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1answer
47 views

Circulation of the gauge potential around an infinitesimal loop: how to get the correct gauge field strength tensor

I've been puzzling with the problem below for more than a hour since it is misleadingly discussed in some textbooks, so I believe it deserves a solution here. Any comments are welcome. I'm trying to ...
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1answer
70 views

Gradient of a two-component field

I have a two-component field: $$\phi(\vec{x}) = \left( \begin{array}{c} \phi_1(\vec{x}) \\ \phi_2(\vec{x}) \end{array} \right)$$ with $\phi^T = (\phi_1, \phi_2)$. And I am trying to evaluate: ...
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2answers
119 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 ...
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1answer
189 views

Potential in Relativistic Scalar Field Theory

My intention is to establish a Soliton equation. I have cropped a page from Mark Srednicki page no 576. I have understand the equation (92.1) but don't understand that how they guessed the ...
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1answer
300 views

Lorentz Invariant Equation of Motion for Scalar Field

I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity. Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
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1answer
30 views

Why Do Stark Manifold Graphs All Have Negative Energy?

I have been studying Rydberg-Stark State Atoms and their Stark Manifolds (like the one on Wikipedia: http://en.wikipedia.org/wiki/File:Hfspec1.jpg) and I was wondering, Why does the y-axis (of Energy ...
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1answer
76 views

Creation and annihilation operators

In our lecture today, we introduced two kinds of creation and annihilation operators. I want to restrict myself to the antisymmetric case: The first operator $a_k^{\dagger}$ creates a state ...
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1answer
82 views

Interpretation of $\vec{x}$ in QFT

I am still at an early stage of studying Quantum Field Theory (I am reading QFT In A Nutshell by A. Zee). In the book I'm reading, it starts from a discrete lattice of material "lumps" labeled by ...
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1answer
80 views

Hermiticity of the quantum field

The quantum field resultant from the quantization of a real classical field is hermitian, but why the quantum field corresponding to a complex classical field should be non-hermitian?
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1answer
694 views

The relation between the movement of electrons and energy

So, I've been enjoying reading a lot of helpful posts, but now, I found myself in the need of asking something. I have a hard time grasping the general concept of electricity / how the relation ...
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2answers
120 views

Visualising the magnetic field [closed]

How can we visualise the magnetic field?How to visualise magnetic field due to current carrying conductor having poles(like north and south for ordinary magnetic). Can we determine the north and the ...
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1answer
57 views

Collected Gravitational Field

I wasn't sure what to call this, I'm not a physicist. I basically have a collection of massive bodies. I to calculate the gravitational field of all those objects collected; how to do this? The ...
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1answer
54 views

Integrating out fields from classical systems

Has anyone ever heard of integrating out fields from classical Lagrangians if they are quadratic?
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1answer
54 views

The speed of light and fields

Does the speed of light apply to the speed of (waves?) in every known field, or does it only apply to the electromagnetic field?
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1answer
123 views

Dimension analysis in Derrick theorem

The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe: What I don't understand from the above statement: why $e(\mu)$ has minimum ...
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1answer
142 views

Finding out Energy value

A Lagrangian is given by, $$L= \left(\frac{\pi}{2}\right)^2 R^d \left[\frac{1}{2}\dot A^2 - V(A_{max})\right]$$ $$E=\left(\frac{\pi}{2}\right)^2R^d V(A_{max}) $$ where V (A) now includes nonlinear ...
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1answer
184 views

Are multipole fields, multipole expansion, and multipole radiation the same thing?

Interaction between electromagnetic radiation and nuclei can be written in terms of multipole radiation. Are multipole fields, multipole expansion and multipole radiation the same thing? I have found ...
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1answer
290 views

sine-Gordon equation

I have derived a solition equation (2 dimensions) from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{1}$$ and also I have got sine-Gordon equation for solition ...
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2answers
180 views

In Noether's theorem, what is a “classical solution of the equations of motion”?

I'm reading a book which states that: for each generator of a global symmetry transformation, there is a current $j^{\mu}_{a}$ which, when evaluated on a classical solution of the equations of ...
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1answer
30 views

Notion of distance in a Conformal Field Theory

I'm confused about the how the notion of distance is used in Conformal Field Theory. Let's take for example the Operator Product Expansion (OPE). In a conformal field theory, due to the scale ...
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1answer
51 views

vanishing of $\Pi^0$ and non-existence of propagator

We know that if we try to quantize the free electromagnetic field without a gauge fixing term added to the Lagrangian, then one of the conjugate momentum density $\Pi^0$ vanishes. We also find that ...
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1answer
74 views

How to obtain the asymptotic behavior of Green's function?

