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32
votes
8answers
2k views

Why are differential equations for fields in physics of order two?

What is the reason for the observation that across the board fields in physics are generally governed by second order (partial) differential equations? If someone on the street would flat out ask ...
16
votes
3answers
2k views
52
votes
10answers
7k 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 ...
19
votes
1answer
600 views

Why does charge conservation due to gauge symmetry only hold on-shell?

While deriving Noether's theorem or the generator(and hence conserved current) for a continuous symmetry, we work modulo the assumption that the field equations hold. Considering the case of gauge ...
13
votes
3answers
1k views

Why can't General Relativity be written in terms of physical variables?

I am aware that the field in General Relativity (the metric, $g_{\mu\nu}$) is not completely physical, as two metrics which are related by a diffeomorphism (~ a change in coordinates) are physically ...
9
votes
4answers
2k views

Lagrangian to Hamiltonian in Quantum Field Theory

While deriving Hamiltonian from Lagrangian density, we use the formula $$\mathcal{H} ~=~ \pi \dot{\phi} - \mathcal{L}.$$ But since we are considering space and time as parameters, why the formula ...
9
votes
4answers
441 views

Is the Lagrangian of a quantum field really a 'functional'?

Weinberg says, page 299, The quantum theory of fields, Vol 1, that The Lagrangian is, in general, a functional $L[\Psi(t),\dot{\Psi}(t)$], of a set of generic fields $\Psi[x,t]$ and their time ...
22
votes
1answer
3k views

Differentiating Propagator, Greens function, Correlation function, etc

For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most ...
24
votes
1answer
935 views

Can lightning be used to solve NP-complete problems?

I'm a MS/BS computer science guy who is wondering about why lightning can't (or can?) be used to solve NP complete problems efficiently, but I don't understand the physics behind lightning, so I'm ...
17
votes
1answer
447 views

Is there a field equation which can reduce into all three flavors of spin (zero, one, one half)?

Is there a known particle field equation of a similar form $$ \begin{equation} (\Gamma^n \pi_n)^2 \Psi = (mc)^2 \Psi \tag{1} \end{equation} $$ such that by reducing the number of degrees of freedom ...
6
votes
2answers
1k views

What does a Field Theory mean?

What exactly is a field theory? How do we classify theories as field theories and non field theories? EDIT: After reading the answers I am under the impression that almost every theory is a ...
6
votes
1answer
252 views

Noether's identities

I have some questions about the Noether's second theorem (generally not covered by field theory books): What is the most general Noether identity for (classical) field theories? Why are Noether ...
6
votes
1answer
786 views

The equipartition theorem in momentum space

Motivated by the answers to this question on turbulence, I'm interested in an explanation and/or derivation/reference of the equipartition theorem in momentum space. To formulate it as a question: ...
7
votes
3answers
245 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 ...
3
votes
1answer
698 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 ...
1
vote
2answers
173 views

Is $\frac{\partial}{\partial \Phi(y)} \Phi (x) = \delta(x-y)$ correct?

As stated in the heading: Is $\frac{\partial}{\partial \Phi(y)} \Phi (x) = \delta(x-y)$ correct? Here denotes $\Phi(x)$ denotes a scalar field. And if yes, why? Any reference where I can read about ...
3
votes
1answer
155 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?
0
votes
2answers
204 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- ...
10
votes
1answer
357 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 ...
14
votes
4answers
2k views

History of Electromagnetic Field Tensor

I'm curious to learn how people discovered that electric and magnetic fields could be nicely put into one simple tensor. It's clear that the tensor provides many beautiful simplifications to the ...
12
votes
0answers
627 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, ...
6
votes
1answer
1k 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 ...
11
votes
2answers
613 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 ...
9
votes
1answer
3k views

The Euler-Lagrange equation in special relativity

How can I derive the Euler-Lagrange equations valid in the field of special relativity? Specifically, consider a scalar field.
8
votes
1answer
196 views

Boundary currents for Asymptotic Symmetry Group (ASG)

In the context of asymptotic symmetry groups, what is a boundary current? Why is it called a "current"? Context: I'm reading Strominger's recent paper on Asymptotic symmetry group of Yang-Mills ...
5
votes
2answers
527 views

