# What is Unitarity: Definition and 36 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? QM Justification Ideas

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: Obeying Full QG Model?

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 Is unitarity necessary for the probabilistic interpretation?

It is usually said that unitarity is necessary for the consistent probabilistic interpretation. But is that really so? Suppose that ##|\psi(t)\rangle## does not evolve unitarily with time, so that ##\langle\psi(t)|\psi(t)\rangle## changes with time. Even then one can propose that probability...
6. ### A Unitarity & EFT: Exploring Finite Amplitude Theory

Hi all... As far as I understand, the concept of "unitarity" is pretty close to that of perturbation; in that it tells you that your amplitudes are finite with energy scale (one solution the Higgs gave in e.g. the Vector Boson Scattering). However, since an EFT comes with a natural cut-off, why...

9. ### 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?
10. ### B How to understand unitarity in QM?

Quote lifted from a thread in the cosmology forum. What does it mean to know the exact state of a QM system? QM predicts probabilities that particles will be in one of multiple states when the particles are observed, and when observed, not all properties of a particle are simultaneously...
11. ### 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...
12. ### A Unitarity and perturbativity constrains on couplings in QFT

Hi all, 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 know what is most essential ? I mean if unitarity constraind ## \lambda## to say less...
13. ### 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...
14. ### 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...
15. ### A Effective Dynamics of Open Quantum Systems: Stochastic vs Unitary Models

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...
16. ### B What is the connection between unitarity and thermodynamics?

A paper I'm reading says that the 2nd Law of Thermodynamics is related to unitarity. And it references: S. Weinberg, "The Quantum theory of fields. Vol. 1: Foundations" Does anyone here know what this might mean?
17. ### Does measurement violate unitarity?

I am taking my first semester of QM so excuse my question if it is way off mark, totally wrong, or very well known. As I understand it, one of the postulates of QM are that states evolve unitarily, a consequence (but not THE defining feature) of unitary transformations is that they are...
18. ### 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...
19. ### S matrix Unitarity Proof, pg 298 Peskin Schroeder

I have a question regarding a derivation in Peskin and Schroeder's QFT book. On page 298, he is discussing a method for defining a gauge invariant S matrix. He does this by defining projection operators ##P_0## that project general particle states into gauge invariant states, and then defining...
20. ### 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...
21. ### How Does Unitarity Conserve Information?

Lenoard Susskind's video courses on Clasical Mechanics and Quantum Mechanics, often mention convervation of information. Susskind likes to call it "the minus first law." In classical physics, it is Liouville's Theorum which tells us that the number of states is conserved in time evolutions...
22. ### 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...
23. ### What it means the theory violates unitarity

What it means "the theory violates unitarity" Hello, I know what unitary transformation is, but what does it mean that the theory does or does not violate unitarity? For example in some textbooks on QFT one can read that the Fermi theory of beta decay, which is not renormalizable, also violates...
24. ### Unitarity angular momentum operators

Hi, I'm confused by a sentence in a set of lecture notes I have on quantum mechanics. In it, it is assumed there is some representation \pi of SO(3) on a Hilbert space. This representation is assumed to be irreducible and unitary. It is then said that the operators J_i, which are said to...
25. ### Unitarity of Time-evolution Operator

I am reading a quantum mechanics book. I did not clearly understand one particular idea. When the book talks about the time-evolution operator U(t,t_0), it says that one very important property is the unitary requirement for U(t,t_0) that follows from probability conservation. My question is...
26. ### Complex numbers from unitarity from information conservation?

I doing some reading on why the wave-function is complex. From what I can tell, it's due to its evolution by unitary operators. But unitary operators seem to have something to do with information conservation. So I wonder if these idea have been developed somewhere in a concise fashion that...
27. ### Unitarity in Spin Foams: Canonical LQG vs. Path Integrals

In canonical LQG, unitarity is presumably guaranteed by the canonical formalism. How does one check for unitarity in the spin foam (path integral) formalism? Do the new spin foams pass the necessary tests?
28. ### Old vs new unitarity cut methods

Hey folks, I've been stumbeling recently about new unitarity methods to obtain one-loop amplitudes by cutting them in all possible channels thereby reducing the full amplitude to products of tree amplitudes (pioneered by Bern, Dixon, Kosower, Dunbar). From what I understand from my QFT...
29. ### Is the PMNS Matrix Unitary? Exploring Neutrino Eigenstates

Hi, Okay, I thought I had created this thread but looks like I didn't hit submit or something. Anyway, my question is, why is the PMNS matrix which is used to go between the mass eigenstates and flavour eigenstates of neutrinos unitary? Is it an assumption (if so, what is the motivation...
30. ### Is there any definitive answer on unitarity in quantum gravity

Given that in GR there's no gauge invariant choice of "equal-time slices", how is unitarity formulated in quantum gravity? I guess the problem may be absent if spacetime is asymptotically flat. But what happens in other cases? In AdS/CFT, the notion of unitarity comes from the CFT side. Is this...
31. ### Is the Scattering Matrix in Quantum Field Theory Inherently Unitary?

What is the reasoning for saying that the scattering matrix in quantum field theory is unitary? Take the initial state to be an electron and a positron. All sorts of crazy products can result in the final state, from photons to Z's to Higgs to an electron/positron with different momenta, to...
32. ### Is Unitarity Preserved by Different Inner Products?

Let V be a finite dimensional complex inner product space with inner product < , >. Let U be unitary with respect to this inner product. If ( , ) is another inner product, is U also unitary with respect to ( , )? The definition of unitary I'm working with is the one that says: U is unitary if...
33. ### What is meant by the breakdown of unitarity at TeV-scale

I read a statement that there is a breakdown of unitarity in the Standard Model at 1 TeV. What exactly is meant by that?
34. ### Understanding the Unitarity of CKM Matrix and Its Conservation of Probability

This is a known fact that CKM matrix, a matrix that is used to connect the weak interaction eigenstates to mass eigenstates is unitary. I have studied that this is due to the conservation of probability. i.e. an up type quark will decay into exactly three type of d quarks, nothing more.
35. ### Who Studies Partial Wave Unitarity in Quantum Mechanics?

Partial Wave Unitarity ?? Is there anyone who deals with "Partial Wave Unitarity" in Quantum Mechanics before??
36. ### Quantum computations, irreversibility, unitarity

A stupid couple of questions... In quantum computations, one typically starts with some initial quantum state on which an operator is applied. This operator must be unitary , right? (I guess that otherwise, it would not corerspond to an actual physical quantum setup). And this implies...