3
votes
0answers
61 views

What is the derivation of the speed of light $c$ that is not based on electromagnetism? [duplicate]

The "speed of light" is not just the speed of electromagnetic radiation, but of any massless particle. Therefore must not there be an expression for $c$ that is not in terms of $\mu_0$ and ...
1
vote
3answers
305 views

Does the the quantum field theoretic process of particle–antiparticle annihilation break the axioms of Special Relativity?

$\textbf{Note that this diagram hasn't anything to do with the question directly.}$ After a particle and its antiparticle annihilate, their energy is converted into a force carrier particle, such ...
6
votes
1answer
109 views

Is the total cross section a Lorentz Invariant?

In Peskin and Schroeder's book (P&S), on the botton of page 106, the authors say that the total cross section transforms as its only non-invariant factor, namely: $$ {1 \over E_{A} E_{B} |v_A - ...
3
votes
0answers
51 views

Most natural tensor structure for a quantum field

A quantum field is described by a Hilbert space. In many instances, the chosen tensor structure on this Hilbert space corresponds to that of space-like separated regions of space-time. The ...
5
votes
1answer
127 views

Problem understanding sign of volume integral in Minkowski space

My professor told me that a 4-dimensional Minkowski - Space Integral I was working on can be written as the product of a metric tensor and a scalar: $\int d^4 k \frac{k^\mu ...
1
vote
1answer
67 views

Distance and time measurement in the famous Superluminal Neutrinos Experiment

I tried to understand the technical aspects of the OPERA/CERN experiment, but apparently it takes some professional experience. Therefore I would like to ask someone better acquainted with such ...
1
vote
1answer
33 views

Relativistic Dynamical System

I have read in a paper that: A relativistic dynamical system must be invariant under infinitesimal inhomogeneous Lorentz transformation. A dynamical system is characterized by the ten generators, ...
2
votes
0answers
45 views

microcausality and locality

There is this thing I got confused: Microcausality is the statement that spacelike separated local field variables commute so that we can specify field variables on a spatial slice as a complete ...
4
votes
1answer
138 views

Non-relativistic limit in a Lagrangian density

What criteria should I consider when determining the non-relativistic limit of a Lagrangian density? For example, how would I take the non-relativistic limit of the following Lagrangian density: ...
6
votes
1answer
170 views

Representations of the Poincare group

Which type of states carry the irreducible unitary representations of the Poincare group? Multi-particle states or Single-particle states?
10
votes
2answers
197 views

Conservation of phase space volume in Rindler space-time

Let us consider Rindler space-time, i.e. Minkowski space-time as seen by a constantly accelerating observer. My question is, does Liouville's theorem, i.e. the conservation of phase space volume in ...
7
votes
1answer
400 views

Boosts are non-unitary!

The boost transformations are not unitary unlike rotations, the boost generators are not Hermitian. When this induces transformations in the Hilbert space, will those transformation be unitary? I ...
2
votes
1answer
133 views

Has QFT successfully mediated between QM and Special Relativity?

I understand that QFT is the theoretical framework for combining QM and Special Relativity, but as I understand it, though even without proof or experimental confirmations; has QFT managed to "behind ...
6
votes
1answer
426 views

Generators of Poincare Groups

How can I determine the generators of the Poincare Group, $P(1,3)$ explicitly? Here $P(1,3)$ means a matrix Lie group.
2
votes
2answers
115 views

A question about relativistic spin operator

The question comes from Ryder's Quantum Field Theory, 2nd edition. The author was looking for relativistic spin operator. It was concluded that it cannot be $J^2:=\mathrm{J} \cdot \mathrm{J}$, where ...
2
votes
2answers
264 views

Why does a Lorentz scalar field transform as $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$?

This problem is from Srednicki page 19. Why $U^{-1}(\Lambda)\phi(x)U(\Lambda) = \phi(\Lambda^{-1}x)$? Can anyone derive this? $\phi$ is a scalar and $\Lambda$ Lorentz transformation.
3
votes
3answers
749 views

Dirac spinor and Weyl spinor

How can it be shown that the Dirac spinor is the direct sum of a right handed Weyl spinor and a left handed Weyl spinor? EDIT:- Let $\psi_L$ and $\psi_R$ be 2 component left-handed and right-handed ...
5
votes
5answers
494 views

What distinguishes time from space in Quantum Field Theory?

