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2
votes
4answers
155 views

Poincare invariant Lagrangians

The Lagrangian density of a Poincare invariant theory should not depend explicitly on the space-time coordinates. Does this mean $$ \partial_\mu \mathcal{L}=0~? $$ If this is the case doesn't the ...
2
votes
0answers
50 views

Show: Lorentz-invariance of solution of Klein-Gordon equation [on hold]

Assume $\psi$ is a solution of the Klein-Gordon equation (KGE). Let $\Lambda$ be a Lorentz transformation. Show: $\phi = \psi(\Lambda^{-1} \cdot )$ is also a solution of the KGE. I try to ...
0
votes
0answers
41 views

Definition of force in a scalar field theory

How do we define the force for a general scalar field theory? In particular what is the scalar force of the below equation of motion: where $\tilde{T}$ is the energy stress tensor of matter and $A$ ...
3
votes
0answers
48 views

Why does this condition ensure that the residue of the propagator is 1?

The corrected propagator is given by $$\Delta'(q)=\frac{1}{q^2+m^2-\Pi^*(q^2)-i\epsilon}$$ ($\Pi^*$ is the sum of all irreducible one-particle amplitudes) I get that the residue of the original ...
6
votes
1answer
116 views

Mathematical interpretation of Poisson Brackets

Lets say we are working in a classical scalar field theory and we have two functional $ F[\phi, \pi](x)$ and $G[\phi, \pi](x)$. In most of the references, starting with two functional the Poisson ...
0
votes
1answer
33 views

Conserved current for a constant translation of a free massless scalar field

In Zinn-Justin's Quantum Field Theory and Critical Phenomena they start with an action for a free massless scalar field: $$S(\varphi) = \frac{1}{2}\int ...
2
votes
1answer
60 views

A Variation on Laplace's equation (context: Yang-Mills N-Instantons, Rajaraman's book)

Statement of the problem I need to solve the equation \begin{align} 0 = \frac{1}{\phi} \partial_{\sigma}\partial_{\sigma} \phi \hspace{20mm} (1) \end{align} where $\phi$ is a scalar field and ...
5
votes
2answers
119 views

Energy and momentum as partial derivatives of on-shell action in field theory

According to L&L, if we fix the initial position of a particle at a given time and consider the on-shell action as a function of the final coordinates and time, $S(q_1, \ldots, q_n, t)$, then... ...
1
vote
0answers
33 views

Total Vs Partial in Lagrange density?

I have a question regarding the red term below. This is the integration by parts during the derivation of the Euler-Lagrange equation for continuous systems. Why is this not the time derivative ...
3
votes
2answers
107 views

Classical Field Theory - Continuum limit in forming the Lagrangian density and the elasticity modulus

I have been looking at taking the continuum limit for a linear elastic rod of length $l$ modeled by a series of masses each of mass $m$ connected via massless springs of spring constant $k$. The ...
1
vote
1answer
34 views

Mass of small fluctuation around vacuum

For a potential $V$, how do we define the mass of a small fluctuation around its vacuum? For example I have the potential $$ V_\mathrm{eff}(\phi) = \frac{1}{2} \left(\frac{\rho}{M^2} - \mu^2\right) ...
1
vote
1answer
67 views

Hermiticity of the quantum field

The quantum field resultant from the quantization of a real classical field is hermitian, but why the quantum field corresponding to a complex classical field should be non-hermitian?
2
votes
0answers
91 views

N=4 SYM from Klebanov-Witten field theory

This is with reference to M. J. Strassler's lectures on "The Duality Cascade" pg. 46. I want to see how $\mathcal{N}=4$ SYM emerges when D3 branes, in the KW setup, are placed at smooth point of the ...
1
vote
2answers
97 views

Two expressions for potential energy in the gravitational field of the earth

Let $M$ be the mass of the earth, considered as a point mass, then the potential energy of a point with distance $r$ away from the center (assume $r > \textrm{radius of earth})$ is $$ U(r) = ...
3
votes
1answer
148 views

Spontaneous Symmetry Breaking

In Spontaneous symmetry breaking we have got that, a field $$\phi= \pm \sqrt{\frac{-m^2}{\lambda}}.$$ Now in order to get the unstable minima we need to guess the mass $m^2 <0 $. But can mass be ...
1
vote
2answers
111 views

Does spatial coupling prohibit resonances due to an external source field?

