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2
votes
1answer
64 views

Why do some fields have a distance limit and other don't? [closed]

I'm not a mathematician or a physicist but interested in quantum mechanics/gravity/relativity. I'm trying to understand some ideas that are presented for laymen, and a lot of them talk about different ...
2
votes
2answers
204 views

How is everything a field?

I've heard before that everything in physics can be thought of as either a field, or its excitation. Is there some intuitive explanation of how I can look at gravity, light, electromagnetism, etc as a ...
1
vote
0answers
34 views

Majorana fermions and the continuum limit of the Ising model

In Paolo Moligini's Analyzing the two dimensional Ising model with conformal field theory lecture notes, it is shown at the end of chapter 3 that the Lagrangian of the continuum limit of the Ising ...
0
votes
1answer
78 views

What is the difference between the momentum in the Fourier transform of a scalar field and the conjugate momentum of the field?

What is the difference between the momentum $p$ in $e^{i\mathbf{p}\cdot{\mathbf{x}}}$ in the Fourier transform of a scalar field and the corresponding conjugate momenta $\pi(x)$ of the scalar field?
1
vote
1answer
51 views

Why do $\psi_a$ and $\bar{\psi}_{\dot{\alpha}}$ represent two different degrees of freedom?

I am taking a course in QFT and I've been introduced to the concept of left-handed (undotted) and right-handed spinors (dotted). I know that left-handed spinors are associated with the irreducible ...
2
votes
2answers
120 views

How to interpret the field configuration in quantum field theory?

We often use the Fock space as the start point for our quantum field theory. In the Fock space we have definite physical meanings for the state. For example, the state $$|k_1k_2...k_n\rangle$$ ...
3
votes
1answer
69 views

Non-perturbative effects: classical or quantum?

Are non-perturbative effects (solitons) classical or quantum effects (corrections) ? (examples ?) My confusion stems from the fact that, for instance, an instanton is a classical solution of the ...
3
votes
1answer
74 views

Simple conceptual question conformal field theory

I come up with this conclusion after reading some books and review articles on conformal field theory (CFT). CFT is a subset of FT such that the action is invariant under conformal transformation ...
1
vote
0answers
67 views

Magnetic field outside the solenoid

I found solution to problem 257 from "300 Creative Physics problems" hard to understand. In that problem we have very long solenoid with coil wounded in one layer. Data such as: density of turns, ...
0
votes
0answers
50 views

Relation between interaction Lagrangian and interaction Hamiltonian

I work with this interaction Lagrangian density $$\mathcal{L}_{int} = ia\bar{\Psi}\gamma^\mu\Psi Z_\mu +ib(\phi^\dagger\partial_\mu \phi - \partial_\mu\phi^\dagger \phi)Z^\mu,$$ where $Z^\mu$ is an ...
20
votes
1answer
371 views

What, to a physicist, are instantons and the Donaldson invariants?

I study gauge theory from a mathematical perspective. To me, one of the most fundamental ideas is the notion of an instanton on a 4-manifold. To be precise, I have a Riemannian 4-manifold and a ...
0
votes
0answers
46 views

Center of mass of a quantum field

In classical field theory the Noether conserved quantities associated to the translation symmetry are the momentum of the field $P^i = \int\! d^3 x\ T^{0i}$, where $T^{\mu \nu}$ is the energy-momentum ...
1
vote
0answers
80 views

Self Study Textbook Progression from QM to QFT? [duplicate]

Hello Physics StackExchange! I will put the TL;DR in the beginning: I need a self contained, relatively hand-holding sequence of textbooks that covers up from the end of Griffith's Intro to QM to ...
0
votes
1answer
219 views

Why four-point vertex function in $\phi^3$ theory?

