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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How can information ever get lost at the event horizon of a black hole?

In the drawing, A and B are two entangled particles in Kruskal coordinates, A is falling into the black hole, B is remaining outside. The lines going through the center are the time coordinates of ...
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309 views

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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207 views

Non-Hermitian Lagrangian in Quantum Field Theory

I have seen more than once non-Hermitian Lagrangian densities being used in effective field theories. Usually the problem of unitarity is explained away with decays into some degree of freedom not ...
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Why is time-evolution unitary - The Heisenberg-picture Version

There are various versions of this question already on this site, which attempt to justify / make plausible that the time evolution of quantum mechanical observables is unitary. Most of these ...
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Do longitudinal and scalar have anything to do with Faddeev-Popov ghosts?

In his this book, Hatfield calls ghosts the negative states appearing in the covariant (Gupta-Bleuler) quantization prescription of the electromagnetic field (page 89). When discussing Yang-Mills ...
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167 views

Infinite-dimensionality of unitary representations of non-compact simple Lie Groups

I have a question about the argument given in On finite-dimensional unitary representations of non-compact Lie groups. I have been looking for a good proof for this claim for a little while now. I ...
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416 views

Gauge invariance and the unitarity

I want to discuss the relation between the unitarity and the gauge invariance. Suppose we have for simplicity an abelian gauge theory (say, EM theory). We want to quantize it in terms of 4-potential $...
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191 views

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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154 views

How to check the unitarity of the theory by having field equation?

Let's have some field equation of some field corresponding to particles with mass $m$ and spin $s$. How to check the unitarity of the theory? May I do it without getting $S$-matrix? May the scalar ...
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221 views

How to show that higher derivative theories (mostly) breaks unitarity

How to show that higher derivative theories (mostly) breaks unitarity? Spinor field $\psi_{a_{1}...a_{n}\dot {b}_{1}..\dot {b}_{m}} $, which refer to the $\left( \frac{n}{2}, \frac{m}{2} \right)$ ...
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104 views

Use of Cutkosky rule, the Optical Theorem and Regge trajectories in pp scattering total cross-section calculation

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 ...
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Analytic cotinuation between Minkowskian and Euclidean space, and causality

We can flip between Minkowkian and Euclidean signature by Wick rotation, and it is a well defined operation, provided there are no non - trivial singularities. Now, Unitarity in Minkowskian space ...
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305 views

Derive Hamilton's Principle of Stationary Action Only from Unitarity in Quantum Mechanics?

In this Question I want to give a derivation of Hamiltons Principle of Stationary action, and my question to the community would be, whether my argument is flawed. The System I want to look at is (...
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200 views

Unitarity of the S-matrix and Feynman Diagrams

There are several questions on the unitarity of the S matrix, but unfortunately non of them answers directly the following question. The S matrix is unitary and that can be proven by the fact that ...
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383 views

Generalized Unitarity cut of Scalar One-loop Box integral

How does one perform the integrals in four particle cuts in generalized unitarity? It would be helpful how one finds solutions to the simplest case, the fully determined box integral given by: $\int_{...
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584 views

Validity of Cutkosky cutting rules for fermions

It is rather obvious for me that the generalized optical theorem (see e.g. Peskin&Schroeder) must hold for S-matrix elements for fermions as it is directly related to the unitarity of the S-matrix....
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62 views

Longitudinal polarization of gluons in loop

I have a short question about the possible gluon polarization in loop diagrams. For external gluons, we only want the 2 transverse polarizations. In Peskin-Schroeder it is explained that in Feynman-...
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176 views

Feynman propagator for Dirac fields and $i\epsilon$ prescription for analytic continuation

The analytic continuation from Euclidean space to Minkowski spacetime is perturbatively well (uniquely) defined to all orders for the Feynman propagator for Dirac fields with the so called "$i\epsilon$...
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Are there any black hole information loss solutions that do not resort to non-locality?

It seems as though all solutions to the information paradox resort to non local effects. What solutions do we have that preserve locality?
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Tensor product of universe Hilbert space and black hole Hilbert space equals?

I'm a newbie struggling to parse concepts important in black hole, holographic principle and related issues. My query comes from Thomas Thiemann’s Modern Canonical Quantum Gen. Relativity, which ...
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115 views

The necessity of ground state in QFT

Why we always want to have a ground state in every physical theory? For example, when we try to quantize Dirac Hamiltonian and encounter a Hamiltonian without a ground state, we take a step back and ...
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2answers
207 views

Do black holes comply with the principle of unitary evolution?

Claus Kiefer, "Quantum gravity", 3rd ed., page 220/221, says in chapter 7 "Quantization of black holes": "A theory of quantum gravity should give a definite answer to the question of whether ...
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194 views

What exactly is black hole complementarity and why is it necessary for solving black hole information paradox?

What exactly is black hole complementarity and why is it necessary for solving black hole information paradox? The first question is about the story of vacuum fluctuation causing Hawking radiations. ...
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What kind of transformation can be applied to qubits?

I have a doubt on what kind of transformations can be applied to qubits. I understand that the transformations need to be reversible , but they also have to preserve the norm: that's why the ...
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118 views

Why are interacting noncommutative quantum field theories with space-time noncommutativity unitary?

