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59 views

Do gravitational waves have field components like electromagnetic waves?

One way I've been led to understand electromagnetic waves (and I accept that this might be a misconception I have) is that they 'self propagate' through empty space by virtue of the wave consisting of ...
0
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1answer
31 views

Placement of indices in canonical commutation relations of coordinates and conjugate momenta as well as fields and conjugate momenta

The canonical commutation relations between generalised coordinates $q_a$ and their conjugate momenta $p^a$ are given by $[q_a,q_b]=[p^a,p^b]=0$ $[q_a,p^b]=i\delta^b_a$. Furthermore, the canonical ...
0
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0answers
41 views

Mass spectrum of field theory

How can I find the mass spectrum of a field theory given a Lagrangian made of a canonical kinetic term and a potential. I mean, I think I have to find the matrix of the quadratic terms in all the ...
2
votes
2answers
53 views

General form for functional derivatives

Working on the hamiltonian formalism applied to canonical field theory, how do I deduce the general form for the functional derivatives $\frac{\delta}{\delta \pi}$ and $\frac{\delta}{\delta \phi}$ ...
2
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2answers
218 views

Sign of Feynman rules with derivative couplings

Feynman rules for derivative couplings always make me confused. For example, the derivative in $gV^\mu\phi^+\partial_\mu\phi^-$ will give you $\pm ip_{-\mu}$, where $\pm$ depends on whether the ...
3
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1answer
108 views

How do (and don’t) particles emerge from fields?

I am aware of the following field- and particle-like notions: QFT particle, a unit of excitation in (the Fock space of) a QFT; SR field, an extremal $A = A(\mathbf x)$ of a Lorentz-invariant action; ...
3
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2answers
52 views

Classical Klein-Gordon theory is a free relativistic theory

The classical Klein-Gordon theory for a real scalar field is called a relativistic free theory. It is called a free theory because the dynamics of the degrees of freedom in the momentum space of the ...
2
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1answer
132 views

Locality defined in terms of the Lagrangian density

I've been reading through Matthew Schwartz's book "Quantum Field Theory and the Standard Model" and in chapter 24 there is a section on locality (section 24.4). In it he defines locality in terms of ...
2
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2answers
31 views

Water flow in salt solutions contemporary exposed to an electrical and constant magnetic field

When a permanent magnet is held motionless close to a salt solution which already has been exposed to an electrical field a flow in the water will be induced and can be detected by applying some ...
1
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2answers
59 views

Why don't people use Hamilton's equations for a relativistic free charged particle?

A charged relativistic free particle has the Hamiltonian in general: $$ \mathcal{H} = \sqrt{p^2c^2+m^2c^4}.$$ I read somewhere that says, it is possible to go further and say that the EoM are ...
0
votes
2answers
30 views

Electric potential inside a shell

Inside a shell, electric field is zero. Then does it have a constant electric potential inside the shell? If $V=\dfrac Ed$, then since field is zero, potential should also have been zero. Please ...
2
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2answers
42 views

Do Weyl fermions carry electric charge?

Do Weyl fermions carry ordinary electric charge? That is, do they interact with, for instance, electrons or photons?
4
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2answers
90 views

Higher than Lagrangian/action?

When you begin learning physics, you start with equations of motion applied to various physics systems. In classical mechanics course you learn, that exists Lagrangian/action of a system, which gives ...
8
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1answer
89 views

Why is a theory Lorentz invariant if the Lagrangian is Lorentz invariant?

For if I started by trying to make the Hamiltonian Lorentz invariant, I would have failed. Indeed, the Hamiltonian is part of a covariant tensor. But how do I know that the Lagrangian is not a part of ...
8
votes
1answer
134 views

Why does Landau theory not fail when dealing with a first order phase transition?

Here is a problem where I can do the calculation, but I am not understanding the philosophy behind it. It is about Landau theory: The Landau theory of phase transitions is based on the idea that the ...
2
votes
2answers
143 views

Does spatial coupling prohibit resonances due to an external source field?

The harmonic oscillator coupled to a sinodial external source $$\frac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C ...
0
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0answers
40 views

Explicit derivative of Chern-Simons current

I know that for a Chern-Simons 3-form $\omega=\operatorname{Tr}\left[F\wedge A-\frac{1}{3}A\wedge A\wedge A\right]$, with $F=A\wedge A +\operatorname{d}A$, I should get ...
5
votes
2answers
193 views

Performing Wick Rotation to get Euclidean action of scalar field

I'm working with the signature $(+,-,-,-)$ and with a Minkowski space-stime Lagrangian $$ \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi $$ The Minkowski action is $$ ...
6
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1answer
84 views

Use partial or covariant derivatives when deriving equations of a field theory?