The harmonic oscillator coupled to a sinodial external source $$\tfrac{\partial^2 x(t)}{\partial t^2}+\omega_0^2 x(t)=F_0\sin(\omega_\text{ext}\ t),$$ has the solution $$x(t)=x(0)\cos(\omega_0 t)+C ...
1
vote
3answers
80 views

About constraints of the first class and electrodynamics

Let's have some theory in hamilton formalism and let's assume that it has the constraints between canonical variables $Q, \pi$. By the Dirac terminology, the set of constraints $F_{a}(Q, \pi) \approx ...
5
votes
0answers
36 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 ...
6
votes
2answers
288 views

(Un)countability in QFT

I am a mathematician self-studying physics, and a currently working on QFT with Srednicki's book. One thing that bothers me is that for a scalar field (in the Hamiltonian version) there is a ...
4
votes
2answers
87 views

Non-local structure of field theory

Can someone explain what is non-local structure of field theory? I know you cannot have $\phi(x) \phi(y)$ term in Lagrangian which indicates the non-locality. However, why I cannot have the non-local ...
3
votes
1answer
621 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 to read it comfortably.Landau`s book is not helping as its content ...
3
votes
1answer
41 views

How do we know what type of gauge field to add to a theory?

I've been watching Leonard Susskind's particle physics lectures and in one lecture, he discusses a very simple gauge theory. We have a complex scalar field $\phi(x)$ with Lagrangian $$\mathscr{L} = ...
3
votes
0answers
60 views

Suggested reading for classical field theory [duplicate]

I am reading a marvelous book Classical Field Theory by E Soper, but it is mathematically too compact and sometimes I am unable to follow the equations. Can anyone suggest a side book for solution of ...
5
votes
1answer
153 views

Why is fundamental physics taught in terms of particles?

According to this paper, there can be no relativistic quantum theory of localizeable particles ("relativity plus quantum mechanics exclusively requires a field ontology"). Sean Caroll has also argued ...
4
votes
3answers
113 views

Complex Dirac field in antiparticle description

I understand that the Dirac equation has negative and positive sets of solutions and this contributes to its quantization by a superposition of two Fourier modes represented as creation and ...
1
vote
1answer
92 views

A Spin up particle in QFT

This appears like a question that is rarely addressed in field theory pedagogy (perhaps because the answer is obvious): how does one describe a particle of definite spin in quantum field theory? For ...
6
votes
2answers
198 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 ...
49
votes
10answers
6k views

What is a field, really?

There was a reason why I constantly failed physics at school and university, and that reason was, apart from the fact I was immensely lazy, that I mentally refused to "believe" more advanced stuff ...
3
votes
1answer
74 views

Lagrangian description of Brownian motion?

I'm interested in the existence of a Lagrangian field theory description of Bronwnian motion, does such a thing exist? Given a particle of some spin $\sigma$, which has a Lagrangian associated with ...
0
votes
1answer
32 views

Action of the Poincare Group on a Scalar Function

Let $F(x^\mu)$ is a scalar function; i.e. $F(x^\mu): \mathbb{R}^{1,3} \rightarrow \mathbb{R}$. How the Poincare Group $P(1,3)$ will act on it; i.e., by which formula I can calculate it for a specific ...
1
vote
0answers
20 views

Energy Tensor, covariant derivate, variation respect to the metric [duplicate]

I'm doing the variation of a Lagrangian respect to the metric, but I am having problem with a particular terminus. My action is: $$ S=\int d^4x \sqrt{-g}[ (\nabla_\mu A^\mu)^2]$$ My lagrangian is: ...
4
votes
2answers
222 views

Mean field theory = large-N approximation?

