Tagged Questions
4
votes
3answers
90 views
Bound State of Only Massless Particles? Follows a Time-Like Trajectory?
Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy ...
4
votes
1answer
110 views
Lorentz invariance of positive energy solutions to the Klein-Gordon equation
I am reading Arthur Jaffe's Introduction to Quantum Field Theory. (You can find it here.) There is an interesting question posed in Exercise 2.5.1:
Solutions to the Klein-Gordon equation propagate ...
3
votes
0answers
102 views
Meaning of spin
I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things:
Mechanical spin (apparently a ...
5
votes
2answers
207 views
Causality and Quantum Field Theory
I have a problem with proof of causality in Peskin & Schroeder, An Introduction to QFT, page 28. To avoid confusion I use three vectors notation, rewriting the Eq. (2.53) for $y=0$ as follows:
...
3
votes
1answer
139 views
Lorentz transformation of classical Klein–Gordon field
I'm trying to see that the invariance of the Klein–Gordon field implies that the Fourier coefficients $a(\mathbf{k})$ transform like scalars:
$a'(\Lambda\mathbf{k})=a(\mathbf{k}).$
Starting from the ...
8
votes
2answers
241 views
In QFT, why does a vanishing commutator ensure causality?
In relativistic quantum field theories (QFT),
$$[\phi(x),\phi^\dagger(y)] = 0 \;\;\mathrm{if}\;\; (x-y)^2<0$$
On the other hand, even for space-like separation
$$\phi(x)\phi^\dagger(y)\ne0.$$
...
1
vote
0answers
158 views
Matrix manipulation for Dirac matrices
From the Dirac equation in gamma matrices, we know that $$\gamma^i=\begin{pmatrix}
0 & \sigma^i \\
-\sigma^i & 0
\end{pmatrix}$$ and $$\gamma^0=\begin{pmatrix}
I & 0 \\
0 & -I
...
6
votes
2answers
372 views
Charge conjugation in Dirac equation
According to Dirac equation we can write,
\begin{equation}
\left(i\gamma^\mu( \partial_\mu +ie A_\mu)- m \right)\psi(x,t) = 0
\end{equation}
We seek an equation where $e\rightarrow -e $ and which ...
3
votes
2answers
197 views
Matrix operation in dirac matrices
If we define $\alpha_i$ and $\beta$ as Dirac matrices which satisfy all of the conditions of spin 1/2 particles , p defines the momentum of the particle, then how can we get the matrix form ?
...
0
votes
1answer
101 views
Scattering Amplitudes in Centre of Mass Frame
I'm reviewing page 59 of the QFT notes here and am a little confused by a reference frame argument. You can compute the second order probability amplitude term for nucleon-nucleon scattering to be
...
4
votes
2answers
290 views
Lorentz invariance of the integration measure
This is regards to the lorentz invariance of a classical scalar field theory. We assume that the action which is $S= \int d^4 x \mathcal{L}$, is invariant under a Lorentz transformation. How do you ...
2
votes
2answers
312 views
Why do many people say vector fields describe spin-1 particle but omit the spin-0 part?
We know a vector field is a $(\frac{1}{2},\frac{1}{2})$ representation of Lorentz group, which should describe both spin-1 and spin-0 particles. However many of the articles(mostly lecture notes) I've ...
1
vote
1answer
166 views
Lorentz Invariant Equation of Motion for Scalar Field
I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity.
Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
3
votes
2answers
352 views
Lorentz transformations in Dirac equation
Let's denote a spinor $\xi$. If $(\theta ,\phi)$ are the parameters of a rotation and pure Lorentz transformation, then how $\xi$ could be written as
$$\xi ~\rightarrow~ \exp\left(\ i ...
5
votes
2answers
284 views
The Lagrangian in Scalar Field Theory
This is perhaps a naive question, but why do we write down the Lagrangian
$$\mathcal{L}=\frac{1}{2}\eta^{\mu\nu}\partial_{\mu}\phi\partial_{\nu}\phi - \frac{1}{2}m^2\phi^2$$
as the simplest ...
4
votes
1answer
79 views
What are relativistic and radiative effects (in quantum simulation)?
I'm reading about Quantum Monte Carlo, and I see that some people are trying to calculate hydrogen and helium energies as accurately as possible.
QMC with Green's function or Diffusion QMC seem to be ...
0
votes
0answers
141 views
Newton Gravitational constant $G$, Plank constant $\hbar$ , Speed of Light $c$ : The Dream Team of moderators?
The 3 great constants of Nature are well known :
The Speed of light $c$ (special relativity)
The Plank constant $\hbar$ (quantum mechanics)
The Newton ...
4
votes
2answers
206 views
Calculating the commutator of Pauli-Lubanski operator and generators of Lorentz group
The Pauli-Lubanski operator is defined as
$${W^\alpha } = \frac{1}{2}{\varepsilon ^{\alpha \beta \mu \nu }}{P_\beta}{M_{\mu \nu }},\qquad ({\varepsilon ^{0123}} = + 1,\;{\varepsilon _{0123}} = - ...
6
votes
3answers
236 views
Is the commutation of all possible operators sufficient to identify a spacelike interval?
It has been claimed (e.g. here) and apparently already been established, that the interval $x - y$ being (called) "spacelike" implies that $\bigl[\hat O (x),\, \hat O' (y)\bigr]=0$ for any two (not ...
