4
votes
1answer
118 views

Non-relativistic limit in a Lagrangian density

What criteria should I consider when determining the non-relativistic limit of a Lagrangian density? For example, how would I take the non-relativistic limit of the following Lagrangian density: ...
0
votes
1answer
130 views

Why do we assume that Dirac spinor $\Psi$ describe the particle, not the field?

It is a well-known fact that Klein-Gordon scalar $\Psi(x)$, $$ (\partial^{2} + m^2) \Psi (x) = 0 $$ as well as 4-vector $A_{\mu}(x)$, $$ (\partial^{2} + m^{2})A_{\mu} = 0,\quad ...
5
votes
1answer
60 views

Gauge fixing of an arbitrary field

How to count the number of degrees of freedom of an arbitrary field (vector or tensor)? In other words, what is the mathematical procedure of gauge fixing?
7
votes
1answer
176 views

Generator of local symmetries

Let us only consider classical field theories in this discussion. Noether's theorem states that for every global symmetry, there exists a conserved current and a conserved charge. The charge is the ...
4
votes
1answer
97 views

Definition of vacuum in field theory; Connection between the classical definition and the connection to QFT

I am a bit confused by what is defined to be a vacuum in field theory. Classically a vaccum state is defined to be the state where the field sits at some minima of the potential $\frac{\partial ...
3
votes
1answer
74 views

Massless Thirring Model in 1+1 Dimensions

In Coleman's paper, "Quantum sine-Gordon equation as the massive Thirring Model" (link to Phys Rev D article), he pointed out that the massless Thirring Model is exactly scale invariant. More over, ...
6
votes
1answer
145 views

Mass generation by Chern-Simons theory

Why the mass generation via a Higgs mechanism is different from that of Chern-Simons theory? I haven't done any formal course in Quantum field theory,so how do I understand this just having some basic ...
2
votes
0answers
102 views

Product of $\gamma^5 \sigma^{\mu\nu}$

I'm trying to prove that $\gamma^5 \sigma^{\mu\nu}=\frac{i}{2}\epsilon^{\mu\nu\alpha\beta}\sigma_{\alpha\beta}$ I started with the left hand side and expanded the $\gamma^5$ to ...
6
votes
1answer
86 views

In which field theories with fermions do string- and fivebrane structures not come up?

A year ago, username @Greg Graviton asked in a thread here about the Spin group as covering of the spatial rotations. A subquestion was: What other groups, even larger than SU(2) are there that ...
2
votes
0answers
75 views

Half-integer Spin and “natural conformal dimension”

If we consider a classical field theory for a massless particle of integer spin $s$, in a curved space-time, one finds that it is "naturally" conformal in a space-time of dimension $2+2s$ For ...
6
votes
2answers
156 views

How does a SCFT avoid the Haag-Lopuszanski-Sohnius theorem?

According to the Haag-Lopuszanski-Sohnius theorem the most general symmetry that a consistent 4 dimensional field theory can enjoy is supersymmery, seen as an extension of Poincarè symmetry, in direct ...
2
votes
1answer
118 views

Book Recommendation- Classical Relativistic Fields

My bare bookshelves are crying out for the addition of a new family member, more specifically a book: Discussing the classical Klein-Gordon field, spinor fields, gauge fields and all other matter ...
2
votes
1answer
304 views

Deriving the Hamiltonian density for a free scalar field

I'm working through my old notes on QFT (cf. Ref 1) and I'm not quite sure how to approach the derivation of the Hamiltonian density for a free scalar field (question 2.3 on page 19) and the ...
7
votes
1answer
248 views

What are the details of the renormalization of Chern-Simons theory?

