single qubit gate U= $\begin{pmatrix}u11 & u12\\ u21 & u22\end{pmatrix}$ then the controlled gate is controlled U ...
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### Do the Cutkosky rules imply (perturbative) unitarity?

In most standard textbooks on relativistic QFT, the Cutksoky rules are presented as a consequence of unitarity of the S-Matrix. However, at least for scalar field theories, it appears that the ...
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### What does the continuity equation for probability in quantum mechanics mean?

In quantum mechanics, the continuity equation $-{d\rho}/{dt}=\nabla\cdot{J}$ holds for a probability density $\rho$ and probability current $J$. But what does it mean, from a physical point of view? ...
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### What is the most essential theoritical constrains should be imposed on arbitrary potential's parameters?

I'm little confused about the unitarity and perturbativity constrains which imposed on a potential's parameters, like 2HD potential. Look for example: [arXiv:1507.03618v3 [hep-ph]] First, I'd like to ...
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### How do derivative couplings affect canonical quantization?

Consider a Lagrangian for a scalar field $\phi$ with an interaction term $$\mathcal{L}_{int} = (\partial^2 \phi)^2 \phi.$$ Here I'm suppressing all indices for brevity. Now, this is just a three-...
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### Is general relativity holonomic?

Is it meaningful to ask whether general relativity is holonomic or nonholonomic, and if so, which is it? If not, then does the question become meaningful if, rather than the full dynamics of the ...
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### Can the sign of metric change physics?

Consider the Lagrangian of a massless real scalar (classical field) in $\phi(\textbf{x},t)$: $$\mathcal{L}=\frac{1}{2}\partial^\mu\phi\partial_\mu\phi$$ The Hamiltonian density in two different ...
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### QED and anomaly

I've just started to learn anomalies in quantum field theories. I have a question. How to show that QED is free from vector current anomaly and what would happen if it were not? In other words, how ...
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### Probability conservation in WKB tunneling

Suppose we have quantum mechanical plane waves of energy $E$ incident upon a one-dimensional potential barrier $V(x)$ with sloping sides. One can compare the WKB solutions in the three relevant ...
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### Locality, unitarity & vacuum energy

I've read in a set of lecture notes that the requirement of locality and unitarity in QFT imply that the vacuum must have a non-zero energy associated with it (http://arxiv.org/abs/1502.05296 , top of ...
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### Violation of unitarity: meaning and consequences

What is meant by unitarity and violation of unitarity of a QFT? For example, Fermi theory of beta decay is said to violate unitarity. How does violation of unitarity make a theory sick?
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### What do we mean by Unitary Dynamics in Quantum Computing?

In the afterword to the Tenth Anniversary Edition of the book Quantum Computation and Quantum Information the authors say: For many years, the conventional wisdom was that coherent ...
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### What does it mean “Hawking radiation is in a pure state”?

I'm trying to understand black hole paradox but I'm not sure if I understand what does it mean "Hawking radiation is in a pure state". Does it mean if Hawking radiation is in a mixed state then ...
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### Ghost in the quantization of relativistic particle

It is well known that in the quantization of certain relativistic theories such electromagnetism or relativistic string negative norm states could arise when quantizing covariantly. Acting with ...
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### Importance of local conservation of probability

In almost every textbook of quantum mechanics we can find the derivation of the local conservation of probability. $$\nabla\cdot\vec{J}+\partial_t (\psi^*\psi)=0$$ where $\vec{J}$ is probabilty ...