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1answer
37 views

Quantum Field Theory: commutator of covariant derivatives

I just started studying qtf and I dont understand the last lecture. In the lecture script a shortcut is defined. $P^j = \frac{1}{i}\partial_j - qA^j$ With this: $[P^j,P^k] = -\frac{q}{i}(\partial_j ...
1
vote
1answer
82 views

Gauge the symmetry $φ \to φ + a(x)$ for a free massless real scalar field

How does one alter the Lagrangian density for a real scalar field $$\frac{∂_μφ∂^μφ}{2}$$ such that is will be invariant under the gauge transformation $φ → φ + a(x)$? For a complex scalar field ...
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0answers
10 views

Is electric field by a charge present where the net field is zero?

I have heard a lot of people say that, at all the points where electric field is zero, electric field by any of the charges never reaches there. It's quite commonly thrown around that electric field ...
1
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1answer
47 views

State counting in the d = 1+2, $\cal{N} = 2$ vector multiplet

The question is from Box 8.2, page 282 of the book "Gauge Gravity Duality" by Ammon and Erdmenger. The link to the specific page from Google Books is here. According to the authors, a $\mathcal{N} = ...
8
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1answer
116 views

Why is $V=(1/2) m^2 \phi^2$ for a free relativistic scalar field of mass $m$?

Bit of a basic question here but how come for a free relativistic scalar field of mass $m$ such as Klein Gordon theory, we take the potential to be $$V=\frac{1}{2} m^2 \phi^2$$ Is the mass term ...
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0answers
48 views

solutions of wave equation with cubic term

Does the following equation $$ \nabla^\mu \nabla_\mu \psi + a \psi^3 = b \psi $$ where $\psi$ is a real function, $a$ and $b$ are real constants, have other solutions that extend beyond a one ...
6
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0answers
218 views

Peskin-Schroeder Problem 3.5, supersymmetric theories regarded as field theories on parameter space w/commuting & anticommuting coordinates?

I know how to do Problem 3.5 of Peskin-Schroeder. Let us organize the fields $\phi$, $\chi_\alpha$, $F$ of Problem 3.5 into a superfield$$\Phi(x + i\theta\sigma\overline{\theta}, \theta) = \phi(x) ...
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1answer
68 views

Conceptual Change thinking needed [closed]

Using Conceptual Change Research To Reason About Curriculum By Glenn D. Berkheimer, Charles W. Anderson, and Steven T. Spees Introduction The kinetic molecular theory is fundamental to the ...
1
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1answer
89 views

What does it mean for an action to be defined “on-shell”?

Some actions like 11D supergravity are defined "on-shell". What does this mean exactly? Can you give me an example? Say for example the Klein-Gordon action. Can this be defined on-shell too?
0
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1answer
44 views

Fourier transform for $W(J)$ in a free QFT

In chapter I.3 and I.4 of A. Zee's QFT in a Nutshell, he starts with the theory $$ \mathcal{L}(\varphi) = \frac 12[(\partial\phi)^2-m^2\varphi^2]+J\varphi $$ Using the path integral approach, he ...
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0answers
34 views

Is this the correct way to obtain $<f|i>$ term in $\phi^4$ interaction theory? [closed]

Lets first write the expectation value of the fields in the interaction picture; $$ ...
0
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1answer
38 views

What does “n-particle reducible” mean?

I am reading Ramond and in page 112 he says "In $\lambda \phi^{4}$ theory, diagrams can be at most three-particle reducible". My question: whether the individual Feynman Diagrams are treated as ...
2
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0answers
49 views

Full form of the Pauli-Fierz action

In Deser's paper on the fully interacting version of the Pauli Fierz theory, he does a rather simple method of treating the Pauli Fierz equation without going with infinite sums, just by treating the ...
3
votes
1answer
89 views

Representation of the Lorentz group

Is there any representation of the Lorentz group where $$U^{-1} f(x) U = f(\lambda^{-1}x)$$ other than the (0,0) representation? If not then is it possible for a field (with a well defined ...
1
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0answers
24 views

Writing the Interaction Hamiltonian for pions in a different way

$\pi^+$, $\pi^-$ and $\pi^0$ are scalars particles with masses approximately equals. Their interaction is, approximately, given by $H_{int}(x) = g \epsilon^{abe}\epsilon^{cde}(\phi^a\partial_\mu ...
0
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0answers
52 views

Mass term in field Lagrangian

In the Klein-Gordon or in the Dirac Lagrangian density, the mass term is quadratic in the field. The other way around, I have heard a quadratic term in a general Lagrangian density be referred to as a ...
0
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0answers
18 views

When considering local phase transformations are we forced to use covariant derivatives?