5
votes
1answer
196 views
Relativistic contraction for a wave packet and uncertainty on momentum
Consider an electron described by a wave packet of extension $\Delta x$ for experimentalist A in the lab. Now assume experimentalist B is flying at a very high speed with regard to A and observes the ...
1
vote
0answers
200 views
Could someone transmit a signal with equally-tuned Casimir plates across the quantum field?
It seems, one could exploit the Casimir effect to send messages across arbitrarily-large distances with carefully-tuned Casimir plates.
Obviously, relativity would preclude FTL information transfer, ...
1
vote
2answers
283 views
Why is ${\partial^i}{\partial_i\phi}$ = ${\partial^i {\phi}}{\partial_i{\phi}}$?
This notation can be found on page 254 of Victor Stenger's Comprehensible Cosmos and in David Tong's Lectures on QFT (Equation 2.4 http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf), and in
EDIT: on ...
4
votes
1answer
105 views
What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT?
What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT? The question is motivated by this preprint arXiv:1203.0609 by Murayama and Watanabe.
Also, what ...
12
votes
3answers
310 views
Are gravitomagnetic monopoles hypothesized?
My understanding is that gravitomagnetism is essentially the same relativistic effect as magnetism. If so, why is it that I've heard so much about magnetic monopoles, but never gravitomagnetic ...
0
votes
2answers
171 views
faster-than-c photons
As far as I know, according to quantum field theory, there are some photons that go faster than c, which is the speed of light in vacuum.
However, there seems to be a paper and a corresponding ...
1
vote
1answer
283 views
How are fundamental forces transmitted?
How are the fundamental forces transmitted? In particular I wonder, are all "processes" local, i.e. without superluminal distant interactions? But if they are local, then particles would have to ...
3
votes
2answers
320 views
Discreteness of Spacetime and Violation of Lorentz symmetry
It is usually said that existence of discrete spacetime violates Lorentz symmetry. What quantity is used to quantify such violation? I mean could someone points a reference for a derivation that shows ...
1
vote
1answer
179 views
Does path integral and loop integral in a Feynman diagram violate special relativity?
Consider a correlation function between two points A(x1,t1) and B(x2,t2), we need to integrate over paths which could be ...
3
votes
1answer
269 views
The Particle-Antiparticle Problem in Relation to Special Relativity
Prelude:
Let’s consider a pair of events $A(t_1,x_1)$ and $B(t_2,x_2)$,having a spacelike separation wrt an inertial frame denoted by K.In the frame K’ moving along the positive x-x’ direction with a ...
7
votes
5answers
854 views
Why Negative Energy States are Bad
The argument is often given that the early attempts of constructing a relativistic theory of quantum mechanics must not have gotten everything right because they led to the necessity of negative ...
11
votes
1answer
184 views
Can the CPT theorem be valid if Lorentz invariance is only spontaneously broken?
Earlier, I asked here whether one can have spontaneous breaking of the Lorentz symmetry and was shown a Lorentz invariant term that can drive the vacuum to not be Lorentz invariant. How relaxed are ...
10
votes
2answers
223 views
The derivation of the Belinfante-Rosenfeld tensor
It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of the ...
9
votes
2answers
348 views
Essential background for QFT study
The preface to Mark Srednicki's "Quantum Field Theory" says that to be prepared for the book, one must recognize and understand the following equations:
$$\frac{d\sigma}{d\Omega} = ...
8
votes
2answers
877 views
Poincare group vs Galilean group
One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
9
votes
3answers
412 views
Spontaneous breaking of Lorentz invariance
Is it possible to spontaneously break Lorentz invariance, i.e., have a Lagrangian that respects LI but a vacuum which does not? If it is possible, why isn't there even the slightest hint of the ...
7
votes
3answers
397 views
Horizon and Unruh radiation for a finite period of acceleration
It's a well known fact that an observer that accelerates at a constant rate from $-c$ at past infinity to $+c$ at future infinity sees a horizon in flat Minkowski spacetime. This is easy to see from a ...
7
votes
1answer
381 views
Is there a rest frame for the Higgs boson?
If there is a non-zero expectation value for the Higgs boson even in "vacuum", since the Higgs boson has a mass unlike photons, then I would expect it to have a rest frame.
So why doesn't a non-zero ...
7
votes
3answers
1k views
Are Classical Field Theory and Quantum Mechanics of a single particle (nonrelativistic or “classical”) limits of Quantum Field Theory?
Recently I talked about QFT with another physicist and mentioned that the Quantum Field Theory of a fermion is a quantisation of its one-particle quantum mechanical theory. He denied this and ...
2
votes
5answers
750 views
Special relativity version of Feynman's “Space-Time Approach to Non-Relativistic Quantum Mechanics”
I'm looking for an article that sets up the framework described by Feynman in Space-Time Approach to Non-Relativistic Quantum Mechanics, but in Special Relativity.
12
votes
3answers
858 views
Why the vacuum polarization does not decrease the speed of light?
On one hand, in the classical electrodynamics polarization of transparent media yields in lowering the speed of light by the factor of $n=\sqrt{\epsilon_r \mu_r}$ (refractive index).
On the other, in ...
6
votes
1answer
2k views
The Euler-Lagrange equation in special relativity
How can I derive the Euler-Lagrange equations valid in the field of special relativity? Specifically, consider a scalar field.
