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9
votes
0answers
141 views

How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
41
votes
9answers
3k views

Why are differential equations for fields in physics of order two?

What is the reason for the observation that across the board fields in physics are generally governed by second order (partial) differential equations? If someone on the street would flat out ask ...
3
votes
3answers
157 views

Interpretation of QED gauge freedom

In quantum (or classical) electrodynamics we are free to make gauge transformations, which change the form of terms in the Feynman diagrams (or the potentials) without affecting any physical ...
1
vote
1answer
38 views

Dimensions of $\phi$ in scalar field theory

On Srednicki page 90-91 (in printed edition) he derives that $$[\phi] = \frac{1}{2}(d-2) \tag{12.10}$$ from $${\cal L}=-\frac{1}{2}\partial^{\mu}\phi\partial_{\mu}\phi -\frac{1}{2}m^{2}\phi^{2} - ...
2
votes
0answers
47 views

What is the relation between dimension and Quantum Field Theory? How does different dimensions change QFT? [closed]

Does the quantisation rules & field operators for scalar or Dirac fields change with dimension? Most books wrote about 3 spatial dimensions, and then upgraded it to 4 spacetime dimensions, keeping ...
3
votes
2answers
109 views

What happens when a field turns on or off?

Short Setup I am curious about the the mechanics of fields, whether electromagnetic, gravitational, etc. So as a specific example in order to simplify (hopefully) how to ask this question, consider ...
1
vote
0answers
35 views

What does 'vector-like' mean?

What are properties of vector-like field/particle? What's the counterpart of it? Chiral like?
2
votes
0answers
25 views

Transformation Law for a scalar field [closed]

The following is taken from Peskin and Schroeder page 36: $$\partial_{\mu}\phi(x) \rightarrow \partial_{\mu}(\phi(\Lambda^{-1}x)) = (\Lambda^{-1})^{\nu}_{\mu}(\partial_{\nu}\phi)(\Lambda^{-1}x)$$ It ...
1
vote
1answer
106 views

Boundary conditions of fields from the stationary action principle

First principle of stationary action Consider a real Klein-Gordon scalar field $\phi$ living in a $D$ dimensional flat spacetime. The field is considered off shell (the on shell condition is defined ...
8
votes
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 ...
0
votes
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
81 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 ...
0
votes
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 ...
3
votes
1answer
160 views

2D square lattice, nearest neighbor and next-nearest connected by springs

For my field theory class I am trying to build the Lagrangian for the following system. Consider a 2D square lattice where the nearest and next-nearest neighbor interactions are modeled by springs ...
0
votes
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
votes
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) ...
-3
votes
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
vote
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
votes
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 ...
2
votes
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
votes
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
votes
0answers
47 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 ...
11
votes
2answers
2k views

Active versus passive transformations

I am a bit confused by the concepts of active and passive transformations. In all the courses I am doing at the moment we do transformations of the form: $$ \phi(x) \rightarrow\phi'(x') = \phi(x) $$ ...
1
vote
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 ...
1
vote
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): $$ ...
0
votes
0answers
51 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
votes
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 ...
2
votes
2answers
68 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 ...
1
vote
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 ...
5
votes
1answer
257 views

Is the long range neutron-antineutron interaction repulsive or attractive?

I can model this interaction as Zee does in "Quantum field theory in a nutshell". In chapter I.4 section "from particle to force" he uses two delta functions for the source. The integral gives ...
0
votes
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 ...
1
vote
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
vote
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
votes
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 ...
3
votes
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. ...
0
votes
0answers
82 views

Current divergenceless

We can define a topological current, \begin{equation} J_{top}^u = \frac{1}{2v} \epsilon^{\mu \nu} \partial_\nu \phi \end{equation} where $\epsilon^{\mu \nu} = − \epsilon^{\nu \mu}$ and $\epsilon^{01} ...
0
votes
0answers
38 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
votes
0answers
38 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 ...
4
votes
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 ...
3
votes
2answers
1k views

Need for a side book for E. Soper's Classical Theory Of Fields

I am reading now E. Soper, Classical Theory Of Fields, now and sometimes it is very hard to follow the equations. So I need a side book on classical field theory to read it comfortably. Landau & ...
3
votes
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 ...
1
vote
0answers
37 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
vote
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
vote
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
vote
0answers
65 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 ...
1
vote
2answers
2k views

How is the direction of Magnetic/Electric Lines of Force Known?

It is shown that the direction of magnetic line is from north to the south and that of the electric line is from positive to negative. How do we/scientists know that the imaginary lines of force or ...
2
votes
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 ...
3
votes
1answer
126 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 ...
0
votes
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 ...