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49
votes
8answers
3k views

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 ...
36
votes
6answers
4k views

Why is information indestructible?

I really can't understand what Leonard Susskind means when he says that information is indestructible. Is that information that is lost, through the increase of entropy really recoverable? He ...
18
votes
1answer
815 views

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 ...
13
votes
2answers
324 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 ...
11
votes
1answer
588 views

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 ...
11
votes
1answer
964 views

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 ...
10
votes
1answer
324 views

Scale invariance plus unitarity implies conformal invariance?

What has the reaction been towards the recent paper claiming to have a proof that scale invariance plus unitarity implies conformal invariance in 4d?
8
votes
2answers
531 views

Why do Faddeev-Popov ghosts decouple in BRST?

Why do Faddeev-Popov ghosts decouple in BRST? What is the physical reason behind it? Not just the mathematical reason. If BRST quantization is specifically engineered to make the ghosts decouple, how ...
8
votes
2answers
1k views

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 ...
8
votes
2answers
135 views

Could you theoretically map the internal distribution of mass in a black hole using Hawking radiation?

Assuming you could measure the qualities of the radiation emanating from all around a black hole, could this be used to determine the internal geometry or makeup of the mass inside?
7
votes
3answers
744 views

Does Wick rotation work for quantum gravity?

Does Wick rotation work for quantum gravity? The Euclidean Einstein-Hilbert action isn't bounded from below.
7
votes
1answer
453 views

Is it possible to derive Schrodinger equation in this way?

Let's have wave-function $\lvert \psi \rangle$. The full probability is equal to one: $$\langle \Psi\lvert\Psi \rangle = 1.\tag{1}$$ We need to introduce time evolution of $\Psi $; we know it in ...
7
votes
3answers
1k views

Relation between unitarity and conservation of probability

In a seminar, I heard that the unitary aspect of representations was important physically, because in quantum mechanics unitarity is closely tied to the conservation of probability. Could someone ...
7
votes
1answer
179 views

Sign in front of QFT kinetic terms

I'd like to know if the sign in front of a kinetic term in QFT important. For the scalar field we conventionally write (in the $ + --- $ metric), \begin{equation} {\cal L} _{ kin} = \frac{1}{2} ...
7
votes
1answer
294 views

Basic question about the S-Matrix, Unitarity and Effective Field Theory

Consider scattering some particles in a state collectively denoted by $i$ to a final state denote by $f$. The scattering amplitude, S-matrix is then defined by: $S_{fi}\equiv \langle ...
6
votes
1answer
257 views

Why is $SU(3)$ chosen as the gauge group in QCD?

Why is $SU(3)$ chosen as the gauge group. Why not $U(3)$? Why does it even have to be unitary?
6
votes
1answer
291 views

Why is $R^2$ gravity not unitary?

I have often heard that $R^2$ gravity (as studied by Stelle) is renormalisable but not unitary. My question is: what is it that causes the theory to suffer from problems with unitarity? My naive ...
6
votes
3answers
176 views

why nontrivially space-like connected event horizons do not respect unitarity?

I want to understand the assertion that the gluing between distant event horizons is forbidden by unitarity. What is exactly the argument that unitarity will necessarily forbid topological nontrivial ...
5
votes
3answers
255 views

Does unitarity imply conservation of energy?

Not too long ago, someone began to discuss the thinking and motivation behind the Lagrangian and its formalism for the Newtonian framework and an intuitive understanding of such formalism. Somehow, it ...
5
votes
2answers
120 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 ...
5
votes
2answers
422 views

using a unitary matrix to transpose

A unitary matrix U is a matrix such that the conjugate transpose of U, when multiplied on the right with U, yields identity. My question is, is it possible to obtain the transpose of any density ...
5
votes
2answers
163 views

Proof of conservation of information [duplicate]

After listening of some lectures of Leonard Susskind about black holes, he mentioned that conservation of information is one of the foundations of physics. After searching the web I cannot seem to ...
5
votes
2answers
240 views

Information Loss in annihilation

The concept of information loss is usually discussed with respect to a black hole. My understanding is that whatever matter you put into the black hole, it has only 3 "hairs" and so one doesn't know, ...
5
votes
1answer
143 views

Why is the Yang-Mills Comparator unitary?

