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0
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0answers
17 views

Coherence of gauge fixing with the corresponding theoretical gauge freedom

I understand that for a gauge fixing to be valid, it needs to be achievable (i.e., become an identity) continuously through a sequence of allowed gauge transformations of the canonical variables, yet ...
0
votes
1answer
46 views

Interpretation of the vector current in field theory

In field theory we write $$J^\mu=\bar{\Psi}\gamma^\mu\Psi$$ But I can't understand why it is so. Could anyone explain each of the terms in the multiplication?
6
votes
2answers
244 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 $$ ...
1
vote
1answer
65 views

Lagrangian gauge theory with physically observable local degrees of freedom

In my answer at What, in simplest terms, is gauge invariance?, I mentioned that in certain contexts there can be a "gauge theory" with a local symmetry that leave the Lagrangian/Hamiltonian invariant ...
2
votes
2answers
131 views

Why is the solution of the $\phi^6$ potential not a soliton?

Consider a theory with a $\phi^6$-scalar potential: $$ \mathcal{L} = \frac{1}{2}(\partial_\mu\phi)^2-\phi^2(\phi^2-1)^2. $$ I solved its equation of motion but found that the general form of its ...
3
votes
0answers
36 views

How do force carrying particles “give” force? [duplicate]

So, I am not taking physics in school, but I do have an interest in it, and I was wondering, in the standard model, all of the force carrying particles (photons, Z Bosons, W Bosons, gluons, and (...
3
votes
3answers
113 views

Why under Lorentz transformations the Higgs boson is a scalar field and under $SU(2)$ it is a doublet?

I am a bit confused about this difference. My understanding is that when we build a $G$-bundle, where $G$ is a gauge group, we have a representation $\rho:G\to GL(V)$ that acts on the fibers of the $G$...
0
votes
0answers
10 views

Quadrupolar interaction

In http://journals.aps.org/prb/pdf/10.1103/PhysRevB.64.195109 Eq.(4), why does the Fourier transform of the quadrupolar interaction function takes the form \begin{equation} F(\mathbf{q})=\frac{F_2}{1+...
10
votes
4answers
350 views

What makes an equation an 'equation of motion'?

Every now and then, I find myself reading papers/text talking about how this equation is a constraint but that equation is an equation of motion which satisfies this constraint. For example, in the ...
6
votes
0answers
115 views

The consistency conditions of constrained Hamiltonian systems

I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
6
votes
2answers
150 views

Beyond Hamiltonian and Lagrangian mechanics

Lagrangian and Hamiltonian formulations are the bedrock of particle and field theories, produce the same equations of motion, and are related through a Legendre transform. Are there more such ...
0
votes
1answer
54 views

Position of indices in QFT

I have recently started studying quantum field theory from the book Quantum Field Theory and the Standard Model by Schwartz. In chapter 2 it is said that, contrary to GR, one can ignore the index ...
4
votes
1answer
388 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 ...
5
votes
1answer
75 views

Yang-Mills potential and principal bundles

In section 2.7.2 of Bertlmann's "Anomalies in quantum field theory", it is stated that since a non-trivial principal bundle (based on a Lie group $G$) does not admit a global section, the Yang-Mills ...
1
vote
0answers
34 views

irrational conformal dimension

I know examples of Conformal Field Theories in which the scaling dimension of certain operators is an integer number or a fractional number. However I do not know any example in which the scaling ...
7
votes
2answers
153 views

Can we make the Dirac representation a gauge theory?

I'm looking for comments and references about an idea : gauging the Dirac representation of the Dirac matrices. What kind of field interaction would it give ? Specifically, the Dirac equation is ...
2
votes
2answers
101 views

Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
0
votes
1answer
20 views

Differences between a field, its field strength, and the force an object experiences within this field

My question is what are the conceptual and intuitive differences between these things. For example, the magnetic field B = F/(|q|v). In this case, B IS the field, and when a charged particle is ...
0
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0answers
42 views

Wind Flow Simuation Equation

I have a data that contains pressure measurements in difference locations. Now i want to do wind flow simulation based on the pressure difference between these places. The problem is i want to do this ...
0
votes
1answer
32 views

constraints on quartic interaction coefficients in double scalar field Lagrangian

Consider the 4-dimensional Lagrangian density with two real scalar fields $\phi_1$ and $\phi_2$: $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi_1 \partial^{\mu}\phi_1 + \frac{1}{2}\partial_{\mu}\phi_2 \...
8
votes
4answers
158 views

How can I tell that a Lagrangian has an $SU(2)\times SU(2)$ symmetry?

this is a very basic question and it probably has a very simple answer. I was reading through some handouts when I came over something that I did not understand. One considered the simple Lagrangian ...
2
votes
2answers
146 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 \...
2
votes
0answers
40 views

Construction of vector bundles of relativistic fields by Mackey's method of induced representation

I recently stumbled on Sternberg's book on group theory and physics. The ideas expressed in the book are really great, but the detailed reasoning is very hard to follow, I find. I am kind of stuck ...
4
votes
1answer
88 views

Significance of symplectic form in classical field theory

I'm trying to understand the significance of construction presented to me in field theory class. Let me first briefly describe it and then ask questions. Given two solutions $\phi_1$, $\phi_2$ of the ...
1
vote
0answers
7 views

Rusting of induction hardened portion when the non hardened portion is chrome plated [closed]

When a ferritic steel component that has a portion of it induction hardened and quenched in oil is chrome plated over the non hardened portion, I see rust formation after some time on the induction ...
3
votes
2answers
113 views

Are the partial derivatives of Lagrangian in the varied action functional derivatives?

