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21 views

How to obtain the Klein Gordon equation for DBI action?

The action for DBI field is given by $$S=d^{4}x\,\sqrt{-g}\left[- V(\phi)\sqrt{1-g^{ij}\partial_{i}\phi\partial_{j}\phi}\right]$$ And the required Klein Gordon is given by $$\square ...
0
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0answers
23 views

Laplacian equations and transformation invariance and homogeneous functions

Functions whose Laplacian is zero are said to be harmonic. 1) Do harmonic functions always imply a conservation law and transformation invariance of some kind? 2) Homogeneous functions do not admit ...
0
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0answers
38 views

What is the relationship between local and global symmetries? [on hold]

A global symmetry has a few different meanings. The obvious one is that for $g = e^{-i\theta}$ if $\theta$ is contant in space then a field $\phi$ transforms $\phi' = e^{-i\theta}\phi$ so that ...
3
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2answers
107 views

Physical difference between gauge symmetries and global symmetries

There are plenty of well-answered questions on Physics SE about the mathematical differences between gauge symmetries and global symmetries, such as this question. However I would like to understand ...
6
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1answer
287 views

What is meant by the term “value” of a scalar quantum field?

During the slow roll of a scalar field, the scalar field is changing its value over time. But what is meant by the term "value" of a scalar field? Since the scalar field is quantized, I don't ...
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0answers
54 views

The group SU(2) and the Higgs field

The Higgs field matrix has the structure $\Phi=\begin{bmatrix} \phi_{+} & -\phi_{0}^{*} \\ \phi_{0} & \phi_{+}^{*} \\ \end{bmatrix}$ How can I show that it keeps this structure under the ...
6
votes
2answers
96 views

When is stress-energy tensor defined as variation of action with respect to metric conserved?

In General Relativity Einstein's equation implies that stress-energy tensor on its RHS is conserved (has vanishing divergence), due to the Bianchi identity. Considering variational principles leading ...
0
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1answer
44 views

Why source point singularities are inevitable in Physical Fields?

Any physical phenomena is explained by stating some relations between certain physical quantities. The physical quantities, if having a certain value for each and every point in space and time are ...
0
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1answer
68 views

How are Lagrangians in QFT constructed?

Various particle equations (like the K-G equation, the Dirac equation, the Proca equation etc.) in QFT are derived by applying the Euler-Lagrange equations to the Lagrangian density. But how are these ...
3
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2answers
45 views

Variation of Lagrangian density $\mathcal{L}$ w.r.t $x_\mu$

If a function $f(x(t),y(t))$ has no explicit dependence on the variable $t$, then $\frac{\partial f}{\partial t}=0$. In quantum field theory, the Lagrangian density ...
0
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0answers
26 views

Longitudinal Polarization and Spin-0 for Massive Vector Fields

I was wondering if anybody would be willing to explain how a plane wave solution of the form $\vec{B^\mu}=\epsilon^\mu{e^{k_0ct+\vec{k}.\vec{x}}}$ for a massive vector field's equations, say for ...
2
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1answer
45 views

4-Gradient Lorentz Transformation

I am currently studying the behavior of a scalar field $\phi$ under a Lorentz transformation $\Lambda$. However I am having trouble understanding why the following holds true: ...
4
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1answer
43 views

What kind of fields can couple naturally to a $p$-form gauge fields in a Lagrangian?

Ordinary $U(1)$ gauge fields can naturally couple to classical fields such as spin-$1/2$ fields via the Dirac Lagrangian, or to complex spin-$0$ fields via the obvious covariant derivative coupling, ...
3
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2answers
263 views

From the viewpoint of field theory and Derrick's theorem, what's the classical field configuration corresponding to particle? Is it a wavepacket?

In the framework of QM, we have known that particle, like electron, cannot be a wavepacket, because if it is a wavepacket then it will become "fatter" due to dispersion and it's impossible. However ...
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0answers
28 views

Definition of a field as a condensate state of bosons

I would like to know if a single boson can create a field or is it a requirement to have a condensate state of them where the number of bosons is not determined. For example, if you create a single ...
0
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0answers
28 views

Functional Gaussian Integral Involving Gradient Square with non-trivial Kernel

I have been trying to solve the following functional gaussian integral. I've had problem finding the inverse kernel. $f(x)$ and $\rho(x)$ are two known scalar fields and they do vanish at infinity. ...
0
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1answer
46 views

Are all forces given by a field conservative forces?

When teaching us electromagnetism, our professor first introduced us to the concept of "field". Several lessons later, he proved that electric field force is a conservative force. But I think the ...
8
votes
1answer
136 views

When is numerical value of Lagrangian evaluated on-shell a full differential?

I noticed recently that for many field equations, Lagrangian evaluated on-shell (i.e. using equations of motions) is a full derivative- a divergence or something, or in other words a boundary term. ...
3
votes
1answer
44 views

Supersymmetrizing bosonic actions at higher orders

Given only the bosonic terms of a supersymmetric action, using a knowledge of the (local) supersymmetry transformations, is there a systematic way of reconstructing the fermionic terms? More ...
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2answers
34 views

Finding the speed of electrons in a magnetic field

So I'm trying to solve this problem in which an electron beam is "drawing a picture" on a TV screen. The electrons are accelerated to a voltage of $3 kV$ by wire coils and are then directed to ...
1
vote
1answer
89 views

Hamilton's equations of motion on Dirac's formalism

I'm having several doubts about the procedure proposed by the Dirac-Bergmann algorithm in order to get the correct equations of motion of electrodynamics (Maxwell's equations). Suppose I've already ...
2
votes
2answers
60 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 $\frac{\delta}{\delta \phi}$ ...
3
votes
1answer
124 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
votes
2answers
56 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 ...
0
votes
1answer
36 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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2answers
33 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
46 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?
1
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2answers
68 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 ...
4
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2answers
92 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
98 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 ...
0
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0answers
45 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 ...
0
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0answers
34 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 ...
0
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0answers
28 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 ...
1
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1answer
75 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 & ...
3
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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 ...
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) ...
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0answers
42 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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0answers
51 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 ...
1
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1answer
26 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 ...
0
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1answer
45 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
46 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 ...
2
votes
1answer
88 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? ...
3
votes
1answer
67 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 ...
1
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2answers
56 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
45 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
39 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
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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
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1answer
51 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
46 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 ...
-1
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1answer
81 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: ...