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Scalar gravity coupled to matter

I am reading Ortin's Gravity and Strings and trying to understand the generalisation of Newtonian Gravity to a relativistic field theory. On page 47 (link above) he motivates the study of the Poisson ...
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2answers
115 views

Finding the action of a discretized Lagrangian

I am trying to find the action associated with the Lagrangian density $$ \mathcal{L} = \frac{1}{2}\left( \frac{\partial\phi}{\partial x} \right)^2 + \frac{1}{2}m^2\phi^2. \tag{1} $$ I am supposed to ...
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1answer
118 views

Regarding the Weyl spinor and its transformation properties

I am trying to prove the Lorentz invariance of the (left-handed) Weyl Lagrangian: $$\mathcal L=i\psi^\dagger\bar\sigma^\mu\partial_\mu\psi$$ A Lorentz transformation is realized as $\psi\to M\psi$, ...
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2answers
129 views

Noether's theorem: meaning of transformation of coordinates

I have a question regarding Noether's theorem. In our introductory QFT class (which is based on the book by Michele Maggiore) we have derived the Noether currents in the same form as displayed in this ...
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1answer
115 views

Is EM interpreted in a principal or vector bundle?

I've read in a few places that EM is a $U(1)$-principal bundle; but is this correct? Isn't it rather an associated vector bundle using the adjoint representation of $U(1)$?
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3answers
376 views

Energy-Momentum Tensor for Electromagnetism in Curved Space

$\newcommand{\l}{\mathcal L} \newcommand{\g}{\sqrt{-g}}$$\newcommand{\fdv}[2]{\frac{\delta #1}{\delta #2}}$I want to calculate the energy-momentum tensor in curved free space by functional ...
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0answers
86 views

Lagrangians densities & interactions in field theory

To avoid ambiguity, this question pertains to the construction of Lagrangian densities (including interaction terms) in terms of their values at single points in spacetime. In classical mechanics in ...
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2answers
107 views

How does Lorentz invariance make $(\Psi_0,J_{\mu}\Psi_0)$ vanish?

Right before equation (10.4.7) in Weinberg's volume 1 on quantum field theory, he said $(\Psi_0,J_{\mu}\Psi_0)$ vanishes due to requirement of Lorentz invariance. As I understand, this term is a ...
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0answers
26 views

Beyond the third time derivative [duplicate]

Why do texts on classical mechanics never mention any derivative of position beyond the jerk, while at the same time being general in the sense of using of generalized coordinates?
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2answers
185 views

Does a field have any physical meaning or significance? [duplicate]

Is the concept of a field just a mathematical construct? Is there any way to realize its existence? For instance, the fact that moving a charge affects other charges in the surrounding not ...
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1answer
69 views

Do different fields interact with each other directly?

There are many different types of fields such as electron field, magnetic field, higgs field, electric field, quarks field etc, my question is do these fields interact directly with each other? ...
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1answer
119 views

Problem to find field equations with Euler-Lagrange in field theory [closed]

I have the Euler-Lagrange equations, as stated in field-theory: $$\partial_\nu \left(\frac{\partial L}{\partial (\partial_\nu \phi_\rho)}\right) - \frac{\partial L}{\partial \phi_\rho}=0$$ However I'...
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1answer
165 views

Should the (On-shell) (2+1)d $N=2$ Chiral Multiplet Contain Two Scalars and Two Majorana Spinors?

In supermultiplets, the bosonic degrees of freedom and the fermionic degrees of freedom need to match in number. The number of degrees of freedom of a field corresponds to the number of independent ...
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1answer
131 views

Doubts with basic renormalization

When we renormalize to obtain the physical mass, the $\Lambda$ dependence of the physical mass is removed by introducing the counterterms in the Lagrangian. So whether we put $\Lambda\rightarrow\infty$...
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0answers
122 views

Mean-field solution of Potts model

The mean-field equation for the three-state Potts model $H= -J∑δσiδσj$ can be derived as follows using this: a) show that $H$ is equivalent to $-J∑Si.Sj$ where, $Si=(1 0) , (-1/2 √3/2 ) , (-1/2 -√3/...
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2answers
112 views

Why is the introduction of a quantization volume necessary for quantization of the EM field

I have been working through the quantization of the electromagnetic field, and every source I find introduces a quantization volume with periodic boundary conditions in the process, in which we fit ...
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1answer
99 views

How do you take the derivative with respect to a rank two tensor?

