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17
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1answer
430 views

Is there a field equation which can reduce into all three flavors of spin (zero, one, one half)?

Is there a known particle field equation of a similar form $$ \begin{equation} (\Gamma^n \pi_n)^2 \Psi = (mc)^2 \Psi \tag{1} \end{equation} $$ such that by reducing the number of degrees of freedom ...
2
votes
1answer
109 views

Noether Charge For Scalar Fields Under Lorentz Transformations

The conserved charge associated with the Lorentz transfomation of a scalar field is given by $Q^{\alpha\beta}=\int d^3x\frac{1}{2}(x^\alpha T^{0\beta}-x^\beta T^{0\alpha})$. The quantities $Q^{ij}$ is ...
1
vote
1answer
79 views

What advantages does action-at-a-distance description have over the field view of forces?

It is written in Jackson (page 3) : In fact, though there are recurring attempts to eliminate explicit reference to the fields in favor of action-at-a-distance descriptions of the interaction of ...
6
votes
1answer
178 views

Mass generation by Chern-Simons theory

Why the mass generation via a Higgs mechanism is different from that of Chern-Simons theory? I haven't done any formal course in Quantum field theory,so how do I understand this just having some basic ...
0
votes
0answers
34 views

What happens if the energy has no lower bound?

In almost all theories that we investigate there is an lower bound on the energy. But is this necessary for a theory to be a good description of reality? I know from quantum field theory, that in its ...
1
vote
1answer
124 views

What is meant by a local Lagrangian density?

What is meant by a local Lagrangian density? How will a non-local Lagrangian look like and what is the problem that we do not consider such Lagrangian densities?
0
votes
4answers
391 views

Does a charge experience no force due to electric field produced by it?

My book "Concepts of Physics (Satish K. Gupta)" says: The electric field of a charge is the space property by virtue of which the charge modifies the space around itself. As a result, if any ...
2
votes
0answers
141 views

Product of $\gamma^5 \sigma^{\mu\nu}$

I'm trying to prove that $\gamma^5 \sigma^{\mu\nu}=\frac{i}{2}\epsilon^{\mu\nu\alpha\beta}\sigma_{\alpha\beta}$ I started with the left hand side and expanded the $\gamma^5$ to ...
1
vote
1answer
40 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 ...
0
votes
2answers
216 views

Understanding field representation of force [duplicate]

I am reading the book The Evolution of Physics. I have a doubt in the topic "The field as representation". In this topic authors give the example of gravitational force represented as a field. In the ...
6
votes
1answer
96 views

In which field theories with fermions do string- and fivebrane structures not come up?

A year ago, username @Greg Graviton asked in a thread here about the Spin group as covering of the spatial rotations. A subquestion was: What other groups, even larger than SU(2) are there that ...
1
vote
2answers
167 views

Classical point particles to classical fields

I often hear that in the continuum limit we can study large numbers of particles as fields. I always imagined that by removing all bounds on the number of particles (while keeping total energy, ...
4
votes
0answers
99 views

One more time about Nordstrom theory

Wikipedia says that Nordstrom theory with equations of motion of the test particle $$\tag{1} \frac{d (\varphi u_{\alpha})}{d \tau} = \partial_{\alpha} \varphi $$ and field equation $$\tag{2} \varphi ...
2
votes
0answers
82 views

Half-integer Spin and “natural conformal dimension”

If we consider a classical field theory for a massless particle of integer spin $s$, in a curved space-time, one finds that it is "naturally" conformal in a space-time of dimension $2+2s$ For ...
0
votes
0answers
57 views

Explanation of the classical coupling of the Higgs Field to Electromagnetism

I'm interested in learning about the classical coupling of the Higgs Field to Electromagnetism. There are numerous sources explaining the Higgs mechanism quantum mechanically, i.e. How does the Higgs ...
1
vote
1answer
46 views

Integrating out fields from classical systems

Has anyone ever heard of integrating out fields from classical Lagrangians if they are quadratic?
1
vote
1answer
66 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: ...
6
votes
2answers
170 views

How does a SCFT avoid the Haag-Lopuszanski-Sohnius theorem?

According to the Haag-Lopuszanski-Sohnius theorem the most general symmetry that a consistent 4 dimensional field theory can enjoy is supersymmery, seen as an extension of Poincarè symmetry, in direct ...
1
vote
1answer
53 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?
4
votes
2answers
200 views

Mean field theory = large-N approximation?

Wikipedia entry of 1/N expansion (or 't Hooft large-N expansion) mentions that It (large-N) is also extensively used in condensed matter physics where it can be used to provide a rigorous basis ...
3
votes
1answer
290 views

What exactly is the connection between the Jacobi and Bianchi identities

While reviewing some basic field theory, I once again encountered the Bianchi identity (in the context of electromagnetism). It can be written as $$\partial_{[\lambda}\partial_{[\mu}A_{\nu]]}=0$$ ...
2
votes
1answer
129 views

Book Recommendation- Classical Relativistic Fields

My bare bookshelves are crying out for the addition of a new family member, more specifically a book: Discussing the classical Klein-Gordon field, spinor fields, gauge fields and all other matter ...
1
vote
1answer
128 views

How to understand dynamics $\dot x_i=\partial_jA_{ij}$ from skew-symmetric potential $A$?