Wikipedia entry of 1/N expansion (or 't Hooft large-N expansion) mentions that It (large-N) is also extensively used in condensed matter physics where it can be used to provide a rigorous basis ...
1
vote
0answers
26 views

Sign of Feynman rules with derivative couplings

Feynman rules for derivative couplings always make me confused. For example, the derivative in $gV^\mu\phi^+\partial_\mu\phi^-$ will give you $\pm ip_{-\mu}$, where $\pm$ depends on whether the ...
4
votes
1answer
105 views

Conceptual question about field transformation

(c.f Conformal Field Theory by Di Francesco et al, p39) From another source, I understand the mathematical derivation that leads to eqn (2.126) in Di Francesco et al, however conceptually I do not ...
3
votes
0answers
87 views

What decides the signs and coefficients of terms in superfield?

I'm working on a problem in 3d field theory and I'm confused about how to write the superfields. Specifically, I'm not sure if the signs and coefficients of terms are purely a matter of convention or ...
1
vote
0answers
36 views

Noether Current when the Lagrangian depends on second derivative of the fields

Let a Lagrangian density for a field theory of $N$ fields $\left\{\phi_i\right\}_{i=1}^N$ be given. Assume that the Lagrangian density depends on the fields, their spacetime derivatives, and their ...
3
votes
1answer
225 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 ...
4
votes
1answer
202 views

Noether's Theorem in Field Theory

This question is regarding Noether's Theorem in general, but also in the application to an example. The example is: Find the conserved current for the Lagrangian ...
3
votes
0answers
49 views

Scalar product of torsional forms - how are the standard identities modified?

It is known that for any smooth, orientable, compact manifold $X$ without boundary and $\alpha \in \Omega^{r}(X), \beta \in \Omega^{r-1}(X)$ it holds \begin{equation} (d\beta,\alpha)= (\beta, ...
2
votes
1answer
86 views

Local versus non-local functionals

I'm new to field theory and I don't understand the difference between a "local" functional and a "non-local" functional. Explanations that I find resort to ambiguous definitions of locality and then ...
13
votes
0answers
598 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, ...
9
votes
1answer
137 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 ...
11
votes
2answers
480 views

What is the nature of electric field? is it quantized? is it a wave?

What I seek here is to understand whether the electric field in its pure form as in between the electron and the proton is uniform or does it have some kind of wave/particle nature or both, does it ...
0
votes
2answers
83 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 ...
2
votes
0answers
30 views

How does the choice of a particular vacuum in a field theory problem decide the number of Goldstone bosons?

How does the field expansion method (by this I mean expanding your fields about a chosen VEV and plugging into a given potential so that the masses of the fields are given by the coefficients in ...
1
vote
0answers
16 views

How does the choice of a basis decide how many Goldstone bosons there are under spontaneous symmetry breaking?

I have a question about how the basis you choose in a field theory problem semmingly decides how many Goldstone bosons you get after spontaneous symmetry breaking. For SU(2), if you choose the 3 Pauli ...
0
votes
2answers
232 views

Understanding field representation of force [duplicate]

I am reading the book The Evolution of Physics. I have a doubt in the topic "The field as representation". In this topic authors give the example of gravitational force represented as a field. In the ...
7
votes
3answers
210 views

If particles are excitations what are their fields?

After reading these : http://www.symmetrymagazine.org/article/july-2013/real-talk-everything-is-made-of-fields http://www.physicsforums.com/showthread.php?t=682522 It was clear to me that all ...
11
votes
2answers
160 views

Inverting the equation for $T_{\mu\nu}$ in terms of $F_{\mu\nu}$

The Stress-Energy Tensor for electromagnetism is given by: $$ T_{\mu \nu} = F_{\mu}\,^{\alpha}F_{\nu\alpha}-\frac{1}{4}g_{\mu\nu}F_{\alpha\beta}F^{\alpha\beta} $$ How can I find $F_{\mu\nu}$ in ...
0
votes
0answers
376 views

Scalar field lagrangian in curved spacetime

I am studying inflation theory for a scalar field $\phi$ in curved spacetime. I want to obtain Euler-Lagrange equations for the action: $$ I\left[\phi\right] = \int ...