Can anyone explain in a simple manner why interacting noncommutative quantum field theories with space-time noncommutativity of the Moyal bracket sort are unitary?
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Canonical Transformations in Quantum Field Theory

In his lecture notes on canonical transformations in quantum field theory, Massimo Blasone defines the boson translation transformation to be \begin{equation} a_k \rightarrow a_k(\theta) = a_k + \...
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Factorisation of tree level amplitudes from unitarity

Is there a simple argument to explain why tree level amplitudes must factorize on their pole into products of lower point tree level amplitudes, not by ispection of Feynman diagrams but as a ...
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45 views

Weyl- Squared Lagrangians

I'm studying conformal gravity theories, in particular I read that if we take $L=\sqrt{g}C_{abcd}C^{abcd}$ where $C$ is the Weyl tensor the theory we get is not unitary. What does it means unitary at ...
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Can any “explicit time-dependence” of an observable in QM be also seen as a unitary transformation

My other question about plausibility of unitary time evolution in the Heisenberg-picture had me wondering: If I can naturally argue the unitary time-evolution for any observable (that would be, the ...
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62 views

Irrational Conformal Field Theory v.s. Non-Unitary Conformal Field Theory?

Unitary conformal field theories (CFTs) with irrational (or including the special case of rational) central charge is called irrational conformal field theory (ICFT). Irrational conformal field ...
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Particle hole symmetry in 2nd quantization

In second quantization one the Particle hole trasnformation is defined as \begin{align} \hat{\mathcal{C}} \hat{\psi}_A \hat{\mathcal{C}}^{-1} &= \sum_B U^{*\dagger}_{A,B} \hat{\psi}^{\dagger}_B \\...
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55 views

Could Time-Evolution be antiunitary?

There are serveral Arguments for Time-Evolution to be unitary, for example, time-evolution should preserve the norm of each given state (because elseways the probabillity Interpretation would not work)...
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28 views

Time-order evolution operator: Wei-Norman form and unitarity

I'm reading a paper[1] in which the propagator is calculated for this kind of Hamiltonian \begin{align} \hat{H}(t) = \omega(t)\hat{J}_3 + \Omega^*(t)\hat{J}_{+} + \Omega(t)\hat{J}_-. \end{align} ...
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Anti-commutative hermitian operators

I have some trouble to prove the next statements: Let $A,B$ two anti-commutative hermitian operators, i.e. $\{A,B\}=AB+BA=0$. Does $A$ and $B$ share any eigenket?. If $U$ is an unitary ...
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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 ...
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224 views

Cutkosky rule for the triangle diagram

Outline - the anomalous vacuum polarization correction Suppose the abelian anomalous gauge theory (with axial gauge field $A$, vector gauge field $V$ and single massless fermion $\psi$): $$ \tag 1 L =...
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412 views

Optical theorem for the given diagram

Assume we have the abelian gauge theory with single fermion. Suppose the following diagram: Here the initial "photon" $\gamma$ is in the same state as the final one, so this is the diagram of self-...
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73 views

Unitarity violation in 2D conformal field theory (CFT)

Why if we have a 4 point function in 2D CFT on the plane with non-OPE singularities this would be a signal of unitarity violation?
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Is the unitarity property of the transition probability in transport theory only given in statistical equilibrium?

Is statistical equilibrium a necessary condition for the unitarity property of the transition probability in transport theory, which states that: $$ \int w(\Gamma_1^\prime,\Gamma_2^\prime; \Gamma_1, \...
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105 views

A Hamiltonian for a left-handed spinor field

In finding a lagrangian for a left-handed spinor field , a textbook claims that a kinetic term such as $ \partial_{\mu} \psi^a \partial^{\mu} \psi_a =\epsilon^{ab}\partial_{\mu}\psi_a \partial^{\mu}\...
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263 views

Peskin-Schroeder, Unitarity of the S matrix, eq 9.61

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 ...
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39 views

How to calculate resources taken up in quantum computation

Suppose I have $n$ qubits namely $\{|\psi_{1}\rangle,|\psi_{2}\rangle.....|\psi_{n}\rangle\}$. I apply a series of unitary operations $U_{1},U_{2}...U_{n}$ (applied in order) to these qubits. Each $...
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515 views

Why is particle number conserved, and what are the bounds on non-conservation?

Think of a modified Mott experiment: You place a single particle in the center of an empty perfect detector. The particle is described by a wave function, which will spread outwards and interact at ...
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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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$S$-matrix and in and out states

So, I have a short one. When observing scattering, we say that the amplitude for transition from one interacting state to some other interacting state same as this amplitude for free hamiltonian ...
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What is the black hole information paradox?

What is the black hole information paradox? My question is about the problem of whether information is lost when something falls into a black hole. Is information eternal? What about if a book falls ...
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Which unitary transformation should I use to change the frame reference properly?

I'm dealing with time-periodic Hamiltonian $H(t)=H(t+T)$ , where $$ i\hbar \partial_t\psi(r,t)=H(r,t)\psi(r,t).$$ The periodicity lies on the potential (i.e. $V(t)=V(t+T)$ inside the $H(r,t)$). The ...
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Gravity and complex numbers

In the lectures of Gary Gibbons on Supergravity held 2009@DAMTP http://www.damtp.cam.ac.uk/research/gr/members/gibbons/gwgPartIII_Supergravity.pdf it is remarkable that when he introduces spinors he ...
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Hamiltonian for a mode-shift operator

I have a discrete multi-level degree of freedom in my quantum system (for photons, for example this), which I write as $|l\rangle$. The degree of freedom is unbounded, i.e. $l$ can take ever positive ...
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Do all unitary operations manifest from time-evolution?

Let $|\psi\rangle$ be an element of a Hilbert space $\mathcal{H}$ and $U$ a unitary operator on $\mathcal{H}$. I am concerned with the actual physical manifestation of such a unitary operator in the ...