When considering local phase transformations $e^{i\theta(x)}$ of the fields $\phi$ and $\phi^*$ corresponding to \begin{equation} \mathcal{L}=\partial_\mu\phi^*\partial^\mu\phi-m^2\phi^*\phi ...
1
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1answer
79 views

Modified gauge fixing condition in Faddeev-Popov approach

Which gauge fixing conditions are allowed to choose for this approach? For example (following the steps of Peskin in 9.4) I can choose a "modified" lorenz gauge ( for a abelian theory): $$ ...
1
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1answer
32 views

Can we use a photon to use it as a changing field in an electric generator? [closed]

In an electric generator we use a changing magnetic field to create electricity. But what if we use a photon's oscillation of EM waves to generate electricity in a metal wire as we do in an electric ...
0
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3answers
54 views

Examples of non-linear field symmetries?

Consider a Lagrangian theory of fields $\phi^a(x)$. Sometime such a theory posseses a symmetry (let's talk about internal symmetries for simplicity), which means that the Lagrangian is invariant under ...
2
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2answers
69 views

Field theory where fields are differential forms, other than electromagnetism [closed]

I am looking for a few examples of field theories (classical or quantum) that can be formulated taking the fields to be differential forms at least of degree 1 (not counting 0-forms) excluiding ...
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0answers
39 views

Is the coordinate transformation of an object the same of the action of a group on this same object?

I am having troubles in understanding frame transformations in physics from the mathematical point of view. What I understand for a coordinate transformation is just a function to one chart to another ...
1
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0answers
39 views

What is the current theory underlying the concept of fields? [duplicate]

When I went to school I was specifically told that fields are material (they occupy some region in space, and they "exist" there) and continuous. Recently, studying quantum physics I came across the ...
3
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3answers
157 views

Are field theories special?

Our best descriptions of the microscopic world, that satisfy many fundamental requirements (as we know them today), are field theories. Is there something fundamental about field interactions, or are ...
0
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0answers
40 views

DBI action with Weyl Invariance

The DBI action, given by $S_{Dp}=-T_p\int d^{p+1}\xi e^{-\phi(\xi)}\sqrt{-\textrm{det}\left(G_{ab}(\xi)+B_{ab}(\xi)+2\pi{\alpha}'F_{ab}(\xi)\right)}$ is diff and Poincaré invariant. I want to ...
0
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0answers
39 views

Hilbert Stress Energy Tensor for fermions + EM field and Yang-Mills theory (fermions + gluons)

@Qmechanic or anyone else who knows the reference. I am trying to find a references to the work(s) where thorough derivation of Hilbert Stress Energy Tensor for fermions + EM fields and Yang-Mills ...
3
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0answers
93 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. ...
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0answers
38 views

signal from uniformly moving charge

As a charge moves, its field changes, and this change can only be propagated outward at the speed of light. Thus the field lines will be curves that keep changing apparent source point and direction. ...
1
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1answer
58 views

Rotation, Boosts and their relation to Spin

Angular momenta are the generators of rotations. For example, $L_1,L_2,L_3$ represents the orbital angular momentum operators which represents rotations in 3-D space in $xy$, $yz$, $zx$ plane. Spin ...
1
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2answers
59 views

Quantum field operators in HEP and CMT

For a real scalar field (which is a bosonic field) we have these commutation relations : $$ \left[\phi(x,t),\phi(y,t)\right]=0 \qquad \qquad \left[\phi(x,t),\pi(y,t)\right]=\delta(x-y).\tag{1}$$ But ...
1
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0answers
66 views

Hamiltonian density for Proca Lagrangian [closed]

The (classical) Proca Lagrangian density for a massive vector field $A_\mu$ is $$ {\cal L} = -\frac{1}{4} F_{\mu\nu} F^{\mu\nu}+\frac{1}{2}m^2 A_{\mu}A^{\mu},$$ where as usual ...
2
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1answer
87 views

How to explain the upgrade from Particles to Fields between Relativistic QM->QFT?