I feel like this question has been asked before but I can't find it. would the Euler Lagrange equation for, say, the standard model Lagrangian be $$\frac{\partial L}{\partial \phi}=\partial_\mu ...
4
votes
1answer
243 views

effect of a simultaneous local and a global $U(1)$ symmetry breaking

EDIT : I am trying to figure out the effect of symmetry breaking in a $U(1)_Y\times U(1)_Z$ invariant lagrangian where $U(1)_Y$ is local symmetry of the Lagrangian and $U(1)_Z$ is a global symmetry of ...
1
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1answer
67 views

Different definitions of the parity transformation for the Dirac spinors

There are two definitions of the parity transformation acting on the Dirac spinors: $\Psi_P = \eta \gamma^0 \Psi$ with $\eta = i$ ($P^2=-1$ as in Srednicki) and $\eta=1$ ($P^2=+1$ as in Peskin & ...
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3answers
3k views

Why treat complex scalar field and its complex conjugate as two different fields?

I am new to QFT, so I may have some of the terminology incorrect. Many QFT books provide an example of deriving equations of motion for various free theories. One example is for a complex scalar ...
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0answers
31 views

Question on basic tensorial calculus on field theory

Working on the Maxwell field as a gauge theory, at some point the following derivative comes up: $\frac{\partial(\partial_iA_0)}{\partial A_0}=0$ which must be, accordingly to the theory, zero. My ...
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0answers
25 views

For two electron that moving parallel,can we using this equation for Electric Field and Magnetic Field?

i suppose we have two electron and they are moving parallel,please see picture: my question is can we use this this equation for it? Griffiths' Introduction to electrodynamics): $$\vec E(\vec ...
3
votes
1answer
52 views

Deriving Hamilton's equations from KdV Hamiltonian

Let $f=f(q,p)$, $g=g(q,p)$ and Possion bracket $$\{f,g\}=\frac{\partial f}{\partial q}\frac{\partial g}{\partial p}-\frac{\partial f}{\partial p}\frac{\partial g}{\partial q}. \tag{1}$$ Then ...
4
votes
1answer
79 views

What gauge field can be constructed from Lorentz symmetry?

You can take a global symmetry and promote it to a local gauge symmetry by introducing an appropriate gauge field and upgrading the partial derivative to a covariant derivative. The photon field ...
1
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0answers
47 views

Non-null hessian condition for regular dynamical systems

I'm "researching" on unquantised Yang-Mills theory. For that I'm studying the Dirac's method for singular constrained systems and having problems to follow the first considerations on that matter. I ...
2
votes
1answer
86 views

Quantization of free real scalar massless field in 2d

Is there a reference to literature where one explicitly constructs quantization of the free real scalar massless field in the 2-dimensional space-time? In particular, how the propagator looks like? ...
0
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0answers
28 views

can different force fields interfere (create interference patterns)

Edit: I have rewritten the question for clarity. I know waves of photons can interfere eachother. What about if you mixed waves of photos with w and z bosons? What about gravitons (if they exist) ...
7
votes
1answer
166 views

Relations between diffeomorphism symmetry theories and invariant $SU(N), N \rightarrow \infty$ theories

Is it possible to have, an exhaustive panorama (as much as possible), about the relations between theories having a diffeomorphism symmetry, and theories having a $SU(N), N\rightarrow\infty$ ...
5
votes
1answer
152 views

Unitary gauge for non-abelian case

I'm reading Chapter 19 of Mandle and Shaw's Quantum field theory. In the first section it is explained that one can go with a $SU(2)$ followed by a $U(1)$ transformation from ...
4
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0answers
41 views

Why is there a minus in the Gauge Field Lagrangian kinetic term? [duplicate]

For vector Gauge fields we usually write the kinetic term: $$ \mathcal{L} ~=~ - \frac{1}{4} F_{\mu \nu} F^{\mu \nu}$$ while for matter fields e.g. for a real scalar: $$ \mathcal{L} ~=~ \frac{1}{2} ...
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1answer
25 views

About field lines and continuity of magnetic and electric fields

In my laboratory class we were doing an experiment with grass seeds and iron filings to visualize the electric and magnetic field lines. So, we were discussing why they appear, because we know that ...
2
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1answer
1k views

Inverse square law in 2+1 dimensional universe from a Yukawa coupling?

