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3
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1answer
15 views

Why does Landau theory not fail when dealing with a first order phase transition?

Here is a problem where I can do the calculation, but I am not understanding the philosophy behind it. It is about Landau theory: The Landau theory of phase transitions is based on the idea that the ...
3
votes
2answers
55 views

Determination of the ground state of a field theory

Consider the Spontaneous symmetry breaking in the theory $$\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{\mu^2}{2}\phi^2+\frac{\lambda}{4!}\phi^4.$$ By the ground state of a ...
0
votes
3answers
73 views

Can the sign of metric change physics?

Consider the Lagrangian of a massless real scalar (classical field) in $\phi(\textbf{x},t)$: $$\mathcal{L}=\frac{1}{2}\partial^\mu\phi\partial_\mu\phi$$ The Hamiltonian density in two different ...
-1
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0answers
28 views

What is the explicit decay width formula for a four body decay?

I'm trying to calculate the decay width for a theory with one particle having a decay mode into 4 particles. Does anyone know the explicit formula for this (not the generalized decay formula).
0
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0answers
17 views

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 ...
0
votes
1answer
63 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 ...
0
votes
1answer
54 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 $\psi\to M\psi$, ...
4
votes
2answers
72 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 ...
1
vote
1answer
60 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 $U(1)$?
4
votes
3answers
196 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 ...
0
votes
0answers
75 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 ...
0
votes
2answers
94 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 ...
0
votes
0answers
26 views

How does the idea of a scalar potential for a 3-vector field generalize to Minkowski space?

How does the idea of a scalar potential for a 3-vector field generalize to Minkowski space? As I guess, I thought one way would be to generalize 3-force to 4-force and replace the 3-gradient with the ...
0
votes
0answers
25 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?
0
votes
2answers
73 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 ...
0
votes
1answer
34 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? ...
0
votes
1answer
93 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 ...
1
vote
1answer
80 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 ...
0
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0answers
25 views

Mass spectrum of field theory

How can I find the mass spectrum of a field theory given a Lagrangian made of a canonical kinetic term and a potential. I mean, I think I have to find the matrix of the quadratical terms in all the ...
2
votes
1answer
97 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 ...
0
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0answers
27 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 ...
2
votes
2answers
56 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 ...
0
votes
1answer
68 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: $$ ...
0
votes
1answer
41 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 $\exp(ipx)$ in the Fourier transform of a scalar field and the corresponding conjugate momenta $\pi(x)$ of the scalar field?
1
vote
1answer
35 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 ...
0
votes
2answers
41 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, ...
1
vote
0answers
54 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 ...
2
votes
1answer
65 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, ...
4
votes
0answers
67 views

Renormalization of Auxiliary Fields

I have the following non-linear sigma model (the base space $\mathcal{M}$ is Euclidean): $$ \mathcal{L}=\dfrac{1}{2\alpha}\int_{\mathcal{M}}\mathrm{d}^2\sigma\ \partial^2X^{\mu}\partial^2X_{\mu} $$ ...
0
votes
1answer
24 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 ...
2
votes
2answers
91 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?
0
votes
1answer
44 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 ...
2
votes
1answer
56 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. ...
1
vote
1answer
89 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 ...
0
votes
1answer
53 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 ...
1
vote
0answers
23 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 ...
0
votes
3answers
113 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 ...
1
vote
0answers
46 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 ...
3
votes
0answers
83 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 ...
2
votes
1answer
90 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 ...
0
votes
2answers
64 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 ...
4
votes
1answer
58 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 ...
1
vote
1answer
56 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 ...
0
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0answers
39 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
votes
1answer
72 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 $l \neq 0$. ...
2
votes
1answer
93 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 ...
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0answers
74 views

Noether's first and second theorems

My understanding of Noether's first theorem is as follows. Consider a set of infinitesimal transformations that leave the action invariant, that are indexed by $n$ linearly independent parameters, ...
3
votes
1answer
73 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
votes
0answers
48 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 ...
1
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2answers
68 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 ...