Consider the following expression for a general QFT action: $$ S ~=~ \int_0^t\mathrm dt~L ~=~\int_0^t\mathrm dt\int_\mathbb {R^3}\mathrm d^3x~\mathcal L ~=~\int\mathrm d^4x~\mathcal L.$$ Here we ...
3
votes
0answers
113 views

Spacetime and uncertainty principle

I only have limited knowledge of relativity and quantumphysics but as far as I know, the uncertainty principle relates the uncertainty of space and momentum of a particle. Einstein however, explained ...
6
votes
4answers
1k views

Do all massless particles (e.g. photon, graviton, gluon) necessarily have the same speed $c$?

I suppose there was a discussion already on speed-of-gravity-and-speed-of-light. But I silly wonder whether all the massless mediators of four fundamental forces, i.e. Graviton: $g_{\mu\nu}$ ...
2
votes
0answers
224 views

Unitary Lorentz transformation on quantized Dirac spinor

I am stuck again on page 59 of Peskin and Schroeder. In particular, I do not know how they get equation (3.110). Let me first give some background in the way that I understand it (but I might be ...
1
vote
1answer
236 views

Trying to rhyme Peskin and Schroeder with Weinberg

This is a follow up question of this one. In the Vol 1, Weinberg derives how a unitary operator $U(\Lambda)$ acts on one-particle states, which is given by equation (2.5.2): \begin{equation} ...
1
vote
1answer
117 views

Question about Weinberg's derivation of a one-particle states under the Poincare group

I'm reading QFT: Vol 1 by Weinberg and I have a (perhaps trivial) question about a statement he makes on page 63. I can follow him to his derivation of equation (2.5.2): \begin{equation} P^\mu ...
6
votes
1answer
247 views

Peskin & Schroeder Chapter 3.1 EoM Lorentz Invariant under Lorentz Invariant Lagrangian

From Peskin & Schroeder QFT page 35: The Lagrangian formulation of field theory makes it especially easy to discuss Lorentz invariance. And equation of motion is automatically Lorentz ...
0
votes
2answers
169 views

What if a particle falls into the center of a central field? [closed]

Given a central field $U(r)$ satisfies $U(r) \rightarrow -\infty$ when $r \rightarrow 0$, then What if a particle falls into the center of a central field? Can you help me analysis this question in ...
6
votes
1answer
264 views

Lorentz transformation of the Spinor Field

I'm reading chapter 3 of Peskin and Schroeder and am stuck on page 43 of P&S. They have defined the Lorentz generators in the spinor representation as: \begin{equation} S^{\mu \nu} = ...
1
vote
1answer
168 views

Properties of Lorentz transformation generator?

In chapter 2 of Srednicki, the author defines: $$ U(1+\delta \omega) = I +\frac{i}{2h}\delta \omega_{\mu \nu} M^{\mu \nu} $$ where the $M^{\mu\nu}$s are hermitian operators and are the generators of ...
1
vote
0answers
53 views

Time reversal invariance and statistics

To what extend does the behaviour of time reversal invariance depend on the statistics of the particle under consideration? More explicitly: To what extend does the action of the time reversal ...
0
votes
1answer
196 views

Why there is the requirement for derivatives no higher than second order in free quantum field equations? [duplicate]

Why there is the requirement for derivatives no higher than second order in free quantum fields equations? We can get the equations for the free fields of an arbitrary spin by using the requirements ...
1
vote
1answer
196 views

Spinor formalism in QFT

We can describe fields by two formalisms: vector and spinor. This is the result of possibility of representation of the Lorentz's group irreducible rep as straight cross product of two $SU(2)$ or two ...
5
votes
3answers
393 views

How does QFT help with entanglement?

I'm a bit confused. QFT is claimed to incorporate both Quantum Mechanics and Special Relativity. Therefore it should address the problem of non-locality caused by entanglement. However when I search ...
1
vote
1answer
268 views

Local gauge invariance and fields

I have one question about local gauge invariance of the spinor and scalar theories. For the scalar complex field with lagrangian $L_{0}$ requirement of local gauge invariance leads us to the ...
2
votes
3answers
182 views

What is the interpretation of the Chern-Simons electromagnetic spin density?