There is a nice result that in 3+1 space time, a Yukawa coupling leads to an inverse square law force as the mass of the scalar field goes to zero. I was wondering what the corresponding force in a ...
3
votes
1answer
340 views

Noether Current when the Lagrangian depends on second derivative of the fields

Let a Lagrangian density for a field theory of $N$ fields $\left\{\phi_i\right\}_{i=1}^N$ be given. Assume that the Lagrangian density depends on the fields, their spacetime derivatives, and their ...
0
votes
1answer
44 views

Mean free path in QFT

I'm trying to understand the hydrodynamic approximation of a general QFT when the large $k$ and $\omega$ DOF have been integrated out i.e that at highly enough temperature every non-trivial QFT ...
3
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0answers
44 views

Running coupling, effective potential and the stability of vacuum

Consider the potential $$V(\phi)=\frac{1}{2}\mu^2\phi^2+\lambda\phi^4$$ where $\phi=\phi(t,\textbf{x})$ is a real scalar field. Let, $\mu^2<0$ and $\lambda>0$ then the potential is bounded from ...
3
votes
1answer
64 views

S-duality of Einstein-Maxwell-Dilaton theory

Consider theory with action $$S = \int d^D x \sqrt{-g} (R - \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2k!} e^{a \phi} F^2 _{[k]} ) $$ where $\phi$ is dilaton and $F_{[k]}$ is ...
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2answers
55 views

Fourier transform of Hamiltonian for scalar field

In the Srednicki notes (http://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf) page 36 he goes from $$H = \int d^{3}x a^{\dagger}(x)\left( \frac{- \nabla^{2}}{2m}\right) a(x) $$ to $$H = \int ...
0
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0answers
44 views

Magnetic monopole in arbitrary dimension

Assume we have D-dimensional space-time in spherical coordinates $(t, r, \theta_1, ..., \theta_k)$. We have Maxwell equations for $k$-form $F^{\alpha_1, ..., \alpha_k}$ $$\partial_{\mu} F^{\mu ...
0
votes
1answer
35 views

Coupling constant in the Yang-Mills action

Intuitively, gauge coupling defines the strength of interactions between fields. But how to interpret the coupling $1/g^2$ in front of the kinetic term of Yang-Mills theories, ...
1
vote
2answers
391 views

Derrick’s theorem

Consider a theory in $D$ spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
1
vote
1answer
40 views

ADHM construction and Momentum Map

while I was reading about ADHM construction I had some troubles with precise geometrical identification of the various quantities. My doubts is well manifest in these two Wikipedia pages 1) ADHM ...
0
votes
1answer
49 views

Active transformation and passive transformation of a scalar field

For the Lorentz transformation $x \to x'=\Lambda x$, the active transformation is $\phi(x) \to \phi'(x)=\phi(\Lambda^{-1}x)$ and the passive transformation is $\phi(x) \to \phi'(x)=\phi(\Lambda x)$. ...
0
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0answers
38 views

QFT: prove Dirac lagrangian is invariant under C, P, T separately

As it is stated in Peskin, $\mathcal{L}=\bar\Psi(i\gamma_{\mu}\partial^{\mu}-m)\Psi$ is invariant under C,P and T transformation separately. I have some problems to see how the partial derivative is ...
4
votes
1answer
165 views

What defines the spin of a certain field? (formally)

Update: see the restatement of the question below! I've seen this question over and over through the archive of questions, but so far the closer to an answer was this. But I still don't understand. ...
3
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0answers
62 views

How do I obtain the SUSY Transformations from Poisson Brackets?

In Friedman's and Van Proyen's Supergravity textbook it is explained how one can get the supersymmetry transformations using the conserved currents. Specifically this is in section 6 where we are ...
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1answer
79 views

Why Different charges attract while they should repel? [closed]

When I started studying magnetic fields, my teacher was always telling me that strong fields push the bodies to weaker fields, so i tried to apply the same concept to charges in the following picture: ...
1
vote
1answer
42 views

Field theory on a lattice, what is this?

I only have the training of undergraduate quantum mechanics and solid state physics. For me, field theory is defined on a continuous space. So, what does lattice field theory mean? Is it similar to ...
1
vote
1answer
59 views

Cosmology: equation of motion for a scalar field in conformal time [closed]

So, I've derived the equation of motion for a scalar field in "normal" time, $t$: $$ \ddot{\phi}+3H\dot{\phi}+\frac{dV(\phi)}{d\phi} $$ Then, using the expressions for the scalar field density, ...