All Questions
39
questions
2
votes
0
answers
113
views
Confused about square of time-reversal operator $T$
I am reading An Introduction to Quantum Field Theory by Peskin & Schroeder, and I am confused about what is the square $T^2$ of time reversal operator $T$.
My guess is that for $P^2$, $C^2$ and $T^...
- 613
0
votes
0
answers
50
views
Discrete symmetries of Hamiltonian and Change of Representation
In quantum mechanics, one could write Hamiltonians for a given quantum system both in coordinate and momentum spaces as mentioned for example in Sakurai book. Does the discrete symmetries such as ...
0
votes
2
answers
122
views
Quantum fluctuations and symmetries?
While reading this piece about symmetry breaking, in section 3 I came across the term "anomalous symmetry breaking", which happens when a symmetry is broken by quantum fluctuations:
Let us ...
- 2,462
-1
votes
1
answer
146
views
Is unitarity intimately "connected" to symmetry?
I have a couple of questions about unitarity and symmetries:
Is unitarity connected to all fundamental symmetries? Is it linked to symmetries like CPT, Lorentz, Poincaré, diffeomorphism, ...
- 2,462
0
votes
1
answer
103
views
Operators localized in space and $\hat{q}$ position operator
I am reading the "Quantum Field Theory lectures of Sidney Coleman". In the first chapter (subchapter 1.2), the author talks about translation invariance. In particular, he states that $U(a)=...
- 3,992
1
vote
0
answers
133
views
Symmetry of infinite harmonic oscillators in quantum field theory
We know that the system (Hamiltonian) of $N$ harmonic oscillators possesses $SU(N)$ symmetry, where
\begin{equation}
H=\hbar \omega \sum_{i=1}^{N}\left( a_{i}^{\dagger } a_{i} +\frac{1}{2}\right) .
\...
- 119
1
vote
1
answer
200
views
Operator Ordering Conventions and Symmetry
Quantization procedures may need operator ordering conventions to avoid ambiguity. In classical theories, classical observables are often described by smooth functions, so the order of observable ...
- 559
0
votes
1
answer
106
views
Time reversal on the field operator
What I roughly know about time reversal operator T is,
$$
T[a] = a^\dagger, T[a^\dagger] = a\\
T[i] = -i, T[t] = -t.
$$
For the number operator $n=a^\dagger a$, I expect $T[n]=n$. Does that mean time ...
- 1
2
votes
1
answer
199
views
What is the Noether continuous symmetry associated with the conservation of total particle number for a free complex Klein-Gordon field?
Obviously I know that the $U(1)$ symmetry is associated with the (number of particles - number of antiparticles) conservation.
However I thought, by Nother's theorem, that every conserved quantity ...
- 2,604
2
votes
0
answers
84
views
Are canonical commutation relations only valid for non-relativistic QM? [closed]
Other questions (such as What is the "secret " behind canonical quantization?) seem to suggest that ultimatley, the motivation behind imposing the canonical commutaiton relation $$[x,p]=i\...
- 2,604
1
vote
2
answers
334
views
Why is a hole a time-reversed electron?
I am trying to understand a paper where the hole wavefunction is transformed into the electron wavefunction in a semiconductor using the time-reversal operator. None of my books mention this concept ...
- 2,122
6
votes
0
answers
120
views
What are the symmetries in fermionic quantum mechanics?
Consider a $d=0+1$ theory of fermions, i.e., fermionic QM:
$$
L=i\psi\partial_t\psi-V(\psi)
$$
The Hamiltonian is just $H=V$.
What is the definition of a symmetry here? I can construct transformations ...
3
votes
0
answers
69
views
Calculation of commutation relations in the SYK model
I'm reading this paper (https://arxiv.org/abs/1604.07818). And I'm having trouble showing an equality. We consider the following $SL(2,R)$ generators.
\begin{align}
D=-t\partial_t-\frac{1}{4},\ P=\...
- 125
3
votes
1
answer
503
views
Define antilinear or antiunitary operator $\Theta$ acting on the ket state and on the bra state consistently?
It is commonly to define an antilinear or antiunitary operator $\Theta$ acting on the ket state $|\alpha\rangle$ such as $$\Theta|\alpha\rangle.$$
It is commonly avoid to pursue a definition an ...
- 4,336
1
vote
2
answers
362
views
Why should we care about representations of spacetime symmetries in quantum mechanics?
Many posts here turn around the question how exactly spacetime symmetries are represented on (projective) Hilbert spaces in quantum mechanics. The question here is why quantum states should live in (...
- 65