# Unitarity Definition and 13 Discussions

In quantum physics, unitarity is the condition that the time evolution of a quantum state according to the Schrödinger equation is mathematically represented by a unitary operator. This is typically taken as an axiom or basic postulate of quantum mechanics, while generalizations of or departures from unitarity are part of speculations about theories that may go beyond quantum mechanics. A unitarity bound is any inequality that follows from the unitarity of the evolution operator, i.e. from the statement that time evolution preserves inner products in Hilbert space.

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1. ### A Why unitary evolution?

The usual justification for why the evolution of physical systems is unitary in quantum mechanics involves arguments like "probabilities must sum to 1" or similar arguments that apply equally to any CPTP map. I'm just curious what justifications people here would use for selecting out unitary...
2. ### B Unitarity in GR + QFT

Does unitarity have to be obeyed in a full quantum gravity model?
3. ### I Unitary operator and eigenvalue

Hello, I recently saw ##U|v\rangle= e^{ia}|v\rangle, \, a \in \mathbb{R}## and am wondering how to come up with this or how to show this. My first thought is based on the definition of unitary operators (##UU^\dagger = I##), I would show it something like this: ##(U|v\rangle)^\dagger =...
4. ### I The need for a "conscious observer"

Does unitarity of the evolution of wavefunction get rid of the need for a "conscious observer", and does collapse in contrast demand a "conscious observer"? For with unitarity there are is no requirement for such an observer, and collapse can't be explained without such an observer. The...
5. ### A Use of the Optical Theorem and Regge trajectories

Cutkosky rule states that: $$2Im \big(A_{ab}\big)=(2\pi)^4\sum_c \delta\Big(\sum_c p^{\mu}_{c}-\sum_a p^{\mu}_{a}\Big)|A_{cb}|^2\hspace{0.5cm} (1)$$ putting ##a=b=p## in Cutkosky rule we deduce the Optical Theorem for ##pp## scattering: 2Im \big(A_{pp}\big)=(2\pi)^4\sum_c \delta\Big(\sum_c...
6. ### I What is "unitary evolution" of something in physics?

What do we mean when we say that a system can't change (in time) because its evolution is unitary?
7. ### A Tree-level unitarity constraints in Two-Higgs Doublet Model

Hi, I'm looking at the unitarity constraints for the Two-Higgs Doublet Model and I'm trying to follow what they do in the attached article, which can also be found here: https://arxiv.org/pdf/hep-ph/0312374v1.pdf. However I do not know how to get the scattering matrices in eq. (7). They say...
8. ### I Proof of unitarity of time evolution in Susskind's book

In "The Theoretical Minimum" of Susskind (p.98) it says that if we take any two basisvectors |i \rangle and |j \rangle of any orthonormal basis, and we take any linear time-development operator U, that the inner product between U(t)|i \rangle and U(t)|j \rangle should be 1 if |i \rangle=|j...
9. ### A Conservation of Information: Neutron Formation and Decay

Has anyone analyzed the process of Neutron formation and decay from the perspective of "information conservation"? Does anyone have any thoughts on what the results of such an analysis would be? What is the status of the observed evidence of reality in respect of whether one should conclude...
10. ### A Collapse from unitarity

Not quite. But it necessarily has to be described by a different quantum model than unitary dynamics if it is an open system and the rest of the universe is not explicitly modeled. For convenience, physicists often want to describe a small quantum system in terms of only its Hilbert space, when...
11. ### Conceptual questions on unitarity and time evolution

From a physical perspective, is the reason why one requires that the norm of a state vector (of an isolated quantum system) is conserved under time evolution to do with the fact that the state vector contains all information about the state of the system at each given time (i.e. the...
12. ### 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/pdf/1502.05296v1.pdf , top of page 3 under heading "What is the problem?"). My question is, why does the locality and...
13. ### Unitarity and locality on patgh integrals

my question is this: you know than in feynman path integra, you integrate eiS/hbar along all the fields. you also know that S is real and that it is the integral of local functions (fields and derivatives of fields). you also know that path integral generates an unitary and local...