It is strange that all books I walked through, non of them explains or motivates how physicists realised that we need to deal with fields instead of particles. Maybe the closest thing I found is the ...
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0answers
7 views

Modeling effects of grounded electrodes

I am trying to model electric fields due to the contributions of many conducting electrodes. So far, I have worked with both positively charged and negatively charged electrodes, but I am now ...
3
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1answer
127 views

Wilsonian Renormalization Group and Symmetries of the EFT

I have am action $S_0$ valid up to energy scale $\Lambda_0$ with renormalisable terms. I want to study the EFT at a lower scale $\Lambda \ll \Lambda_0$, by using the Wilsonian RG. It will give me an ...
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0answers
157 views

Scattering, Perturbation and asymptotic states in LSZ reduction formula

I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix ...
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0answers
26 views

Books for field theory [duplicate]

I am a math student, studying P.D.E. of some EM theory. I am new to field theory and I don't even know what a Lagrangian density, Hamiltonian density, or gauge field theory is. Could you please ...
3
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0answers
89 views

Is the phrase “coupling constant” interchangable with “ strength of interactions”?

Can I use the terms coupling constant and strength of interactions, interchangeably, or are there more subtleties to the term coupling constant that I am not aware of? Coupling Constants from ...
2
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0answers
65 views

Lagrangians not related via a total time derivative lead to same Noether symmetries?

Having answered my initial two questions (v1), I now consider a third possibility. Consider two Lagrangians that both lead to equivalent equations of motion. Suppose that they are not related via a ...
0
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1answer
56 views

Complex Inner Product for Integral Expressions

I am currently working through some QFT derivations and running into conceptual problems. In particular, I am deriving the free field Hamiltonian of the form: $H_{k} = \frac{1}{2} \int d^{3}k ...
1
vote
1answer
67 views

Classical Field Theory Using Geometry

I would like to know if there are good introductory courses on Classical Field Theory taught in a differential geometry approach yet one doesn't need a background in those mathematical subjects but ...
4
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1answer
55 views

Is there a systematic way to obtain all conserved quantities of a system?

I'd like to know whether, given a system, there's a way to obtain all the conserved quantities. For instance if the system consists of electric and magnetic fields, the fields must satisfy Maxwell's ...
3
votes
1answer
106 views

Charge not conserved in scalar QED? [duplicate]

Since conservation of charge seems to be a well known concept, I am hoping that I am missing something and that the conclusion is incorrect. However, I have been unable to disprove this. Let me ...
0
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0answers
14 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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0answers
65 views

Fayet-Iliopolous Parameters from Separation of NS5-branes in $(x_{7}, x_{8}, x_{9})$: An ambiguity as to which gauge group the FI parameter belongs

hep-th/9611230v3, page 12 explains how, for a configuration of D3s along $(x_{1}, x_{2}, x_{6})$, and NS5's along $(x_{1}, x_{2}, x_{3}, x_{4}, x_{5})$, the Fayet-Iliopolous D-term coefficient $\zeta$ ...
1
vote
1answer
71 views

A question to gauge fixing in nonabelian gauge theories

In quantum gauge theories it is usual to fix the gauge with the equation $\partial^\mu A_\mu = 0$ where $A_\mu$ is the gauge connection. From this gauge fixing condition the remaining gauge degree of ...
1
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1answer
48 views

How to divide areas in electric field lines based on field strength?

A negative charge is surrounded by four positive charges. They are all of the same strength. The electric field lines are plotted below. I am looking for the property of the drawn 'red lines' that ...
3
votes
1answer
192 views

Is the Dirac equation equivalent to the Klein-Gordon equation for its left handed component?

The Dirac equation $$(i\gamma^a\partial_a - m)\psi=0\tag{0}$$ is given by a first order operator acting on a Dirac spinor, which is the direct sum of a left handed spinor and a right handed spinor. ...
6
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2answers
210 views

What canonical momenta are the “right” ones?

I'm doing some classical field theory exercises with the Lagrangian $$\mathscr{L} = -\frac{1}{4}F_{\mu \nu}F^{\mu \nu}$$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. To find the ...
0
votes
3answers
144 views

How many fields that we know of permiate the universe?

The Higgs field, as I understand it reading layman's articles, permeated the entire universe only a fraction of a second after the big bang. Are there any other fields that they know about or ...
2
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2answers
164 views

General relativity without curvature?

Is there a reformulation of general relativity without curved space time, just with fields (like classical E&M)? Edit: removed the part about E&M with curvature (multiple posts).