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1answer
44 views

Expectation Value of Unitary Time Evolution Operator in Quantum Mechanics

Does the expression $\langle \Psi_i|U(t)|\Psi_i\rangle$ have a specific meaning, where $U(T)$ is the unitary time evolution operator of $\Psi$, and $\Psi_i$ is the initial state of $\Psi$? If so, ...
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16 views

unitarity bound

Unitarity bound implies that cross-section of no process can grow arbitrarily high with energy. But if the cross section of an interaction becomes constant after a certain energy, does that seem like ...
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3answers
87 views

Prove time-dependent hamiltonian is hermitian from unitarity of time-evolution operator

When we solve the Schrodinger equation for the time-evolution operator: \begin{equation} i\hbar\frac{\partial}{\partial t}U(t,t_{0})=HU(t,t_{0}), \end{equation} We have three cases to be treated ...
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1answer
52 views

How is the Born rule consistent with unitary evolution?

Consider a system $|\Psi_T \rangle_{t = 0} = |\Psi_E \rangle \otimes |\Psi_S \rangle$ where $|\Psi_S \rangle$ is a system that collapses into an eigenstate upon measurement. $|\Psi_E \rangle$ is the ...
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1answer
31 views

Unitary Bose gas

A unitary Bose gas (more about it [here]) is defined to occur when the scattering length diverges. What I don't understand, however, is which quantity/matrix is actually unitary? I mean, they could ...
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0answers
87 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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0answers
20 views

Scalar fields of different masses and Bogoliubov coefficients

Suppose we have scalar field $$ \hat{\theta} = \sum_{k}\left( \varphi^{+}(t)\hat{A}^{\dagger}_{k}e^{ikx} +e^{-ikx}\varphi^{-}\hat{A}_{-k}\right) $$ with time-dependent frequency: $$ ...
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2answers
172 views

Why is wavefunction collapse always non unitary?

The 'wavefunction collapse' upon measurement is usually referred to as being a non-unitary transformation, since it does not preserve the norm of the state vector. Indeed, if a linear superposition ...
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1answer
60 views

What is the time evolution operator in quantum mechanics [duplicate]

I'm curious about what happen to a system when the configuration of the system changes. If we have a system in a state $|\psi_{\textrm{in}}\rangle$ and we change the configuration of the system, the ...
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1answer
76 views

A wave function that is normalized initially remains normalized

Suppose that $\Psi(x,t)$ is normalized at time $t=0$. Show that this implies that $\Psi(x,t)$ is normalized at all other times. I know that this makes intuitive sense, and we'd certainly want our ...
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1answer
51 views

Deriving the form of generators of transformations

I'm struggling to understand a bit of quantum mechanics relating to the transformation generators. This specific bit contains quite a few guesses and assumtions which probably do make sense in ...
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2answers
106 views

How can I make this toy quantum random walk model unitary?

Take a toy $(1+1)$-dimensional lattice model of the universe. A particle begins at $x=0$ at $t=0$. It has an amplitude ${1}/{\sqrt{2}}$ to move one step to the left and amplitude ${1}/{\sqrt{2}}$ to ...
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0answers
79 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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3answers
254 views

What experiment supports the axiom that quantum operations are reversible?

Among the axioms of quantum mechanics there is one axiom that says transformations of a quantum state need to be continuous, linear, and reversible (and this together with the other axioms results in ...
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2answers
182 views

The black hole paradox

I recently read in the news that Stephen Hawking claims to have solved the Black Hole Information paradox. I researched a bit about the paradox and the research that Stephen Hawking did to solve it. ...
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0answers
56 views

About equivalence of two ways of “derivation” of Standard model

Two ways of SM derivation I know two methods of SM lagrangian "derivation". The first one, which I will call as Weinberg way, is based on approaches of SM as theory with spontaneusly broken ...
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3answers
208 views

Why does Hamiltonian follow the property $H^*_{ij} = H_{ji} $?

I was reading Feynman's Lectures III's Hamiltonian Matrix. There I found this property of Hamiltonian Matrix: The Hamiltonian has one property that can be deduced right away, namely, that ...
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3answers
92 views

Can the sign of metric change physics?

Consider the Lagrangian of a massless real scalar (classical field) in $\phi(\textbf{x},t)$: $$\mathcal{L}=\frac{1}{2}\partial^\mu\phi\partial_\mu\phi$$ The Hamiltonian density in two different ...
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0answers
112 views

QED and anomaly

I've just started to learn anomalies in quantum field theories. I have a question. How to show that QED is free from vector current anomaly and what would happen if it were not? In other words, how ...
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0answers
82 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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1answer
250 views

Probability conservation in WKB tunneling

Suppose we have quantum mechanical plane waves of energy $E$ incident upon a one-dimensional potential barrier $V(x)$ with sloping sides. One can compare the WKB solutions in the three relevant ...
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2answers
173 views

Violation of unitarity: meaning and consequences

What is meant by unitarity and violation of unitarity of a QFT? For example, Fermi theory of beta decay is said to violate unitarity. How does violation of unitarity make a theory sick?
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1answer
127 views

What do we mean by Unitary Dynamics in Quantum Computing?

