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3
votes
1answer
78 views

Is $\phi^4$ theory in 4d conformally invariant at the classial level?

I used to believe the three following statements to be true (at the classical level only): From scale invariance full conformal invariance follows. Scale invariance is present if there are no ...
3
votes
1answer
222 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 ...
0
votes
1answer
40 views

Lagrangian density with explicit $x_\mu$ dependence

In the Quantum Field Theory book, by Ryder, he says that a Lagrangian density of a field can also be an explicit function of $x_\mu$ if the field interacts with external sources. Can someone give an ...
5
votes
0answers
60 views

Spin-dependence of the directionality of dipole radiation

I am interested in understanding how and whether the transformation properties of a (classical or quantum) field under rotations or boosts relate in a simple way to the directional dependence of the ...
4
votes
0answers
61 views

Reality of the action in QFT

Following Ramond, 1.5 Field Theory, it is mentioned that the classical Lagrangian density in (workable for HEP) QFT theories has to be Real, otherwise total probability is not conserved. Can someone ...
4
votes
0answers
95 views

Axion Model Field Theory Problem

This is a homework problem for a field theory class dealing with an axion model. Originally, we are given that $$S[a]=\int_Md^4x \frac{1}{2}(\partial_{\mu}a(x))^2$$ has a continuous global ...
3
votes
0answers
179 views

Questions about classical and quantum scale invariance

This is kind of a continuation of this and this previous questions. Say one has a free "classical" field theory which is scale invariant and one develops a perturbative classical solution for an ...
2
votes
0answers
189 views

What are the equations of motion for the scalar field in the tetrad formalism?

The action of a massless scalar field in curved spacetime is given by: \begin{equation} S(\phi)=\int d^{4}x \sqrt{-g}\left(g^{\mu\nu}\phi_{,\mu}\phi_{,\nu}\right) \end{equation} Now the action can ...
2
votes
0answers
95 views

Problems while doing $\dfrac{\partial}{\partial(\partial_\mu \phi)}$ and $\dfrac{\partial}{\partial(\partial_\mu A_\mu)}$

In David Tong's lectures, he gives two Lagrangians as examples to derive the equations of motion: $$\mathcal{L} = \dfrac{1}{2}\eta^{\mu\nu}\,\partial_\mu\phi\,\partial_\nu \phi-\dfrac{1}{2}m^2\phi^2, ...
2
votes
0answers
76 views

Possible Error in deriving conformal generator

My professor gave me the following derivation for the full generator of the Lorentz transformations. The starting point is to consider a subgroup of the conformal group that leaves the origin fixed ...
2
votes
0answers
104 views

Similarities between laminar-turbulence transition and others like BCS-BEC crossover, quark-hadron transition etc

From my limited readings on fluid dynamics, my understanding is that as the system changes from near-laminar flows to full turbulence, the dimensionless Reynolds number changes from $ R << 1$ to ...
1
vote
0answers
27 views

classical extrema to Lagrangian field equation

Local extrema to the classical Lagrangian field equation are minima and are termed instantons. In classical field theory we do not distinguish between global and local extrema of the action. Can we ...
1
vote
0answers
143 views

Taylor expansion in classical 1D harmonic chain (classical field theory)

I'm struggling with something apparently really easy but not entirely straightforward. In "Condensed Matter Field Theory" of Altland and Simons the classical 1D harmonic chain is treated as ...
0
votes
0answers
25 views

Free Complex scalar field and conservation principle

In a free complex scalar field, the difference between the number of Particles and antiparticles is conserved. This constarint can be satisfied with a simultaneous creation of equal number of ...
0
votes
0answers
77 views

Book on Noether theorem and classical field theory

I couldn't follow the derivation of Noether theorem in my QFT book, and have some problems with classical field theory and functional derivatives etc. Is there a book which gives an introduction to ...
0
votes
0answers
218 views

Counting Degrees of Freedom in Field Theories

I'm somewhat unsure about how we go about counting degrees of freedom in CFT, and in QFT. Often people talk about field theories as having 'infinite degrees of freedom'. My understanding of this is ...
0
votes
0answers
21 views

Does a time-evolving gravitational field or potential have any important/interesting effects?

I have learned from classical electromagnetism that a time-evolving magnetic field gives rise to a contribution to an electric field, and vice-versa. Do gravitational fields have an analogous effect ...
0
votes
0answers
76 views

Conserved charge from conserved current associated with translational invariance

(c.f Di Francesco, 'Conformal Field Theory' P.45) Di Francesco calls the conserved charge arising from the conserved current associated with a translation invariant theory the 'four momentum'. While ...
0
votes
0answers
134 views

How to do this index notation differentiation?

I am studying classical Maxwell fields and I am stuck on this differentiating part. How can I derive the result given below ? $$\dfrac{\partial}{\partial(\partial A_{\mu}/\partial x_{\nu})} ...