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Questions tagged [unitarity]

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 unitary state transformations.

In quantum mechanics, a unitary operator satisfies $U^\dagger U = UU^\dagger = 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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Why do we not have spin greater than 2?

It is commonly asserted that no consistent, interacting quantum field theory can be constructed with fields that have spin greater than 2 (possibly with some allusion to renormalization). I've also seen (see Bailin and Love, Supersymmetry) that we…
James
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Is there a symmetry associated to the conservation of information?

Conservation of information seems to be a deep physical principle. For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory. We may wonder if there is an underlying symmetry, in some space, which may explain this…
Trimok
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Why is information indestructible?

I really can't understand what Leonard Susskind means when he says in the video Leonard Susskind on The World As Hologram that information is indestructible. Is that information that is lost, through the increase of entropy really recoverable? He…
HDE
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Why is the information paradox restricted to black holes?

I am reading Hawking's "Brief answers". He complained that black holes destroy information (and was trying to find a way to avoid this). What I don't understand: Isn't deleting information quite a normal process? Doesn't burning a written letter or…
Hans Hinterseher
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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 spacetime itself, we consider only the dynamics of…
user4552
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Why is the Yang-Mills gauge group assumed compact and semi-simple?

What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories? I'd think that these hypotheses lead to physically "nice" theories in some way, but I've never, even…
joshphysics
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Reflection positivity for general fields

In the Euclidean QFT obtained by "Wick-rotating" a unitary QFT, the correlation functions satisfy a property called reflection positivity, see e.g. this Wikipedia article for the case of a scalar field. What's the correct formulation if you have…
Yuji
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Quantum mechanics - how can the energy be complex?

In section 134 of Vol. 3 (Quantum Mechanics), Landau and Lifshitz make the energy complex in order to describe a particle that can decay: $$ E = E_0 - \frac{1}{2}i \Gamma. $$ The propagator $U(t) = \exp(-i H t)$ then makes the wavefunction die…
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Unitary quantum field theory

What do physicists mean when they refer to a quantum field theory being unitary? Does this mean that all the symmetry groups of the theory act via unitary representations? I would appreciate if one could provide some references where the definition…
Yaniel Cabrera
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Where does the $i$ come from in the Schrödinger equation?

I am currently trying to follow Leonard Susskind's "Theoretical Minimum" lecture series on quantum mechanics. (I know a bit of linear algebra and calculus, so far it seems definitely enough to follow this course, though I have no university physics…
EelkeSpaak
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Determine if Theory is Unitary from Lagrangian

Question: Given a quantum theory specified with a Lagrangian and the degrees of freedom to be varied, what is the procedure to determine if the theory is unitary or not? Concrete example to aid discussion: (Taken from discussion of some simple…
John
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How does the Ward-Takahashi Identity imply that non-transverse photons are unphysical in QED?

Peskin and Schroeder say that the Ward Identity of QED proves that non-transverse photon polarizations can be consistently ignored, but I'm confused about the details. Setup One starts by considering some process with an external photon whose…
user26866
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Again: why do quantum computations need to be reversible?

In quantum computing, there is famous "law" which is to say that all the computation must be reversible. I understand that, for simplicity, it may be easier to consider reversible operation, and that they are general enough to make us happy to stick…
tobiasBora
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Why do quantum gates have to be reversible?

One possible reason I have come up with is that we are modeling quantum gates by unitary matrices. And since unitary operations are reversible we have to be able reverse the operation in the physical world as well. This is simply done by…
Heye
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Irreducible Representations Of Lorentz Group

In Weinberg's The Theory of Quantum Fields Volume 1, he considers classification one-particle states under inhomogeneous Lorentz group. My question only considers pages 62-64. He define states as $P^{\mu} |p,\sigma\rangle = p^{\mu} |p,\sigma\rangle…
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