All Questions
Tagged with definition quantum-field-theory
110 questions
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How are $t$ and $u$ channel processses different? [duplicate]
I do not understand how the diagrams for t and u channel processes given on wikipedia are different, and why it is meaningful to list them. Below are the two processes I reference:
It seems to me ...
- 860
2
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0
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43
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How are Fermionic and vector valued quantum field theories rigorously defined?
A scalar (spin 0) quantum field is rigorously defined as an operator valued distribution. By Wick rotating to Euclidean space we can view a quantum field theory as a measure over distributions. How ...
- 3,992
-4
votes
1
answer
136
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What exactly in QFT makes a field/particle on- or off-shell?
If we are to write down a quantum field definition, could we tell if the definition is on- or off-shell?
If we are to write down a quantum field interaction, could we tell from the expression and not ...
- 2,042
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0
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98
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Calculate scalar QED vertex using LSZ formula
I am self-studying QFT using the Schwartz book "Quantum field theory and the standard model", and I am reading chapter 9 about Scalar QED.
I am trying to calculate the following vertex using ...
- 675
3
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1
answer
290
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What is "free" and what is "interacting" in the interaction picture?
How do we rigorously and systematically discern between the "free" and the "interacting" part of a Hamiltonian? That is, how can we find $\hat{H}_{\text{free}}$ and $\hat{H}_{\text{...
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Why care that 1-particle states $a^{\dagger}_{\mathbf{p}}|0\rangle$ have $\langle\mathbf{p}|\mathbf{q}\rangle$ which are lorentz invariant?
When defining momentum eigenstates, Peskin+Schroeder (in Chapter 2) define
$$
|\mathbf{p}\rangle = \sqrt{2E_\mathbf{p}} a^{\dagger}_{\mathbf{p}}|0\rangle.
$$
The prefactor of these states $\sqrt{2E_\...
- 3,764
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3
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114
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What is the difference between $u$ and $t$ channels in Feynman diagrams?
My question is very simple: can someone explain to me the difference between the $u$-channel and the $t$-channel in Feynman diagrams? I can't understand what is the "role change" in $u$-...
7
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75
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Analogue of (anti)commutation relation for anyons
In textbook quantum field theory, bosons obey something like
$$[b_\sigma(\vec{x}, t),b_{\sigma'}(\vec{y}, t)^\dagger]\propto \delta_{\sigma \sigma'}\delta(\vec{x} - \vec{y})$$
and fermions obey ...
- 3,295
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0
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54
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Existence of matching of free and interaction fields
When using the interaction picture in QFT to describe a field with a Hamiltonian $H = H_0 + V$, where $H_0$ is the free Hamiltonian, there is a crucial step in which we assume that at some time $t_0$ ...
- 2,210
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1
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496
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What is the difference between Born approximation and tree-level processes?
The answer to this question says that Born approximation is essentially equivalent to the tree-level. This can be seen from the Feynman-diagrammatic version of Born series discussed in many NRQM ...
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1
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Definition of “quasi-locality” in Wilsonian RG scheme
I’m studying about the holographic RG with this paper.
In that paper they say Wilsonian action expects quasi locality, but I’m not sure what “quasi-locality" exactly means.
If quasi-locality ...
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2
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1
answer
112
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The definition on vacuum-vacuum amplitude with current in chapter of External Field Method of Weinberg's QFT
I'm reading Vol. 2 of Weinberg's QFT. As what I learnt from both P&S and Weinberg, the generating function is defined as
$$
Z[J] = \int \mathcal{D}\phi \exp(iS_{\text{F}}[\phi] + i\int d^4x\phi(x) ...
- 23
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1
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Equivalent definitions of Wick ordering
Let $\phi$ denote a field consisting of creation and annihilation operators. In physics, the Wick ordering of $\phi$, denoted $:\phi:$, is defined so that all creation are to the left of all ...
- 3,992
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76
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Is there any difference between Wick time order and Dyson time order?
Reading A Guide to Feynman Diagrams in the Many-Body Problem by R. Mattuck, I am getting the feeling that I missed something subtle related to time order. When deriving the Dyson series for the ...
- 5,841
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1
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219
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Renormalization group equation, the Callan-Symanzik equation, and renormalization group flow
I am learning about the renormalization group and I am getting confused on some terminology.
For the massless $\phi^4$ theory the Callan-Symanzik equation is:
$$\big[ M \frac{\partial}{\partial M} + \...
- 3,992
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88
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What is intrinsic parity? Why is negative intrinsic parity possible?