In the afterword to the Tenth Anniversary Edition of the book Quantum Computation and Quantum Information the authors say: For many years, the conventional wisdom was that coherent ...
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140 views

Ghost in the quantization of relativistic particle

It is well known that in the quantization of certain relativistic theories such electromagnetism or relativistic string negative norm states could arise when quantizing covariantly. Acting with ...
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4answers
157 views

Importance of local conservation of probability

In almost every textbook of quantum mechanics we can find the derivation of the local conservation of probability. $$\nabla\cdot\vec{J}+\partial_t (\psi^*\psi)=0$$ where $\vec{J}$ is probabilty ...
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2answers
56 views

Ballentine's proof of (one half of) Stone's theorem

Reading Ballentine's "Quantum Mechanics; A Modern Development" I got stuck on his really short proof of what I think is Stone's theorem. On page 65 (paperback, reprint of 2008) he writes about about a ...
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1answer
138 views

What does it mean “Hawking radiation is in a pure state”?

I'm trying to understand black hole paradox but I'm not sure if I understand what does it mean "Hawking radiation is in a pure state". Does it mean if Hawking radiation is in a mixed state then ...
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1answer
78 views

What sort of operations can be applied on a Hilbert spaces?

I was reading the paper No Universal Flipper for Quantum States. In this paper they have tried to prove by contradiction that a universal flipping machine cannot exist. By flipping I mean if I have a ...
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1answer
1k views

Why is time evolution unitary?

Is the reason why the time evolution operator is unitary based on purely physical arguments, i.e. that the physical processes that an isolated system undergoes shouldn't depend on any particular ...
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0answers
91 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 ...
2
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1answer
124 views

Embedding of particles into fields

For the classification of particles (Wigner 1939), we look for unitary representations of the Poincaré/Lorentz group. There are are only infinite-dimensional (non-trivial) unitary representations! To ...
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1answer
55 views

What does it mean to have a degenerate $S$-matrix?

The Coleman-Mandula theorem $D>2$ assumes that the quantum field theory may not have a degenerate $S$-matrix. But what does it mean to have a degenerate $S$-matrix? The $S$-matrix if I got it ...
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2answers
176 views

How can an inverted anharmonic potential $V(x)=-x^4$ have discrete bound states?

I've been watching the lectures on mathematical physics by Carl Bender on youtube where he uses the non-Hermitian Hamiltonian methods to prove that the inverted anharmonic potential $V(x)=-x^4$ has a ...
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1answer
190 views

When is a unitary operator a quantum gate?

Quantum gates we use like X, Y, Z, H, CNOT, etc. are all unitary. When can an arbitrary unitary operator be considered as a quantum gate?
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1answer
58 views

Is the process on initialization of qubits unitary?

It is said in some texts, that quantum computer undergoes only 2 types of transofrmations: 1) unitary evolution while computing and 2) non-unitary transformation ...
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1answer
70 views

Unitarity of a transformation, and reversibility, imply one another?

Are these concepts equivalent? And if not, which one implies the other one? A transformation $\hat U$ is unitary when $\hat U^{-1} = \hat U^{\dagger}$. A reversible transformation $\hat A$ admits an ...
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2answers
238 views

Thought experiment about no-cloning theorem and FTL information

The quantum no-cloning theorem states that one cannot "build" a perfect cloning device for arbitrary quantum systems. There also exists a famous thought experiment where Alice transmits information ...
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0answers
120 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. ...
4
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1answer
483 views

Clarifications needed on Gauge Fixing and Ghosts [closed]

The first time some kind of gauge fixing appears is during the Gupta-Bleuler procedure, which is used to be able to quantize the photon field: The basic gauge invariant Lagrangian leads to $\Pi_0=0$ ...
4
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1answer
151 views

Why does S-matrix unitarity imply the cross section $\sigma$ $\propto$ $\frac {1}{s}$?

I'm currently learning for an oral exam in theoretical physics and as a learning aid protocols of older exams exist. In one protocol the question was asked: Why is the scattering cross section ...
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0answers
69 views

How can physics claim that information cannot be destroyed? [duplicate]

I watched a video featuring Leonard Susskind in which he took a small bowl of water and added three drops of food coloring. He swirled it around. At first you could tell where the drops must have ...
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2answers
104 views

System without ground state is not real in nature?

We know that Coulomb force is real phenomena in nature and with Coulomb potential $V(x) \thicksim -\frac{1}{|x|}$ lowest energy is bounded in hydrogen atom. But it's mathematically clear that if ...
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2answers
248 views

Unitarity and renormalizability

What is the difference between the unitarity of the theory and its renormalizability? Can we say that renormalizable theory is unitary after renormalization? The questions have arisen after I have ...
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0answers
26 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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2answers
395 views

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 ...
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0answers
53 views

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 ...
1
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1answer
179 views

Why does the state space contain states with negative norm and what would be an example?

My lecture script of Quantum Field Theory states that " the state space contains states with negative norm ". Why does it have to be like this and what would be an example fo such a state?
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0answers
75 views

Ghosts in theories of gravity and holographic theories

I want to understand when a theory leads to ghosts in gravity. Is there any relation between ghosts and non-linear higher order theories? Ghost is a clasical or quantum field concept?
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2answers
200 views

Why does the action have to be hermitian?

The hermiticity of operators of observables, e.g. the Hamiltonian, in QM is usually justified by saying that the eigenvalues must be real valued. I know that the Lagrangian is just a Legendre ...
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1answer
207 views

Trace operation on dynamic equation: physical meaning?

Suppose we have Heisenberg equation of motion for some observable $A$, $$ i\hbar\frac{dA}{dt}= -[H,A] $$ since the trace of any finite dimensional commutator structure vanish(not something like ...