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0
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2answers
111 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
57 views

Complex Inner Product for Integral Expressions

I am currently working through some QFT derivations and running into conceptual problems. In particular, I am deriving the free field Hamiltonian of the form: $H_{k} = \frac{1}{2} \int d^{3}k ...
1
vote
1answer
76 views

Classical Field Theory Using Geometry

I would like to know if there are good introductory courses on Classical Field Theory taught in a differential geometry approach yet one doesn't need a background in those mathematical subjects but ...
6
votes
1answer
78 views

Is there a systematic way to obtain all conserved quantities of a system?

I'd like to know whether, given a system, there's a way to obtain all the conserved quantities. For instance if the system consists of electric and magnetic fields, the fields must satisfy Maxwell's ...
3
votes
1answer
115 views

Charge not conserved in scalar QED? [duplicate]

Since conservation of charge seems to be a well known concept, I am hoping that I am missing something and that the conclusion is incorrect. However, I have been unable to disprove this. Let me ...
6
votes
1answer
199 views

Functional derivatives as distributions

I have asked this on math stack exchange, due to its mostly mathemtical content, but aside from one upvote and minimal views it has not garnered any attention, so I am trying here as well. This isn't ...
7
votes
2answers
230 views

What canonical momenta are the “right” ones?

I'm doing some classical field theory exercises with the Lagrangian $$\mathscr{L} = -\frac{1}{4}F_{\mu \nu}F^{\mu \nu}$$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. To find the ...
1
vote
0answers
66 views

Fayet-Iliopolous Parameters from Separation of NS5-branes in $(x_{7}, x_{8}, x_{9})$: An ambiguity as to which gauge group the FI parameter belongs

hep-th/9611230v3, page 12 explains how, for a configuration of D3s along $(x_{1}, x_{2}, x_{6})$, and NS5's along $(x_{1}, x_{2}, x_{3}, x_{4}, x_{5})$, the Fayet-Iliopolous D-term coefficient $\zeta$ ...
1
vote
1answer
82 views

A question to gauge fixing in nonabelian gauge theories

In quantum gauge theories it is usual to fix the gauge with the equation $\partial^\mu A_\mu = 0$ where $A_\mu$ is the gauge connection. From this gauge fixing condition the remaining gauge degree of ...
1
vote
1answer
61 views

How to divide areas in electric field lines based on field strength?

A negative charge is surrounded by four positive charges. They are all of the same strength. The electric field lines are plotted below. I am looking for the property of the drawn 'red lines' that ...
3
votes
1answer
229 views

Is the Dirac equation equivalent to the Klein-Gordon equation for its left handed component?

The Dirac equation $$(i\gamma^a\partial_a - m)\psi=0\tag{0}$$ is given by a first order operator acting on a Dirac spinor, which is the direct sum of a left handed spinor and a right handed spinor. ...
0
votes
3answers
189 views

How many fields that we know of permiate the universe?

The Higgs field, as I understand it reading layman's articles, permeated the entire universe only a fraction of a second after the big bang. Are there any other fields that they know about or ...
2
votes
5answers
543 views

Euclidean geometry in non-inertial frame

Refer, "The classical theory of Fields" by Landau lifshitz (Chap 3). Consider a disk of radius R, then circumference is $2 \pi R$. Now, make this disk rotate at velocity of the order of c(speed of ...
3
votes
2answers
184 views

General relativity without curvature?

Is there a reformulation of general relativity without curved space time, just with fields (like classical E&M)? Edit: removed the part about E&M with curvature (multiple posts).
0
votes
1answer
84 views

In field theory, why are some symmetry transformations applied to the field values while other act on the space that the fields are defined on?

My basic understanding is that a field theory consists of symmetry groups, a space $S$ that the symmetry groups act on and of fields defined on that space $S$. In other words, the space $S$ is the ...
1
vote
1answer
141 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 ...
1
vote
2answers
107 views

Why Kink can not tunnel to vacuum, and is topologically stable?