Hans de Vries (who happens to be a no-longer-active physics.SE user) has an online book (referenced below) in which ch. 6 is a presentation of an object he calls the Chern-Simons current, ...
3
votes
1answer
175 views

Connection between particles and fields and spinor representation of the Poincare group

Let's have a definition of massive particle as an irreucible representation of the Poincare group. Then, let's have a spinor field $\psi_{\alpha \alpha_{1}...\alpha_{n - 1}\dot {\beta} \dot ...
2
votes
1answer
445 views

What is the meaning of Non-Relativistic theory in Condensed Matter Physics?

I an attempt to evade the Goldstone Theorem, it is argued in Gilbert and Klein and Lee's paper that in a non-relativistic field there exists a preferred direction which can be used to evade ...
0
votes
1answer
172 views

Special relativity and quantum mechanics

I know how the Dirac's equation about the relativistic quantum mechanics works. Can anyone tell me how can one combine special relativity and quantum mechanics as a whole - special relativity is valid ...
4
votes
2answers
451 views

Why do we say that irreducible representation of Poincare group represents the one-particle state?

Only because Rep is unitary, so saves positive-definite norm (for possibility density), Casimir operators of the group have eigenvalues $m^{2}$ and $m^2s(s + 1)$, so characterizes mass and spin, and ...
3
votes
1answer
214 views

Photon mass and life time

In this article, the author tried to explain that, Einstein's theory may not valid because he says "photon can decay because it may have minute amount of mass". I'm totally in a conundrum state that ...
4
votes
1answer
108 views

Can we obtain non-Lorentzian metric from Lorentzian metric, through renormalization methods?

Since low-energy, non-relativistic thermal field theories are defined in Euclidean spacetime, while high-energy relativistic theories are define in Minkowski spacetime, I was wondering if there are ...
2
votes
0answers
345 views

The connection between classical and quantum spins

I have two questions, which are connected with each other. The first question. In a classical relativistic (SRT) case for one particle can be defined (in a reason of "antisymmetric" nature of ...
5
votes
2answers
488 views

The problem of a relativistic path integral

Many books have described the path integral for non-relativistic quantum. For example, how to get the Schrödinger equation from the path integral. But no one told us the relativistic version. In fact, ...
3
votes
1answer
170 views

How can “quantum particles have positive masses, even though the classical waves travel at the speed of light”?

Clay Mathematics Institute writes about the Yang-Mills and mass gap problem on this page http://www.claymath.org/millennium/Yang-Mills_Theory/: The successful use of Yang-Mills theory to describe ...
8
votes
2answers
527 views

What's wrong with this QFT thought experiment?

In quantum field theory, the propagator $D(x-y)$ doesn't vanish for space-like separation. In Zee's book, he claims that this means a particle can leak out of the light-cone. Feynman also gives this ...
4
votes
1answer
184 views

What if EM or QCD was spontaneously broken?

Suppose that Standard Model Higgs mechanism broke electromagnetism, by e.g. veving the charged component of the doublet, so that the photon was massive with $m_\gamma\sim v$. Could such a Universe ...
4
votes
2answers
267 views

Why do single particle states furnish a rep. of the inhomogeneous Lorentz group?

Following up on this question: Weinberg says In general, it may be possible by using suitable linear combinations of the $\psi_{p,\sigma}$ to choose the $\sigma$ labels in such a way that ...
3
votes
1answer
133 views

Volume element $\mathrm{d}^4k =\mathrm{d}k^0 \,|\mathbf{k}|^2\,\mathrm{d}|\mathbf{k}| \,\mathrm{d}(\cos\theta) \,\mathrm{d}\phi$ in Minkowski space?

Suppose we have an integral $$\int \mathrm{d}^4k \,\ f(k)$$ we want to evaluate and that we're in Minkowski space with some metric $(+,-,-,-)$. Is it true that: $$\mathrm{d}^4k = \mathrm{d}k^0\ ...
6
votes
3answers
280 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 ...
3
votes
1answer
155 views

Difference between vector and pseudo-scalar

In physics, a pseudo-scalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not. Can someone show me ...
4
votes
1answer
223 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 ...
6
votes
2answers
489 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 ...