Winding number in the topology of magnetic monopoles

I am reading on magnetic monopoles from a variety of sources, eg. the Jeff Harvey lectures.. It talks about something called the winding $N$, which is used to calculate the magnetic flux. I searched ...
4
votes
1answer
118 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 ...
4
votes
1answer
792 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 ...
4
votes
1answer
459 views

QED BRST Symmetry

This is a homework problem that I am confused about because I thought I knew how to solve the problem, but I'm not getting the result I should. I'll simply write the problem verbatim: "Consider QED ...
1
vote
0answers
49 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 ...
6
votes
3answers
888 views

Gauge fixing choice for the gauge field $A_0$

In many situations, I have seen that the the author makes a gauge choice $A_0=0$, e.g. Manton in his paper on the force between the 't Hooft Polyakov monopole. Please can you provide me a ...
5
votes
3answers
380 views

Meaning of kinetic part in the Lagrangian density?

What is the physical meaning of the kinetic term in the classical scalar field Lagrangian $$\mathcal{L}_{kin}~=~\frac{1}{2}(\partial_\mu\phi)(\partial^\mu\phi)~?$$ It gives how does the field change ...
5
votes
2answers
559 views

Are there solitary waves in $\phi^4$ theory in 3+1 dimensions?

In 3+1 dimensions with signature +1 -1 -1 -1, $$ \mathcal{L}= \frac{1}{2}\partial^\mu\phi\partial_\mu\phi -\phi^2/2 -\phi^4/4$$ field equation: $$\square\phi+\phi+\phi^3=0$$ (check this) ...
3
votes
2answers
635 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
4answers
205 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
1answer
119 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 ...
2
votes
1answer
142 views

Spin tensor and Lorentz group operator in bispinor case

For infinisesimal bispinor transformations we have $$ \delta \Psi = \frac{1}{2}\omega^{\mu \nu}\eta_{\mu \nu}\Psi , \quad \delta \bar {\Psi} = -\frac{1}{2}\omega^{\mu \nu}\bar {\Psi}\eta_{\mu \nu}, ...
2
votes
0answers
416 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 ...
2
votes
2answers
224 views

Does a constant factor matter in the definition of the Noether current?

This is a very basic Lagrangian Field Theory question, it is about a definition convention. It takes much more time to typeset it than answering, but here it is: Consider a field Lagrangian with only ...
2
votes
2answers
938 views

Pair production - mathematically?

Allover the web i am only seeing a statement similar to this: Pair production is not possible in vaccum, 3rd particle is needed so that conservation of momentum holds. Well noone out of many ...
2
votes
1answer
362 views

How to tell local and non-local in QFT?

I'm taking QFT course in this term. I'm quite curious that in QFT by which part of the mathematical expression can we tell a quantity or a theory is local or non-local?
1
vote
1answer
170 views

What is meant by a local Lagrangian density?

What is meant by a local Lagrangian density? How will a non-local Lagrangian look like and what is the problem that we do not consider such Lagrangian densities?
1
vote
0answers
79 views

How to introduce generating function in Hamiltonian formalism for field theories?

Let's have hamiltonian $$ H(\psi , P ,\partial_{i}\psi ) = P\partial_{0}\psi - L(\psi , \partial_{\mu}\psi ), \quad P = \frac{\partial L}{\partial (\partial_{0}\psi)}. \qquad (.0) $$ I tried to ...
4
votes
3answers
425 views

Calculating lagrangian density from first principle

In most of the field theory text they will start with lagrangian density for spin 1 and spin 1/2 particles. But i could find any text where this lagrangian density is derived from first principle.
3
votes
2answers
288 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
vote
1answer
132 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 ...
1
vote
1answer
216 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
106 views

Klein-Gordon, gauge transformation [closed]

It must be really simple, but I cannot get why can we add an $i e \frac{\partial \Lambda}{\partial x}$ in the second row below. The propagation of a charged scalar particle, along the x-axis and in ...
0
votes
2answers
246 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 ...
0
votes
0answers
101 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) ...