I am learning classical field theory and am trying to find the momentum density of the electromagnetic lagrangian as part of an example of Noether's Theorem. The derivative I am encountering is: $$ \...
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1answer
83 views

What is the difference between the momentum in the Fourier transform of a scalar field and the conjugate momentum of the field?

What is the difference between the momentum $p$ in $e^{i\mathbf{p}\cdot{\mathbf{x}}}$ in the Fourier transform of a scalar field and the corresponding conjugate momenta $\pi(x)$ of the scalar field?
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1answer
75 views

As the magnetic field propagates does it have a momentum that can be felt by another magnetic field of the same charge?

If I have a solenoid and a permanent magnet, and I placed the magnet an inch away from the solenoid, oriented in a position where the magnet would be repelled as the solenoid is turned on. Is it a ...
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2answers
84 views

Field theory for a finite temperature normal fluid

Can normal-fluid (not superfluid) hydrodynamics be derived from some classical field theory? Here I mean conservation (continuity) equations for mass (density), momentum, and energy (entropy, ...
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0answers
63 views

Noether Current and Feynman Diagrams

My question is simple. Assume that there is no anomaly and we have found from the lagrangian that there is a conserved current. I want to know what this means in terms of feynman diagrams, not in ...
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1answer
79 views

If time-like paths are geodesics, what physical principle applies to space-like intervals?

If I have a number of particles interacting with one another locally, then the center of mass of the system moves along a geodesic. Taking this further with the particles interacting via an EM field, ...
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0answers
97 views

Renormalization of Auxiliary Fields

I have the following non-linear sigma model (the base space $\mathcal{M}$ is Euclidean): $$ \mathcal{L}=\dfrac{1}{2\alpha}\int_{\mathcal{M}}\mathrm{d}^2\sigma\ \partial^2X^{\mu}\partial^2X_{\mu} $$ ...
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1answer
41 views

Meaning of these terms for stress fields?

I'm from a math & comp sci background and I'm currently looking at facture theory which deals with stress fields. Can someone explain to me what the following terms represent in the context of a ...
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2answers
107 views

Why don't we take this term $D_{\mu}D_{\nu}F^{\mu\nu}$ in Lagrangians?

Why don't we take $$D_{\mu}D_{\nu}F^{\mu\nu}$$ in Lagrangians?
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1answer
72 views

quantum fluctuations and the virtual particles

In the introduction of chapter-12 of “An Introduction to Quantum Field Theory” by Peskin and Schroeder I encountered this line: “The quantum fluctuatuations at arbitrarily short distances appear in ...
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1answer
78 views

Poincare non-invariance in real world and field theory

This may be a very blunt question but I wonder why we always use Poincare invariant Lagrangians in field theory. After all, the entire world around us is by no means homogeneous, isotropic and so on. ...
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1answer
151 views

Equivalence principle for test fields

My question is very simple. We all know that, for a test particle(classical) in a gravitational field, the motion is only determined by the geodesic lines(let's forget about the initial conditions for ...
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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 ...
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0answers
81 views

What's the shape of electric field line in a rectangular metal under varying magnetic field

We know that,the shape of electric field line in a cylinder under varying magnetic field is circle,and I wonder,what's the situation if it is a piece of metal with rectangular cross section? I think ...
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3answers
198 views

The Higgs field vs the Higgs boson

As I see it the Higgs boson is the mediating particle of the Higgs field and get its own mass from the Higgs field. Isn´t this circular? I mean, for instance, an electron creates a radial electric ...
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0answers
58 views

Why are the particles called irreps of Poincare group? [duplicate]

Why are particle excitations called irreducible representation of the Poincare group? It will be very helpful if someone can illustrate with one concrete example of a particle. EDIT : But how does ...
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0answers
232 views

What is the reason for chiral anomalies in condensed matter systems?

If you consider a massless relativistic fermion theory and you perform a chiral transformation, then you realize that while the classical action remains invariant under this transformation the ...
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1answer
105 views

Invariance of Fermionic action under Lorentz transformations

Suppose I have an Lagrangian $$\mathcal{L} = \frac{1}{2}g_{ab} \bar{\psi}^a \Gamma^k \partial_k \psi^b $$ and I want to show it's invariance under the infinitesimal Lorentz transformations $$\delta \...
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2answers
223 views

what is the result of change in gravitational flux?

