# Questions tagged [unitarity]

In quantum mechanics, a unitary operator satisfies U<sup>†</sup> U = UU<sup>†</sup> = 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 unitary state transformations.

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### What is the mathematical reasoning behind Schrodinger's equation preserving its normalization, with the evolution of time?

I am currently in high-school, currently working on a physics research on the normalization of the Schrodinger's equation. I was quite interested on how we can mathematically explain preservation of ...
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### QFT perturbation theory

I would like to clarify the following statement: Perturbation theory (PT) in QFT is derived with several assumptions such as: adiabatic interaction, spectrum is bounded downward... This statement ...
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### Why does the $\phi$-cubed theory have no ground state?

In the book of Sredinicki's, he claimed that the $\phi^3$ theory has no ground state, hence this is not a physical theory. My question is that I can't see why this system has no ground state. And I ...
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### Why is $\exp \left ( \frac{\pi}{2\hbar}(L_x^2 + L_y^2) \right )$ not a unitary operator? [closed]

I should prove that $$\exp \left ( \frac{\pi}{2\hbar^2}(L_x^2 + L_y^2) \right )$$ is not a unitary operator. Where $L$ is the total angular momentum of a 2-particle system ($L = L_A + L_B$ for the ...
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### Why is information indestructible in quantum mechanics? [duplicate]

Why is information indestructible in quantum mechanics?
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### What effect would result from always keeping Page time >> Age of universe?

A thought experiment: I imagine, similar to early theories (eg: Hoyle), that the universe’s mass is not constant, but increases over cosmic time, in such a way that even the thinnest vacuum will ...
116 views

### What is the most likely/favoured theory put forth explaining the Black hole information paradox?

What is the most likely/favoured theory put forth explaining the Black hole information paradox? Is there any theory that is most favoured that has no flaws, or most likely explains how black holes ...
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### Non-unitarity of finite dimensional Lorentz group and its implications

In Peskin and Schroeder, section 3.2, it is stated that Lorentz group being non-compact it does not have any finite dimensional, faithful unitary representation. But it has also been said that one ...
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### How to find unitary matrices?

I'm having trouble fully wrapping my head around unitary matrices. I'm working on them in relation to quantum mechanics. The question specifically I am working on is: Given the Pauli matrices \$\...
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### Is *Conservation of Distinction* a true conservation law in mainstream physics?

Both Leonard Susskind and Francis Heylighen have written about the Conservation of Distinction but it seems Susskind more closely connects this (law?) with unitarity in quantum mechanics. Heylighen ...
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### Equivalence between ghosts?

Ok. I'm trying to get the terminology right about the term ghost in physics. Is there any equivalence between these terms? Faddeev-Popov ghosts Paul-Villars ghosts Landau ghost The vanishing ...
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### Cutkofsky cutting rules questions

Consider the two photon exchange diagrams above. The Cutkofsky rules tell us that the imaginary part of each of these diagrams can be obtained by cutting through the graphs in all possible ways such ...
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### Wrong sign for the Laplacian in Schrodinger equation?

Suppose after some calculations I arrive at an equation of the form: $$[\nabla^2 +V(\mathbf{r})]\psi(\mathbf{r})=k^2\psi(\mathbf{r}) \tag{1}$$ As you can see here the ...
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### Why does unitarity require the Higgs to exist?

A standard argument that the Higgs boson must exist is that without it, amplitudes in the Standard Model at the TeV scale violate unitarity. This is explained in section 21.2 of Peskin and Schroeder ...