Why the kink $$\phi(x)=v\tanh(\frac{x}{\xi}) ,$$ can not tunnel into vacuum $+v$ or $-v$ (Spontaneous symmetry breaking vacuum). From the boundary condition ($x\rightarrow \pm\infty, ...
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0answers
51 views

How can the VEV of a field be a function of spacetime?

Often in the discussion of effective action and effective potential (say, in the context of $\phi^4-$theory )the one-point function in presence of source is defined as \begin{equation} \frac{\delta ...
0
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0answers
21 views

Where do certain relations relevant to helicity eigenstates come from in Peskin and Schroeder?

On pages 46-47 of Peskin and Schroeder, equations 3.52 and 3.53 are introduced when we have picked specific values of the numerical two-component spinor $\xi$. We choose a basis of ...
3
votes
1answer
169 views

Permutation symmetry - a continuous symmetry?

From quantum mechanics it is known that permutation between identical particles does not change the Hamiltonian. Assuming that the quantum system consists of a very high number of particles such that ...
1
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0answers
61 views

Noether's 2nd Theorem and Local Gauge Identities

I am trying to derive the so called Gauge Identities: \begin{equation} D_\nu\frac{\delta S}{\delta\phi} = 0 \end{equation} Where $D_\nu$ is an operator involving derivatives and $\frac{\delta ...
2
votes
2answers
78 views

What does it mean to differentiate a spinor-valued field?

Peskin and Schroeder, equation 3.28, states that the Klein-Gordon equation $$(\partial^2+m^2)\psi=0 \tag{3.28}$$ is a valid choice of equation for a Dirac spinor field. Their explanation makes sense ...
12
votes
1answer
787 views

Could this model have soliton solutions?

We consider a theory described by the Lagrangian, $$\mathcal{L}=i\bar{\Psi}\gamma^\mu\partial_\mu\Psi-m\bar{\Psi}\Psi+\frac{1}{2}g(\bar{\Psi}\Psi)^2$$ The corresponding field equations are, ...
4
votes
1answer
71 views

Is local chiral symmetry qualitatively the same as gauge symmetries?

I am confused by the role that local chiral symmetry plays in chiral perturbation theory. For the case of chiral QCD with three quark flavors, the Lagrangian is invariant under global ...
3
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2answers
83 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
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3answers
105 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 ...
0
votes
1answer
175 views

How to obtain the asymptotic behavior of Green's function?

This question arose from Eq.(9.135) and Eq.(9.136) in Fradkin's Field theories of condensed matter physics (2nd Ed.). The author mapped quantum-dimer models to an action of monopole gas in $(2+1)$ ...
0
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0answers
31 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 ...
4
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2answers
113 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
108 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 $\psi\to M\psi$, ...
13
votes
2answers
790 views

Energy-Momentum Tensor in QFT vs. GR

What is the correspondence between the conserved canonical energy-momentum tensor, which is $$ T^{\mu\nu}_{can} := \sum_{i=1}^N\frac{\delta\mathcal{L}_{Matter}}{\delta(\partial_\mu f_i)}\partial^\nu ...
4
votes
3answers
346 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 ...
1
vote
1answer
96 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 $U(1)$?
0
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0answers
85 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
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 ...
0
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0answers
43 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
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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?
0
votes
1answer
118 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 ...
0
votes
2answers
150 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 ...
1
vote
1answer
62 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? ...
1
vote
1answer
145 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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votes
2answers
2k 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
122 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 ...
1
vote
2answers
790 views

Proving the Lorentz invariance of the Lorentz invariant phase space element

I have been looking around for a satisfactory answer to prove that $$\frac{d^3\vec{p}}{2E_{\vec{p}}}$$ where $E_{\vec{p}}=+\sqrt{(|\vec{p}|c)^2+(mc^2)^2}$, is Lorentz invariant. The standard answer ...
0
votes
0answers
101 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
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2answers
93 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
94 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: $$ ...
1
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1answer
72 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
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2answers
77 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
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0answers
59 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 ...