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92 views

Mass term in field Lagrangian

In the Klein-Gordon or in the Dirac Lagrangian density, the mass term is quadratic in the field. The other way around, I have heard a quadratic term in a general Lagrangian density be referred to as a ...
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0answers
19 views

When considering local phase transformations are we forced to use covariant derivatives?

When considering local phase transformations $e^{i\theta(x)}$ of the fields $\phi$ and $\phi^*$ corresponding to \begin{equation} \mathcal{L}=\partial_\mu\phi^*\partial^\mu\phi-m^2\phi^*\phi ...
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2answers
85 views

Field theory where fields are differential forms, other than electromagnetism [closed]

I am looking for a few examples of field theories (classical or quantum) that can be formulated taking the fields to be differential forms at least of degree 1 (not counting 0-forms) excluiding ...
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1answer
34 views

Can we use a photon to use it as a changing field in an electric generator? [closed]

In an electric generator we use a changing magnetic field to create electricity. But what if we use a photon's oscillation of EM waves to generate electricity in a metal wire as we do in an electric ...
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1answer
276 views

Is the long range neutron-antineutron interaction repulsive or attractive?

I can model this interaction as Zee does in "Quantum field theory in a nutshell". In chapter I.4 section "from particle to force" he uses two delta functions for the source. The integral gives ...
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3answers
64 views

Examples of non-linear field symmetries?

Consider a Lagrangian theory of fields $\phi^a(x)$. Sometime such a theory posseses a symmetry (let's talk about internal symmetries for simplicity), which means that the Lagrangian is invariant under ...
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0answers
42 views

Is the coordinate transformation of an object the same of the action of a group on this same object?

I am having troubles in understanding frame transformations in physics from the mathematical point of view. What I understand for a coordinate transformation is just a function to one chart to another ...
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0answers
40 views

What is the current theory underlying the concept of fields? [duplicate]

When I went to school I was specifically told that fields are material (they occupy some region in space, and they "exist" there) and continuous. Recently, studying quantum physics I came across the ...
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3answers
164 views

Are field theories special?

Our best descriptions of the microscopic world, that satisfy many fundamental requirements (as we know them today), are field theories. Is there something fundamental about field interactions, or are ...
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0answers
85 views

Current divergenceless

We can define a topological current, \begin{equation} J_{top}^u = \frac{1}{2v} \epsilon^{\mu \nu} \partial_\nu \phi \end{equation} where $\epsilon^{\mu \nu} = − \epsilon^{\nu \mu}$ and $\epsilon^{01} ...
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0answers
61 views

DBI action with Weyl Invariance

The DBI action, given by $S_{Dp}=-T_p\int d^{p+1}\xi e^{-\phi(\xi)}\sqrt{-\textrm{det}\left(G_{ab}(\xi)+B_{ab}(\xi)+2\pi{\alpha}'F_{ab}(\xi)\right)}$ is diff and Poincaré invariant. I want to ...
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0answers
42 views

Hilbert Stress Energy Tensor for fermions + EM field and Yang-Mills theory (fermions + gluons)

@Qmechanic or anyone else who knows the reference. I am trying to find a references to the work(s) where thorough derivation of Hilbert Stress Energy Tensor for fermions + EM fields and Yang-Mills ...
4
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0answers
174 views

Scattering, Perturbation and asymptotic states in LSZ reduction formula

I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix ...
3
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2answers
1k views

Need for a side book for E. Soper's Classical Theory Of Fields

I am reading now E. Soper, Classical Theory Of Fields, now and sometimes it is very hard to follow the equations. So I need a side book on classical field theory to read it comfortably. Landau & ...
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0answers
95 views

Is the phrase “coupling constant” interchangable with “ strength of interactions”?

Can I use the terms coupling constant and strength of interactions, interchangeably, or are there more subtleties to the term coupling constant that I am not aware of? Coupling Constants from ...
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0answers
67 views

signal from uniformly moving charge

As a charge moves, its field changes, and this change can only be propagated outward at the speed of light. Thus the field lines will be curves that keep changing apparent source point and direction. ...
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2answers
66 views

Quantum field operators in HEP and CMT

For a real scalar field (which is a bosonic field) we have these commutation relations : $$ \left[\phi(x,t),\phi(y,t)\right]=0 \qquad \qquad \left[\phi(x,t),\pi(y,t)\right]=\delta(x-y).\tag{1}$$ But ...
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1answer
81 views

Rotation, Boosts and their relation to Spin

Angular momenta are the generators of rotations. For example, $L_1,L_2,L_3$ represents the orbital angular momentum operators which represents rotations in 3-D space in $xy$, $yz$, $zx$ plane. Spin ...
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2answers
3k views

How is the direction of Magnetic/Electric Lines of Force Known?

It is shown that the direction of magnetic line is from north to the south and that of the electric line is from positive to negative. How do we/scientists know that the imaginary lines of force or ...
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1answer
98 views

How to explain the upgrade from Particles to Fields between Relativistic QM->QFT?

It is strange that all books I walked through, non of them explains or motivates how physicists realised that we need to deal with fields instead of particles. Maybe the closest thing I found is the ...
3
votes
1answer
170 views

Wilsonian Renormalization Group and Symmetries of the EFT

I have am action $S_0$ valid up to energy scale $\Lambda_0$ with renormalisable terms. I want to study the EFT at a lower scale $\Lambda \ll \Lambda_0$, by using the Wilsonian RG. It will give me an ...
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0answers
10 views

Modeling effects of grounded electrodes

I am trying to model electric fields due to the contributions of many conducting electrodes. So far, I have worked with both positively charged and negatively charged electrodes, but I am now ...
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0answers
27 views

Books for field theory [duplicate]

I am a math student, studying P.D.E. of some EM theory. I am new to field theory and I don't even know what a Lagrangian density, Hamiltonian density, or gauge field theory is. Could you please ...
2
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0answers
72 views

Lagrangians not related via a total time derivative lead to same Noether symmetries?

Having answered my initial two questions (v1), I now consider a third possibility. Consider two Lagrangians that both lead to equivalent equations of motion. Suppose that they are not related via a ...
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2answers
112 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
58 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 ...
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1answer
78 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
80 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
118 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
204 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
232 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 ...
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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
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1answer
85 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
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1answer
68 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 ...
4
votes
1answer
242 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. ...
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3answers
219 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 ...
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5answers
564 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 ...
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2answers
185 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).
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1answer
86 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 ...
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vote
1answer
146 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
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
190 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
vote
0answers
62 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 ...
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2answers
81 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 ...
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1answer
791 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, ...
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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 ...
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2answers
84 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 ...
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3answers
108 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
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1answer
177 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 $(2+1)$ ...