What is intrinsic parity? It seems that it is a concept only for relativistic quantum physics. Why is it not relevant for non-relativistic quantum mechanics?
- 1,075
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1
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235
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Simple definition for the generator of an infinitesimal transformation
Studying quantum mechanics, or QFT, the concept of generator $G$ of an infinitesimal transformation $T$ keeps showing up. My problem is that I don't have in mind a solid (dare I say "rigorous&...
- 4,635
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131
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Difference between Bogoliubov-Shirkov renormalization group and Wilson's Renormalization group
I just learned the Wilsonian renormalization group from a QFT lecture, I heard that there is another renormalization group called Bogoliubov-Shirkov renormalization group which is a true group instead ...
- 161
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1
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75
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Definition of the left-right derivative symbol in the Klein-Gordon scalar product [duplicate]
At the start of QFT, studying the Klein-Gordon scalar field, it is often mentioned that the following is the definition of the scalar product in the space of the solutions:
$$\langle f _{\vec{k}}|f_{\...
- 4,635
1
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1
answer
138
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On the $\ast$ map in the Osterwalder-Schrader axioms
I'm studying "A Mathematical Introduction to Conformal Field Theory" by Schottenloher and there is one point on the Osterwalder-Schrader axioms that I am a bit confused about. They are ...
- 37.4k
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90
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What is the difference between wavefunction renormalization and field strength renormalization?
A while ago I asked a question asking what is field strength renormalization (What exactly is field strength renormalization?). I now have a better way of thinking about this, which is that it relates ...
- 3,992
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Contact terms in Schwinger-Dyson equation and Ward-identity
I am reading Weigand's notes for the derivation of Ward-identity.
The Second last paragraph on page 133, says the following statement
"The Schwinger-Dyson equation and the Ward-identity show ...
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4
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2k
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What are Quantum Field Theories?
Every time I read about quantum field theories, I wrongly assume and associate the theory to the Standard Model, that is, our current theory of particles and interactions.
However, it seems that the ...
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148
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What is the definition of bound state in quantum field theory?
I asked a question a while a go what is a bound state and the question was closed because there is a similar question.
Now since best description we have to describe nature in quantum field theory
How ...
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1
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318
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Is the charge-conjugation symmetry in cond-mat physics different from that in QFT?
In condensed matter physics, the terms "particle-hole symmetry" and "charge-conjugation symmetry" are often used interchangeably. As far as I understand, they refer to the ...
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224
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Wilsonian RG vs. continuum RG
As far as I understand one classifies the renormalization group (RG) into the Wilsonian RG and the continuum RG. The Wilsonian RG gives finite predictions by introducing a cutoff $\Lambda$ and absorbs ...
- 405
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1
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449
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Rigorous Theory of Path integrals [duplicate]
Does there exist a mathematical rigorous theory of the Feynman-Path-Integral in Quantum Mechanics or Quantum Field Theory?
- 428
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4
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1k
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What exactly is field strength renormalization?
One thing I have not fully understood is what field strength renormalization is. In Peskin & Schroeder's book "An Introduction to Quantum Field Theory" (Section 7.1) they introduce it as ...
- 3,992
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Do these two expressions for correlation function have the same physical interpretation?
I have learned that
the $k$-point correlation function is
\begin{equation*}
\left<\Omega\left|T\prod_{n=1}^k\hat{\phi}(x)\right|\Omega\right> = \frac{1}{Z_0}\prod_{n = 1}^k\left(-i\frac{\delta}{...
- 1,853
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1
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305
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Time ordering of integral [closed]
Is $$T\int\mathrm{d}^4x\phi^4(x)$$ just notation for $$\int\mathrm{d}^4x~T\phi^4(x)$$ since after integrating we have no time dependence anymore?
- 405
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1
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Scattering ${\cal M}$- and $S$-matrix
I am reading QFT book, like Introduction to QFT by Peskin and Schroeder, I would like to know conceptually what is the difference between $S$-matrix and invariant matrix element ${\cal M}$ in ...
- 326
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491
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What is the definition of $n$-loop 1PI diagrams in QFT? [closed]
What is the precise definition of a $n$-loop one-particle irreducible ($1$PI) diagram?
For example, consider the following diagrams.
Is the first diagram a $0$-loop $1$PI diagram?
Is the second ...
- 4,276
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1
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44
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The difference between operator condition, differential condition and algebraic condition?
It is well known that the gauge potential $A_\mu=(\phi,-\vec{A})$ has gauge symmetry and one could impose Lorenz and Coulomb gauge simultaneously to it to eliminate redundant degrees of freedom. In ...