So as I understand it the order of $\phi$ in a scalar Quantum field theory is indicative of the number of lines entering a given vertex. For example for $\phi^3$ this leads to vertices like the one ...
31
votes
1answer
1k 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 ...
0
votes
0answers
44 views

Stress-Energy Tensor of Riemann's Curvature Field

Einstein, in "The Foundation of the General Theory of Relativity," as well as most modern lecturers in the subject, use a pseudo-tensor for the stress-energy of the gravitational field. By ...
-1
votes
2answers
90 views

Fermion Lagrangian with linear momentum versus quadratic momentum

$$ L = \bar{\psi} (\gamma^\mu (p_\mu -A_\mu)- m)\psi \tag{1} $$ $$ L = \bar{\psi} ((\gamma^\mu( p_\mu-A_\mu))^2 - m^2)\psi \tag{2} $$ Is there a difference between the two Lagragians in equations 1 ...
3
votes
0answers
55 views

What is a field? [duplicate]

What is a field? Lengthy texts about fields have been published but none ever answer the simple question "What do you mean when you say the world field."
1
vote
1answer
146 views

Field theory: equivalence between Hamiltonian and Lagrangian formulation

Let $\mathscr{B}$ be a space of physics we have and $\mathscr{T}$ be the duration. Let $\mathscr{L}$ be a lagrangian density of the field such that the action is a functional of ...
0
votes
0answers
35 views

How can we get the interaction hamilton $H_\text{int}$ from the Lagrange $L$?

After we quantize the free field we continue on determining the form of $H$. We can impose, by example: $$H=H_0+\lambda V_\text{int}$$ My question is, can we determine $H_\text{int}$ by the ...
0
votes
1answer
37 views

Non-abelian gauge covariant derivative acting on non-algebra-valued quantities

How does a gauge covariant derivative in a non-abelian field theory act on various quantities which are not valued in the algebra, and why? In particular, how does it act on a scalar valued function ...
0
votes
0answers
97 views

Book on Noether theorem and classical field theory

I couldn't follow the derivation of Noether theorem in my QFT book, and have some problems with classical field theory and functional derivatives etc. Is there a book which gives an introduction to ...
44
votes
9answers
4k 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 ...
3
votes
3answers
177 views

Interpretation of QED gauge freedom

In quantum (or classical) electrodynamics we are free to make gauge transformations, which change the form of terms in the Feynman diagrams (or the potentials) without affecting any physical ...
1
vote
1answer
47 views

Dimensions of $\phi$ in scalar field theory

On Srednicki page 90-91 (in printed edition) he derives that $$[\phi] = \frac{1}{2}(d-2) \tag{12.10}$$ from $${\cal L}=-\frac{1}{2}\partial^{\mu}\phi\partial_{\mu}\phi -\frac{1}{2}m^{2}\phi^{2} - ...
2
votes
0answers
54 views

What is the relation between dimension and Quantum Field Theory? How does different dimensions change QFT? [closed]

Does the quantisation rules & field operators for scalar or Dirac fields change with dimension? Most books wrote about 3 spatial dimensions, and then upgraded it to 4 spacetime dimensions, keeping ...
3
votes
2answers
114 views

What happens when a field turns on or off?

Short Setup I am curious about the the mechanics of fields, whether electromagnetic, gravitational, etc. So as a specific example in order to simplify (hopefully) how to ask this question, consider ...
1
vote
0answers
39 views

What does 'vector-like' mean?

What are properties of vector-like field/particle? What's the counterpart of it? Chiral like?
2
votes
0answers
32 views

Transformation Law for a scalar field [closed]

The following is taken from Peskin and Schroeder page 36: $$\partial_{\mu}\phi(x) \rightarrow \partial_{\mu}(\phi(\Lambda^{-1}x)) = (\Lambda^{-1})^{\nu}_{\mu}(\partial_{\nu}\phi)(\Lambda^{-1}x)$$ It ...
1
vote
1answer
125 views

Boundary conditions of fields from the stationary action principle

First principle of stationary action Consider a real Klein-Gordon scalar field $\phi$ living in a $D$ dimensional flat spacetime. The field is considered off shell (the on shell condition is defined ...
8
votes
1answer
127 views

Why is $V=(1/2) m^2 \phi^2$ for a free relativistic scalar field of mass $m$?

Bit of a basic question here but how come for a free relativistic scalar field of mass $m$ such as Klein Gordon theory, we take the potential to be $$V=\frac{1}{2} m^2 \phi^2$$ Is the mass term ...
0
votes
1answer
38 views

Quantum Field Theory: commutator of covariant derivatives

I just started studying qtf and I dont understand the last lecture. In the lecture script a shortcut is defined. $P^j = \frac{1}{i}\partial_j - qA^j$ With this: $[P^j,P^k] = -\frac{q}{i}(\partial_j ...
1
vote
1answer
104 views

Gauge the symmetry $φ \to φ + a(x)$ for a free massless real scalar field

How does one alter the Lagrangian density for a real scalar field $$\frac{∂_μφ∂^μφ}{2}$$ such that is will be invariant under the gauge transformation $φ → φ + a(x)$? For a complex scalar field ...
0
votes
0answers
11 views

Is electric field by a charge present where the net field is zero?