As a change in magnetic flux results in induced EMF (electromotive force) likewise what is the result of a change in gravitational flux? UPDATE: Gravitational flux according to me has only ...
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1answer
111 views

Why should Ward identities only be used with the effective action (as opposed to the generating functional for connected diagrams)?

My question is about the derivation of Ward identities. I will sketch it here in the case of an O(N) symmetric model and point out what it bothering me when I am done. I am being very sloppy with the ...
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1answer
78 views

Sign of matter Lagrangian term in curved space

In field theory the (matter) Lagrangian $\mathcal{L}_m$ is uncertain upto an overall constant multiplying factor (i.e. $\mathcal{L}_m$ and $a\mathcal{L}_m$ yield the same field equation(s) on ...
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0answers
75 views

Conservation of momentum in field theory

By studying electrodynamics a while now, I came to this question on the conservation of momentum. In Newtonian mechanics the Third Law allows us to prove the conservation of momentum, with the ...
2
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1answer
110 views

How can one prove that there cannot exist a conformal primary, in the case of free field theory, that doesn't saturate the unitarity bound?

In free field theory, the full list of conformal primaries, is given by the Twist-2 operators. These have $\Delta = l+2$, which is also the saturation condition for the unitarity bound for $l \neq 0$. ...
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1answer
85 views

What gauge field can be constructed from Lorentz symmetry?

You can take a global symmetry and promote it to a local gauge symmetry by introducing an appropriate gauge field and upgrading the partial derivative to a covariant derivative. The photon field ...
2
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1answer
134 views

Hamiltonian field equations constraints

Let's consider the Lagrangian $$\mathcal{L}~=~-\frac{1}{2}(\partial_\mu\phi^\nu)^2+\frac{1}{2}(\partial_\mu\phi^\mu)^2+\frac{1}{2}m^2\phi_\mu \phi^\mu,$$ with Minkowski metric $\eta_{\mu\nu}={\rm ...
3
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1answer
107 views

Noether's theorem in field theory: Jacobian factor

Following my earlier question in this Phys.SE post I have another question regarding the derivation I am struggling through! Considering the variation in the Lagrange density for $x'=x+\delta x$ and ...
2
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0answers
128 views

Index notation for a Lagrangian with second derivatives

I'm finding the field equations for a hypothetical Lagrangian with dependence on the second derivative of a scalar field, $L\left(\phi,\phi_{,\mu},\phi_{,\mu\nu}\right)$, and in the analogue to the ...
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2answers
121 views

Noether's theorem in classical field theory

I am trying to understand the continuum version of Noethers theorem from this source (p 15- 17) however I am stuck on a couple of points. I will go through what I have so far and then ask my questions ...
0
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1answer
91 views

Entanglement entropy in (1+1)d field theory with dynamical critical exponent $z>1$

It was well known that for (1+1)d CFT(z=1) case, we can use the tool of conformal map to derive the formula of entanglement entropy for a finite interval: S ~ $c \log L$. L is the length of the ...
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1answer
47 views

A question on the functional dependence of the Lagrangian density

I understand that in classical mechanics the state of a particle at a given instant in time is given by its position $q$ and its velocity at that point $\dot{q}$, and given that, for any given point $...
2
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1answer
115 views

In general, can a Lagrangian density depend on space-time explicitly?

In an exercise on classical field theories, I'm trying to derive the general formula of the Energy-momentum tensor. According to the formula in the lecture notes, this tensor includes a term of minus ...
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2answers
166 views

How to count the number of modes/polarizations of a Gaussian field theory?

A Gaussian (free) field theory is described by a quadratic action of the field, e.g. $S=\int\psi^\dagger K\psi$ (or $S=\frac{1}{2}\int\phi^\intercal K\phi$ for real fields). Usually one just need to ...
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0answers
162 views

Precisely speaking, does photon become massive or the phonon become massive, due to Higgs mechanism in superconductor?

Consider the low-energy field theories of superfluids and superconductors. In superfluids, the spontaneous breaking of the order parameter's phase creates phonons as the massless Goldstone bosons.(...
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1answer
408 views

Euclidean classical action

This is the Euclidean classical action $S_{cl}[\phi]=\int d^{4}x\ (\frac{1}{2}(\partial_{\mu}\phi)^{2}+U(\phi))$. It would be nice if somebody could explain the structure of the potential. I don't ...