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1
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What are Wilson Coefficients?
I have seen this terminology in several papers but I haven't managed to find an explanation of what they actually are. I understand that they are related to effective field theory.
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Two definitions of vectors and general spinor transformations
The usual definition of a vector is that its components transform contravariantly under the change of coordinate chart on the underlying manifold -- it is an element of the tangent bundle of the (let'...
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1
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Defining propagators as vacuum expectation values of products of field operators
I am studying Mandl and Shaw's book on QFT and I am trying to understand the different definitions of the propagator functions, or $\Delta$-functions. One $\Delta$-function is defined (and derived) in ...
- 311
1
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1
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243
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What does effective quantum field theory mean?
By renormalization, we have renormalized quantum field theory, usually, we call the theory by effective QFT. What does effective quantum field theory mean? It means we have different quantum field ...
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0
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23
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NLO and NLL difference [duplicate]
The next-to-leading order (NLO) Feynman diagram is the next leading process having more vertices than the tree-level diagram, but what is next-to-leading-logarithm (NLL)?
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1
answer
1k
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Definition and proof of Symmetry Factor of Feynman Diagram
Studying QFT, I was told that symmetry factor is defined by:
if there are $m$ ways of arranging vertices and propagators to give identical parts of a diagram (keeping the outer ends of external lines ...
- 1,774
1
vote
1
answer
203
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Requirement of Jordan-Wigner string in creation operator on Fock state
Our lecture notes described the action of the particle creation operator on a fermionic Fock state:
$$c_l^\dagger |n_1 n_2...\rangle = (-1)^{\sum_{j=1}^{l-1}n_j}|n_1 n_2 ... n_l+1 ...\rangle.$$
I am ...
- 2,654
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Is this definition of the Fourier Transform of a quantum field operator rigorous?
Let there be a a quantum field operator $\hat\phi(t,\vec{x})$ which, because it acts (pointwise) on a separable Hilbert space, I expect I can write as
$$\hat\phi(t,\vec{x}) = \sum_n\sum_m\phi^n_m(t,\...
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What does it mean for QFT to be unitary?
I understand the statement that 'X QFT is unitary' is shorthand for saying 'the S-matrix of X QFT is unitary', cf. e.g. this Phys.SE post.
Is there some definition of unitarity that is stronger than ...
- 1,042
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1
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590
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What is a "Born diagram"?
In the introduction of this article, the following statement is made regarding the partonic picture for hadronic scattering amplitudes:
To leading order in $\alpha_S (Q^2)$, the "hard-scattering ...
- 5,421
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2
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What does "propagate" mean in QFT?
Studying QFT, one finds the term "the field propagates" and I'm not sure I understand what it means. For example, in QED, one finds that $A_0$ "doesn't propagate" because its ...
- 6,049
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1
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Is the self-energy well-defined?
We know that we can calculate the Green function $G(\tau;\lambda)= -\langle \mathcal{T}c(\tau)c^*\rangle$ of an interacting Hamiltonian $H=H_0 + \lambda V$ using connected Feynman diagrams. Of course, ...
- 2,183
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663
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Definition of the $S$-Matrix in Schwartz QFT-Book: Why is $\langle f, t_f | i, t_i \rangle$ in the Schroedinger picture, and not Heisenberg-picture?
On page 51, (equation 5.1), Mathew Schwartz introduces the $S$-matrix as
\begin{align}
\langle f| S | i \rangle_{Heisenberg} = \langle f, \infty | i, -\infty \rangle_{Schrödinger}
\end{align}
Were $|i,...
- 6,980
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3
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Difference between QFT and quantum mechanics
It is often said Quantum mechanics is $d=0$ and QFT can have $d = \infty$. What does this mean and how does it makes tunneling possible in Quantum mechanics and not in Quantum Field Theory? What is $d$...
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Nonrenormalizable but quantizable theory: gravity?
In p.8 of Michio Kaku book Introduction to Superstrings and M-Theory-Springer (1998), he said
The gravitational force. Gravity research was totally uncoupled from research in the other interactions. ...
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Dualities in Physics and Fourier Transforms
In many articles, authors compare physical dualities to Fourier transforms.
For example:
Joseph Polchinski, in his article "String Duality" (hep-th/9607050v2), writes: "Weak/strong ...
- 63
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2
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556
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How should I think about the word "coupling" in quantum field theory?
People doing any form of quantum field theory (QCD, string theory etc) always use the word "couple" and I am not sure exactly what it means. If a QFT couple to gravity I can make an educated ...
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