What is a good, simple argument as to why Chern-Simons theory' is renormalisable? Any good books/references dealing with this effectively? Why does the $\beta$-function vanish? Thanks!
1
vote
1answer
93 views

Dimension analysis in Derrick theorem

The following image is taken from p. 85 in the textbook Topological Solitons by N. Manton and P.M. Sutcliffe: What I don't understand from the above statement: why $e(\mu)$ has minimum ...
2
votes
0answers
81 views

Path integral measure and symmetry

For a generic field theory the path integral measure is defined as, \begin{equation} \mathcal{D}\Phi = \prod_i d\Phi(x_i), \end{equation} where $\Phi$ is a generic field (i.e. it may be scalar, ...
2
votes
0answers
290 views

The connection between classical and quantum spins

I have two questions, which are connected with each other. The first question. In a classical relativistic (SRT) case for one particle can be defined (in a reason of "antisymmetric" nature of ...
0
votes
0answers
27 views

Localizations of nonlinear waves and characterizations

Let's say a object is radiating energy over the time and the rate of radiation is not high. Now what conditions can ensure us to guess the object as localized object. Actually My question is what ...
1
vote
0answers
81 views

Dimension dependence

The question is related to this one The time averaged total energy, $\bar E$, has the following $\varepsilon$ expansion in $D$ dimension: \begin{equation} ...
1
vote
2answers
159 views

Dimensions in lagrangian potential

According to Mankowski flat space dimensions We can write, $$L= \int \text{dt} \text d^d{x} \left[ \frac{1}{2} \dot\phi^2 - \frac{1}{2} \left(\frac{\partial \phi}{\partial r} \right)^2 ...
1
vote
1answer
126 views

Finding out Energy value

A Lagrangian is given by, $$L= \left(\frac{\pi}{2}\right)^2 R^d \left[\frac{1}{2}\dot A^2 - V(A_{max})\right]$$ $$E=\left(\frac{\pi}{2}\right)^2R^d V(A_{max}) $$ where V (A) now includes nonlinear ...
0
votes
0answers
76 views

Difference between oscillon and quasi breather

How do we differentiate between oscillon and quasi breather ? Which equation can give me the property of these wave? I know the solition equation and got it for different potential, need to know when ...
0
votes
0answers
89 views

Derrick’s theorem(2)

Related post : Derrick’s theorem Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) ...
0
votes
2answers
151 views

Derrick’s theorem

Consider a theory in D spatial dimensions involving one or more scalar fields $\phi_a$, with a Lagrangian density of the form $$L= \frac{1}{2} G_{ab}(\phi) \partial_\mu \phi_a \partial^\mu \phi_b- ...
0
votes
1answer
91 views

Vortex in D dimensions soliton

let us consider the two-dimensional configuration shown in Fig. 3.1a. The lengths of the arrows represent the magnitude of φ, while their directions indicate the orientation in the $φ_1 -φ_2$ plane. ...
0
votes
1answer
176 views

sine-Gordon equation

I have derived a solition equation (2 dimensions) from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{1}$$ and also I have got sine-Gordon equation for solition ...
0
votes
0answers
135 views

Domain wall and kink solutions from solitions equations

A general solition equation can be obtaion from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{92.6}$$ where $x_0$ is a constant of integration when we drived this ...
-1
votes
1answer
127 views

Symmetry breaking with Lagrangian

I have been studying the spontaneous symmetry braking from Zee (Quantum Field theory ) and found in the page 224, he wrote the lagrangian as $$\mathcal{L}= \frac{1}{2}\{ λ (∂φ)^2 + μ^2φ^ 2\} − ...
1
vote
0answers
128 views

A fundamental equation for solitary wave and dimension analysis [closed]

According to the scalar Field theory we write Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$ What I want to do is ...
1
vote
1answer
120 views

Comparing interaction potential in standard $ϕ^4 $theory

I am posting this question again because, Willie Wong asked me to do it. So it is a continuing post of the Interaction potential in standard ϕ4 theory. I have been studying about solitions so I had ...
-2
votes
1answer
485 views

$\phi ^4$ theory explaining [closed]

In $φ^4$ theory we often write the Lagrangian as $$\mathcal{L}=\frac{1}{2}\partial^\mu \phi \partial_\mu \phi -\frac{m^2}{2}\phi^2 -\frac{\lambda}{4!}\phi^4 \tag {1}$$ If I want to write from the ...
3
votes
2answers
230 views

Higher order covariant Lagrangian

I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
-1
votes
1answer
85 views

How the nonlinear equation can be written like this?