This question arose from Eq.(9.135) and Eq.(9.136) in Fradkin's Field theories of condensed matter physics (2nd Ed.). The author mapped quantum-dimer models to an action of monopole gas in $(2+1)$ ...
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0answers
47 views

Noether current scale transform of EM

I'm trying to solve a question about scale tranform of free EM. I got the next trnaform rules (these two line where EDITed later) $\delta x = -bx$ $\delta A = bA$ the current I got $D^\mu = ...
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0answers
32 views

Super weyl transformation of superfiled R [closed]

Can anyone guide me how to find super weyl transformation of R (main superfield of SUGRA)? I think that I need super weyl transformation of super vielbein and super connection and using the ...
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1answer
51 views

Obtaining momentum operator $P^\mu$ from Lagrangian and energy-momentum tensor $T^{\mu\nu}$

I am pretty new to quantum field theory. Given the Lagrangian density, $$ \mathcal{L} = \frac{1}{2} ( \partial_\mu \phi ) ( \partial^\mu \phi ) - \frac{1}{2} m^2 \phi^2 $$ and its energy-momentum ...
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0answers
60 views

Relation between $f(R)$ gravity and Tensor–vector–scalar (TeVeS) gravity

We know that there is a relation between f(R) gravity and scalar-tensor gravity. By applying the Legendre-Weyl transform, we can receive brans-dicke gravity from $f(R)$ gravity. If we start with the ...
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0answers
49 views

Difference between a “source dipole” and a “force dipole”

I know quite well what a dipole is and in general what multipole moments are (in the context of, for instance, electrodynamics). What I find myself confused by is something called a "force dipole" in ...
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0answers
55 views

In SUSY, why do fermions and gauge bosons in the same multiplet both transform in the adjoint representation of the gauge group?

I'm trying to understand a certain point about supersymmetry. We are dealing with a N=1 (i.e, one supersymmetric flavour), massless, four dimensional theory. Then the vector multiplet consists of a ...
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0answers
47 views

Mixed two-point vertex in QFT

I am considering a theory with two fields, say $\phi$ and $\psi$. The Lagrangian contains quadratic terms, i.e., propagators for both fields and a quartic interaction term for one of the fields. ...
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1answer
111 views

How to find the Hamiltonian density for electromagnetic field? And, how to solve the stress tensor for electromagnetic field? [closed]

How to find the Hamiltonian density for electromagnetic field? And, how to solve the stress tensor for electromagnetic field?
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0answers
65 views

What's the conserved stress energy tensor? [closed]

I've worked on this problem for forever and still don't really see the solution. Any help appreciated. Say we have the Lagrangian for a scalar field that's $U(1)$ charged,$$\mathcal{L} ...
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0answers
40 views

Total Vs Partial in Lagrange density?

I have a question regarding the red term below. This is the integration by parts during the derivation of the Euler-Lagrange equation for continuous systems. Why is this not the time derivative ...
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1answer
105 views

A Spin up particle in QFT

This appears like a question that is rarely addressed in field theory pedagogy (perhaps because the answer is obvious): how does one describe a particle of definite spin in quantum field theory? For ...
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0answers
20 views

Energy Tensor, covariant derivate, variation respect to the metric [duplicate]

I'm doing the variation of a Lagrangian respect to the metric, but I am having problem with a particular terminus. My action is: $$ S=\int d^4x \sqrt{-g}[ (\nabla_\mu A^\mu)^2]$$ My lagrangian is: ...
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0answers
51 views

Difference between Gravitational and Matter Scalar Fields

In the context of Scalar-Tensor theories of gravity (for example in Brans-Dicke) what is the difference between gravitational and matter scalar Fields? My doubt comes from "The scalar-tensor Theory ...
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0answers
77 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 ...
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1answer
104 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 ...
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0answers
18 views

How does the choice of a basis decide how many Goldstone bosons there are under spontaneous symmetry breaking?

I have a question about how the basis you choose in a field theory problem semmingly decides how many Goldstone bosons you get after spontaneous symmetry breaking. For SU(2), if you choose the 3 Pauli ...
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0answers
52 views

Where does the potential energy associated with the field go if it is removed? [closed]

I have an electric field and a certain charged particle in it that has a certain potential energy associated with it. Where does the energy go if I remove the field?
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0answers
152 views

Green Function for Proca Equation

I have tried to find a retarded and advanced Green function for Proca field equation. $(\Box - \mu^2)A^{\mu}=J^{\mu}$ where $\mu$ is the mass term. How I did it: first: I made Fourier ...
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0answers
122 views

Why does Principle for least action hold for classical fields [duplicate]

Let $\mathscr L (\phi(\mathbf x), \partial \phi(\mathbf x))$ denote the Lagrangian density of field $\phi(\mathbf x)$. Then then actual value of the field $\phi(\mathbf x)$ can be computed from the ...
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0answers
85 views

Dimension dependence

The question is related to this one The time averaged total energy, $\bar E$, has the following $\varepsilon$ expansion in $D$ dimension: \begin{equation} ...
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0answers
65 views

Global part of a local symmetry?

What is exactly meant by "Global part of a Local symmetry"? What are its implications on a field theory at classical level? What are its implications at quantum level? How is it related to symmetry ...
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0answers
132 views

A fundamental equation for solitary wave and dimension analysis [closed]

According to the scalar Field theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$ What I want to do is ...
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0answers
89 views

relevant 4-dimensional theory with interacting vector field

A simple langragian that gives the simplest interaction is $\mathcal{L}=(\partial\phi)^2+(m\phi)^2$ where $m$ is some constant. Does anyone know of theory in four dimensions which is physically ...
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2answers
643 views

Partial derivative of Lagrangian density for vector field

The lagrangian density of a massless vector field is $ \mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$, where $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}$ Expanding out gives ...
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2answers
217 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- ...
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2answers
225 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 ...
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1answer
64 views

Is there a field for which neutral particle and antiparticle, can be considered as positive and negative charge?

I apologize, but QFT is not my domain. What I ask is connected with the question Do the fields exist without charges? . By analogy with the electron and proton, that carry the electric charges of the ...
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1answer
81 views

Definition: Coupling [closed]

What does it mean to say that 2 fields are coupled? More generally, what does "coupling" mean?