In chapter 15.2 of Peskin, the comparator is defined, as some object $U\left(y,\,x\right)$ which transforms as: $$ U\left(y,\,x\right) \mapsto V\left(y\right) U\left(y,\,x\right) ...
4
votes
3answers
754 views

Unitarity of S-matrix in QFT

I am a beginner in QFT, and my question is probably very basic. As far as I understand, usually in QFT, in particular in QED, one postulates existence of IN and OUT states. Unitarity of the S-matrix ...
4
votes
2answers
148 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 ...
4
votes
1answer
282 views

When can a classical field theory be quantized?

Given a classical field theory can it be always quantized? Put in another way, Does there necessarily need to exist a particle excitation given a generic classical field theory? By generic I mean all ...
4
votes
2answers
116 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 ...
4
votes
1answer
673 views

Help with Cutkosky cutting rules for fermions

I know that a cut boson propagator is replaced with the mass shell delta function. But what happens when you cut a fermion propagator? Do you just replace the denominator with a mass shell delta ...
4
votes
1answer
93 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 ...
4
votes
1answer
401 views

About Boltzmann H-theorem

What is the assumption for Boltzmann H-theorem? One can derive it just from the unitarity of quantum mechanics, so this should be generally true, does it imply a closed system will always thermalize ...
4
votes
1answer
491 views

Holstein-Primakoff and Dyson-Maleev representation

In Holstein-Primakoff and Dyson-Maleev representation, spin operators are represented by bosonic operators. Roughly speaking, a state with $S^z=S-m$ corresponds to a state containing $m$ bosons. In ...
4
votes
0answers
48 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 ...
3
votes
1answer
170 views

Lorentz transformation implemented by a non-unitary operator.

One often come across in QFT sentences like the following, for instance: ...under a Lorentz transformation $\Lambda$ implemented by the unitary operator $U(\Lambda)$, a Dirac field transforms ...
3
votes
1answer
154 views

Supersymmetry and non-compact $R$-symmetry group?

The $R$-symmetry for $N$ supercharges is $U(N)$. Is it possible to generalize $R$-symmetry [let's take $U(4)$) to be something like $U(2,2)$ (maybe analogous to Wick rotation of $SO(3,1)$ to ...
3
votes
1answer
802 views

What is known on violations of unitarity or locality?

Recently the amplituhedron become a hot topic. I realized that two of the central pillars that QFT is based on, unitarity and locality, are no longer playing an important part (due to gravitational ...
3
votes
2answers
172 views

Feynman's $i \epsilon$ prescription in loop expansion

I have some questions about the $i\epsilon$ factor in Feynman diagrams. First, what is the physical meaning of $i\epsilon$ in loop amplitudes. Second, how does it ensures unitarity? And third, Dyson ...
3
votes
1answer
142 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 $\Pi_0=0$ ...
3
votes
0answers
86 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 ...
3
votes
0answers
266 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 ...
2
votes
1answer
56 views

Unit determinant for relevant symmetry groups in QFT

When treating QFT we want our theory to be invariant under different symmetry groups, for example, the Standard Model is a non-abelian gauge theory with the symmetry group $U(1)×SU(2)×SU(3)$. ...
2
votes
2answers
248 views

Unitarity in QFT and measuring unitarity

I am trying to make sense of statements about unitarity in this popular science article about Nima and Jaroslav's new idea. My first query is that it is claimed that unitarity is a pillar of quantum ...
2
votes
2answers
705 views

Constructing the exponential form of a unitary operator

I think I've got this figured out but wanted to make sure I'm doing this right. Working with operators that satisfy bosonic commutation relations $[b,b^\dagger] = 1$, I define a very general unitary ...
2
votes
1answer
82 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 ...
2
votes
3answers
127 views

Shankar's Active/Passive Change of Basis

I'm working my way through Shankar's Quantum Mechanics (7th printing, and I'm doing it alone, so I apologize if I have core concepts completely wrong). He has a section on Active and Passive ...
2
votes
1answer
36 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 ...
2
votes
3answers
135 views

Admixtures of longitudinal and timelike photons!

In the quantization of electromagnetic field the physical states $|\psi\rangle$ are found to obey the following relation: $[a^{(0)}(k)-a^{(3)}(k)]|\psi\rangle=0$ It is explained as the physical ...
2
votes
1answer
127 views

Does unitarity apply in between measurements?

Sorry if this is a silly question (engineer here), but I was wondering if the math in particle physics assumes that unitarity applies even between measurements. In other words, I take it that the ...
2
votes
0answers
63 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 ...
2
votes
0answers
39 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 ...