We consider a scalar theory in a $1+D$ dimensional flat Minkowski space-time, with a general self-interaction potential, whose action can be written as \begin{equation} A=\int dt\, d^D\! x ...
1
vote
1answer
177 views

Interaction potential analysis from $\phi^4$ model

In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by $$S=\int d^d\! x ...
0
votes
1answer
96 views

Oscillon and soliton

I want to know the major difference between oscillon and soliton in terms of radiating energy with respect to time and position. And what about their localization?
3
votes
1answer
113 views

Definition of Local Function

Now a days I am studying Srednicki's QFT book. In its third chapter it is written that Any local function of φ(x) is a Lorentz scalar, [...] . Now my question is: What is a local function?
-3
votes
1answer
285 views

Creation and Annihilation operator [closed]

In this page I want to know, why the equation (1.32) introduced creation and annihilation operator. Please elaborate.
0
votes
2answers
232 views

Difficulties with bra and ket notation

I have problem in understanding equation (1.23), I croped this image from Mark_Srednicki "Quantum field theory". Can anyone show me the reason for the equation (1.23)?
-1
votes
1answer
192 views

Scalar field lagrangian and potential

This question is a continuation of this Phys.SE post. Scalar field theory does not have gauge symmetry, and in particular, $\phi\to\phi−1$ is not a gauge transformation. but why? and I want see the ...
2
votes
0answers
47 views

Is Inflation modelled by a field?

If Inflation is modelled by a field - is this a classical field or a quantum field? If classical are there good reasons not to quantise it? What are the implications of such a quantisation?
7
votes
3answers
449 views

Why is the Yang-Mills gauge group assumed compact and semi-simple?

What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories? I'd think that these hypotheses lead to physically ...
9
votes
1answer
268 views

Auxiliary fields in supersymmetry

I know that auxiliary fields can be used to close the supersymmetry algebra in case the bosonic and fermionic on-shell degrees of freedom do not match. Could somebody please elaborate on this concept ...
3
votes
1answer
521 views

Local and Global Symmetries

Could somebody point me in the direction of a mathematically rigorous definition local symmetries and global symmetries for a given (classical) field theory? Heuristically I know that global ...
1
vote
1answer
249 views

Lorentz Invariant Equation of Motion for Scalar Field

I'm trying to understand why you can't write down a first order equation of motion for a scalar field in special relativity. Suppose $\phi(x)$ a scalar field, $v^{\mu}$ a 4-vector. According to my ...
3
votes
0answers
106 views

Asymptotic limit of the two kink solution of the sine-gordon equation

I am reading a paper on the sine-gordon model. The solution for a two kink solution is given as: ...
5
votes
0answers
323 views

Gaussian Integrals : Functional determinant expressed as a trace

Be $A_{ij}$ a symmetric matrix. Then I can easily write $$ \int \exp\left(-\frac{1}{2}\sum_{i,j}x_i A_{ij} x_j+\sum_{i} B_i x_i\right)\; d^nx= \sqrt{(2\pi)^n}\exp\left\{-\frac{1}{2}\mathrm{Tr}\log ...
2
votes
1answer
148 views

What's the difference between background field and dynamical gauge field?

Dynamical gauge fields are assumed to be able to respond to sources. What's the difference in the Lagrangians between a background field and a dynamical field?
6
votes
1answer
248 views

Quantum Field Theory: why fields are equal to zero on the boundary?

One of the first assumptions, when introducing the Lagrangian and Hamiltonian in an undergraduate course on QFT is $$ \phi(x)=0\,\text{on the boundary} $$ and this is widely used in many situations ...
4
votes
1answer
923 views

What is the essence of BCFW recursion techniques?

I have recently briefly read about new methods as the Britto-Cachazo-Feng-Witten (BCFW) on-shell recursion method. Can anybody please tell me about the essence of it? What does it mean for the ...
4
votes
1answer
252 views

When can a classical field theory be quantized?

Given a classical field theory can it be always quantized? Put in another way, Does there necessarily need to exist a particle excitation given a generic classical field theory? By generic I mean all ...