I have heard a lot of people say that, at all the points where electric field is zero, electric field by any of the charges never reaches there. It's quite commonly thrown around that electric field ...
3
votes
1answer
180 views

2D square lattice, nearest neighbor and next-nearest connected by springs

For my field theory class I am trying to build the Lagrangian for the following system. Consider a 2D square lattice where the nearest and next-nearest neighbor interactions are modeled by springs ...
0
votes
0answers
52 views

solutions of wave equation with cubic term

Does the following equation $$ \nabla^\mu \nabla_\mu \psi + a \psi^3 = b \psi $$ where $\psi$ is a real function, $a$ and $b$ are real constants, have other solutions that extend beyond a one ...
6
votes
0answers
238 views

Peskin-Schroeder Problem 3.5, supersymmetric theories regarded as field theories on parameter space w/commuting & anticommuting coordinates?

I know how to do Problem 3.5 of Peskin-Schroeder. Let us organize the fields $\phi$, $\chi_\alpha$, $F$ of Problem 3.5 into a superfield$$\Phi(x + i\theta\sigma\overline{\theta}, \theta) = \phi(x) ...
-3
votes
1answer
90 views

Conceptual Change thinking needed [closed]

Using Conceptual Change Research To Reason About Curriculum By Glenn D. Berkheimer, Charles W. Anderson, and Steven T. Spees Introduction The kinetic molecular theory is fundamental to the ...
1
vote
1answer
102 views

What does it mean for an action to be defined “on-shell”?

Some actions like 11D supergravity are defined "on-shell". What does this mean exactly? Can you give me an example? Say for example the Klein-Gordon action. Can this be defined on-shell too?
0
votes
1answer
45 views

Fourier transform for $W(J)$ in a free QFT

In chapter I.3 and I.4 of A. Zee's QFT in a Nutshell, he starts with the theory $$ \mathcal{L}(\varphi) = \frac 12[(\partial\phi)^2-m^2\varphi^2]+J\varphi $$ Using the path integral approach, he ...
2
votes
0answers
40 views

Is this the correct way to obtain $<f|i>$ term in $\phi^4$ interaction theory? [closed]

Lets first write the expectation value of the fields in the interaction picture; $$ ...
0
votes
1answer
46 views

What does “n-particle reducible” mean?

I am reading Ramond and in page 112 he says "In $\lambda \phi^{4}$ theory, diagrams can be at most three-particle reducible". My question: whether the individual Feynman Diagrams are treated as ...
2
votes
0answers
56 views

Full form of the Pauli-Fierz action

In Deser's paper on the fully interacting version of the Pauli Fierz theory, he does a rather simple method of treating the Pauli Fierz equation without going with infinite sums, just by treating the ...
4
votes
1answer
114 views

Representation of the Lorentz group

Is there any representation of the Lorentz group where $$U^{-1} f(x) U = f(\lambda^{-1}x)$$ other than the (0,0) representation? If not then is it possible for a field (with a well defined ...
12
votes
2answers
2k views

Active versus passive transformations

I am a bit confused by the concepts of active and passive transformations. In all the courses I am doing at the moment we do transformations of the form: $$ \phi(x) \rightarrow\phi'(x') = \phi(x) $$ ...
1
vote
0answers
26 views

Writing the Interaction Hamiltonian for pions in a different way

$\pi^+$, $\pi^-$ and $\pi^0$ are scalars particles with masses approximately equals. Their interaction is, approximately, given by $H_{int}(x) = g \epsilon^{abe}\epsilon^{cde}(\phi^a\partial_\mu ...
1
vote
1answer
92 views

Modified gauge fixing condition in Faddeev-Popov approach

Which gauge fixing conditions are allowed to choose for this approach? For example (following the steps of Peskin in 9.4) I can choose a "modified" lorenz gauge ( for a abelian theory): $$ ...
0
votes
0answers
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 ...
0
votes
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 ...
3
votes
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 ...