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58 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 ...
1
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0answers
28 views

Approximation of skeleton diagrams

I'm studying the diagrammatics for a Bose system (in the superfluid phase) developed by Gavoret and Nozieres (Annals of Physics 28 349 (1964)). In this paper, they show how to solve the problem using ...
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1answer
135 views

Why does Einstein say contradictions arise from treating the EM field as lines of force?

EDIT - I have included the context of the quote I am interested in, as people seem to be as baffled by Einstein's quote as I am: In a 1920 address Einstein says this: Think of waves on the ...
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0answers
66 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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2answers
54 views

Is there an analogue of a geodesic for the evolution of the electromagnetic field? [duplicate]

For a charged particle moving in free space, we can say from the homogeneity of space-time, that it moves along a geodesic. Is there an analogous principle for the evolution of the electromagnetic ...
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1answer
63 views

What are the spaces over spacetime points in which a field takes its values? Is it always the same?

When it comes to the fibrations encountered in field theories of physics, are the fibers over the base space always the same?
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1answer
77 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 ...
1
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0answers
69 views

Spontaneous Symmetry Breaking

In Spontaneous symmetry breaking we have got that, a field $$\phi= \pm \sqrt{\frac{-m^2}{\lambda}}.$$ Now in order to get the unstable minima we need to guess the mass $m^2 <0 $. But can mass be ...
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1answer
115 views

Non-relativistic limit in a Lagrangian density

What criteria should I consider when determining the non-relativistic limit of a Lagrangian density? For example, how would I take the non-relativistic limit of the following Lagrangian density: ...
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2answers
59 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 ...
6
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1answer
121 views

Symmetries in physics

Can you explain me some of the mathematical details of such concept as symmetries? In physics, we have some manifold, and fields are functions on this manifold. On the one hand, we have symmetries of ...
1
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1answer
55 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
130 views

Why do we assume that Dirac spinor $\Psi$ describe the particle, not the field?

It is a well-known fact that Klein-Gordon scalar $\Psi(x)$, $$ (\partial^{2} + m^2) \Psi (x) = 0 $$ as well as 4-vector $A_{\mu}(x)$, $$ (\partial^{2} + m^{2})A_{\mu} = 0,\quad ...
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1answer
56 views

How to obtain Maxwell's Lagrangian from complex scalar fields?

I've looked in several books and they all show how to obtain electrical interactions by forcing local gauge invariance of any complex scalar field Lagrangian (like Klein-Gordon or Dirac). I manage to ...
6
votes
1answer
93 views

Intuition for actions written as integrals over spacetime

Right now I'm simply looking for an intuitive explaination of actions that integrate over a 4-volume element, $d^4x$ rather than a parameter say $\lambda$. More specifically I'm well versed in action ...
5
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1answer
60 views

Gauge fixing of an arbitrary field

How to count the number of degrees of freedom of an arbitrary field (vector or tensor)? In other words, what is the mathematical procedure of gauge fixing?
2
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1answer
128 views

Noether's Theorem in Field Theory

This question is regarding Noether's Theorem in general, but also in the application to an example. The example is: Find the conserved current for the Lagrangian ...
7
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1answer
175 views

Generator of local symmetries

Let us only consider classical field theories in this discussion. Noether's theorem states that for every global symmetry, there exists a conserved current and a conserved charge. The charge is the ...
5
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3answers
213 views

Meaning of kinetic part in the Lagrangian density?

What is the physical meaning of the kinetic term in the classical scalar field Lagrangian $$\mathcal{L}_{kin}~=~\frac{1}{2}(\partial_\mu\phi)(\partial^\mu\phi)~?$$ It gives how does the field change ...
4
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1answer
97 views

Definition of vacuum in field theory; Connection between the classical definition and the connection to QFT

I am a bit confused by what is defined to be a vacuum in field theory. Classically a vaccum state is defined to be the state where the field sits at some minima of the potential $\frac{\partial ...
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1answer
73 views

Massless Thirring Model in 1+1 Dimensions

In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (link to Phys Rev D article), he pointed out that the massless Thirring Model is exactly scale invariant. More over, ...
3
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0answers
52 views

Complex scalar fields conserved charges

I'm currently studying field theory and I'm having some trouble with conserved charge given in field components. If we have a complex scalar action of a field $\phi=(\phi_1,\phi_2)^T$ that is ...
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1answer
415 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
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1answer
89 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 ...
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1answer
66 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
145 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 ...
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0answers
31 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 ...
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4answers
262 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 ...
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0answers
102 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 ...
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1answer
37 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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2answers
193 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
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1answer
85 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 ...
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2answers
157 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, ...
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0answers
95 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
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0answers
74 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 ...
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0answers
55 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 ...
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1answer
38 views

Integrating out fields from classical systems

Has anyone ever heard of integrating out fields from classical Lagrangians if they are quadratic?
1
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1answer
64 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
156 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 ...
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1answer
50 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?
2
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1answer
132 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
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1answer
234 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
118 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 ...
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1answer
117 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 ...
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0answers
27 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 ...
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0answers
74 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
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1answer
204 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
104 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
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1answer
195 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 ...
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2answers
172 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 ...