We speak of a dynamical system with a potential if there is a scalar possibly depending on coordinate such that the vector field is exactly the (negative) gradient of the potential. That means each ...
0
votes
0answers
28 views

Modeling Spacetime In A Corpuscular Or Statistical Way

When I first read about Newton's gravity, it really bothered me. I didn't understand how shaking a lighter at the other end of the universe would instantly influence the lighter that was in front of ...
1
vote
0answers
75 views

How to introduce generating function in Hamiltonian formalism for field theories?

Let's have hamiltonian $$ H(\psi , P ,\partial_{i}\psi ) = P\partial_{0}\psi - L(\psi , \partial_{\mu}\psi ), \quad P = \frac{\partial L}{\partial (\partial_{0}\psi)}. \qquad (.0) $$ I tried to ...
1
vote
1answer
291 views

Tracelessness of energy-momentum tensor and massless photons

I have read the statement that the tracelessness of the energy-momentum tensor is demanded by the condition of photons being massless. I see how this comes about starting from the canonical ...
2
votes
1answer
120 views

Spin tensor and Lorentz group operator in bispinor case

For infinisesimal bispinor transformations we have $$ \delta \Psi = \frac{1}{2}\omega^{\mu \nu}\eta_{\mu \nu}\Psi , \quad \delta \bar {\Psi} = -\frac{1}{2}\omega^{\mu \nu}\bar {\Psi}\eta_{\mu \nu}, ...
2
votes
1answer
215 views

Primary constraints for Hamiltonian field theories

I am currently trying to carry out the construction of the generalised Hamiltonian, constraints and constraint algebra, etc for a particular field theory following the procedure in Dirac's "Lectures ...
1
vote
2answers
206 views

Can a scalar field model gravity? How accurate would be the results? Are there any difficulties with such a model?

Newtonian gravity can be described by the equation: $$ \nabla^2 \phi = 4 \pi \rho G $$ where $\rho$ is the mass density, $\phi$ is the gravitational potential, and G is the universal gravitational ...
8
votes
1answer
184 views

Boundary currents for Asymptotic Symmetry Group (ASG)

In the context of asymptotic symmetry groups, what is a boundary current? Why is it called a "current"? Context: I'm reading Strominger's recent paper on Asymptotic symmetry group of Yang-Mills ...
3
votes
2answers
419 views

Coordinate Transformation of Scalar Fields in QFT

By definition scalar fields are independent of coordinate system, thus I would expect a scalar field $\psi [x]$ would not change under the transformation $x^\mu \to x^\mu + \epsilon^\mu $. Correct? ...
2
votes
1answer
344 views

Deriving the Hamiltonian density for a free scalar field

I'm working through my old notes on QFT (cf. Ref 1) and I'm not quite sure how to approach the derivation of the Hamiltonian density for a free scalar field (question 2.3 on page 19) and the ...
8
votes
1answer
256 views

What are the details of the renormalization of Chern-Simons theory?

What is a good, simple argument as to why Chern-Simons theory' is renormalisable? Any good books/references dealing with this effectively? Why does the $\beta$-function vanish? Thanks!
1
vote
1answer
100 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 ...
0
votes
0answers
325 views

Scalar field lagrangian in curved spacetime

I am studying inflation theory for a scalar field $\phi$ in curved spacetime. I want to obtain Euler-Lagrange equations for the action: $$ I\left[\phi\right] = \int ...
0
votes
0answers
46 views

Physical and dynamical components the four potential

I have a question regarding the four-potential and its gauge symmetry. We have a gauge freedom: $A_{\mu} \rightarrow A_{\mu} + \partial_{\mu}\chi$ Such a transformation does not alter the EM field. ...
0
votes
1answer
64 views

Definition: Coupling [closed]

What does it mean to say that 2 fields are coupled? More generally, what does "coupling" mean?
2
votes
0answers
94 views

Path integral measure and symmetry

For a generic field theory the path integral measure is defined as, \begin{equation} \mathcal{D}\Phi = \prod_i d\Phi(x_i), \end{equation} where $\Phi$ is a generic field (i.e. it may be scalar, ...
6
votes
1answer
170 views

Proof that we can always find a gauge transformation such that $A_0=0$?

I'm trying to follow Coleman's proof from his lectures "Aspects of Symmetry" on page 200-201. He proofs it is always possible to work in the temporal gauge for a general Yang-Mills-Higgs theory. I ...
3
votes
3answers
196 views

Are Field Lines an accurate depiction of reality?

Field lines are used for explaining a wide variety of phenomenon. But is it really an accurate depiction of reality? Is it more accurate to imagine a field in a different manner. For instance, using ...
2
votes
0answers
337 views

The connection between classical and quantum spins

I have two questions, which are connected with each other. The first question. In a classical relativistic (SRT) case for one particle can be defined (in a reason of "antisymmetric" nature of ...
1
vote
0answers
82 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} ...
1
vote
2answers
194 views

Dimensions in lagrangian potential

According to Mankowski flat space dimensions We can write, $$L= \int \text{dt} \text d^d{x} \left[ \frac{1}{2} \dot\phi^2 - \frac{1}{2} \left(\frac{\partial \phi}{\partial r} \right)^2 ...
1
vote
1answer
132 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 ...
1
vote
1answer
152 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 ...
1
vote
0answers
56 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 ...
0
votes
0answers
94 views

Derrick’s theorem(2)

Related post : 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) ...
0
votes
2answers
170 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- ...
0
votes
1answer
100 views

Vortex in D dimensions soliton

let us consider the two-dimensional configuration shown in Fig. 3.1a. The lengths of the arrows represent the magnitude of φ, while their directions indicate the orientation in the $φ_1 -φ_2$ plane. ...
1
vote
1answer
205 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 ...