In particle mechanics Lagrangian $L$ depends upon position, velocity (and may be explicitly on time), whereas in field theory the Lagrangian density ${\cal L}$ similarly (or analogously) depends upon ...
0
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0answers
50 views

Functional Differetiation of a complex functional

Suppose I have a simple functional $$F=\int{dx\;\phi^{*}(x)\phi(x)}\tag{1}.$$ Assuming $\phi(x)$ and $\phi^{*}(x)$ are independent and I take a functional differential with respect to $\phi(x)$ and $\...
4
votes
1answer
163 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 ...
0
votes
2answers
94 views

The “harmonic paradigm” in physics

Disclaimer: I know this is a vague question, so if this is not the appropriate thread, please direct me to the correct one. On page 5 of Anthony Zee's Quantum Field Theory in a Nutshell he speaks of ...
-1
votes
1answer
79 views

Derivation in Modern Supersymmetry by Terning

I am trying to do some calculations from Modern Supersymmetry by Terning and I am stuck on how he derived a particular term. Specifically, I am looking at 2.67 on page 27. My current work is below. $$...
2
votes
0answers
60 views

Jet bundles for physicists

In order to make Classical Field Theory rigorous we need the idea of jet bundles. I've seem some books on the subject, but most of them are aimed at mathematicians and tend to go quite deep in the ...
0
votes
1answer
39 views

By special relativity, a particle can only couple to an EM field? [closed]

By special relativity, the Lagrangian for the coupling must be $$ u_i A^i . $$ Here $u_i $ is the four-velocity, and $A^i$ is the four-potential. So, a particle can only couple to an EM field? ...
7
votes
1answer
287 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 ...
2
votes
1answer
64 views

Lorentz transformation of an antisymmetric tensor

I'm trying to find the infinitesimal Lorentz transformation of a rank 2 antisymmetric tensor. Looking through Peskin, all I can see is the transformation of a vector, and even there it is simply given....
5
votes
1answer
73 views

Electron - neutrino scattering effective Lagrangian

The electron and neutrino can interact through an intermediary Z boson, via the Lagrangian: $$ L= \frac{1}{2} \partial_\mu \phi_Z \partial^\mu \phi_Z - \frac{1}{2} m_Z ^2 \phi_Z ^2 -g_{\nu} \phi_Z \...
2
votes
0answers
62 views

Field solution for spacetimes with identified regions

For a spacetime surgery wormhole, we have a manifold such that, for two connected compact sets $D_1$ and $D_2$, we remove $D_1$ and $D_2$ from the manifold and identify their boundaries. According to ...
-1
votes
1answer
23 views

Parity tranformation on Lagrangian of free fields

Free lagrangians of scalar, Dirac field and vector fields are always invariant under Parity. I am able to get this result mathematically, but I want to know if there is any obvious reason for it. ...
2
votes
1answer
45 views

Problem with magnetic field due to relative motion

We know that, moving charge produces magnetic field in the surrounding space. Consider this scenario : A charge 'q' is moving with a constant speed 'v' in the direction of positive x axis of a ...
0
votes
1answer
60 views

Hamiltonian - Fourier transform of order parameter [closed]

I have a rather simple task, but it seems I can't move forward with the solution. I have a Hamiltonian as seen in the picture. I have to use the Fourier transform of the order parameter $\phi(x)$ and ...
79
votes
9answers
15k views

What is a field, really?

There was a reason why I constantly failed physics at school and university, and that reason was, apart from the fact I was immensely lazy, that I mentally refused to "believe" more advanced stuff ...
0
votes
1answer
46 views

Vector Integrals: can I take out the vector outside of the integral?

Question: Solution: The notation used is: $(x,y,z)$ is for rectangular coordinates, $(\rho,\varphi,z)$ for cylindrical coordinates and $(r,\theta,\varphi)$ for spherical coordinates. ${ { \hat ...
0
votes
1answer
86 views

Number of degrees of freedom in the Standard Model Lagrangian

Consider a Lagrangian $L$ which depends on a number of fields $F_1$, $\cdots$, $F_N$ and their (spacetime) derivatives. Each of those fields $F_n$ is valued in $\mathbb{R}^{k_n}$. Is the Standard ...
7
votes
2answers
134 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
votes
0answers
25 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 \phi+\frac{\...
0
votes
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 ...
3
votes
2answers
150 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
votes
1answer
299 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 ...
0
votes
0answers
59 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 ...
39
votes
4answers
15k views

Why correlation functions?

While this concept is widely used in physics, it is really puzzling (at least for beginners) that you just have to multiply two functions (or the function by itself) at different values of the ...
40
votes
1answer
5k views

Differentiating Propagator, Greens function, Correlation function, etc

For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most ...