Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use ...

learn more… | top users | synonyms (1)

0
votes
0answers
34 views

Definition of mass gap [duplicate]

Why do we say that a system with mass gap has correlation function which decays exponentially and one without a mass gap has a slower power law decay?
2
votes
1answer
153 views

Massless Dirac equation is Weyl covariant

Does somebody know how to show that the following equation is Weyl invariant? $$\gamma^ae_a^\mu D_\mu \Psi=0$$ where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant ...
3
votes
1answer
160 views

S-Matrix and normalization of states

I'm trying to understand what is the S-matrix in QFT. People say that it has to be a unitary matrix, but that I guess will change with a different normalization of the incoming and outgoing states. My ...
4
votes
0answers
127 views

What is the fundamental difference between ghost and auxiliary fields?

I am somehow confused by the notion of auxiliary fields, such as for example the fields $F$ and $D$ which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST ...
1
vote
1answer
40 views

What are Maximally Helicity Violating (MHV) Amplitudes?

Definition of MHV amplitudes on Wikipedia: In theoretical particle physics, maximally helicity violating amplitudes are amplitudes with n external gauge bosons, where n-2 gauge bosons have a ...
0
votes
0answers
47 views

Interpretation of Dirac Spinor components in Chiral Representation?

I failed to find any book or pdf that explains clearly how we can interpret the different components of a Dirac spinor in the chiral representation and I'm starting to get somewhat desperate. This is ...
2
votes
1answer
64 views

How does interpreting negative energy electrons as positrons solve the negative energy problem?

How does interpreting negative energy electrons as positive energy positrons solve the negative energy problem? How does change of “interpretation” without fixing the mathematics have such a profound ...
2
votes
0answers
24 views

Bulk Symmetry corresponding to Yangian Symmetry of Planar N=4?

4D N=4 Super Yang Mills in the planar limit has an infinite dimensional symmetry known as Yangian symmetry. Dualities respect symmetries, so what does this symmetry correspond to in the $AdS_5\times ...
4
votes
1answer
150 views

A question about the energy of turning on and off interaction adiabatically in QFT

I read a saying as follows: In a theory with no particles which decay and no bound states, the turning on and off of the interactions merely serves to limit the effective range of forces. In this ...
4
votes
1answer
247 views

Are the Møller wave operators $\Omega_\pm$ related to $\lim_{t\rightarrow\infty}U(t)$ from field theory?

When we want to compute correlation functions $\langle\Omega|\,T\hat{\phi}(x_1)\ldots|\Omega\rangle$ in an interacting quantum field theory, we relate it to the free-field objects $|0\rangle$ and ...
13
votes
3answers
1k views

What does the ordering of creation/annihilation operators mean?

When a system is expressed in terms of creation and annihilation operators for bosonic/fermionic modes, what exactly is the physical meaning of the order in which the operators act? For example, for ...
1
vote
0answers
32 views

Minimization of a quaradic-like expression when calculating the generating functional for free Dirac field

The generating functional for a free Dirac field is $$Z_0[\eta,\bar{\eta}]=\int D\bar{\psi}D\psi \mathrm{exp}\{i\int [\bar{\psi}(x)S^{-1}\psi(x)+\bar{\eta}(x)\psi(x)+\bar{\psi}(x)\eta(x)]dx\}$$ where ...
0
votes
2answers
332 views

The virtual particles are only a fictive tool in equations? DO they exist or DON'T? And if they exist, why do we call them VIRTUAL?

There is no "action at a distance" in nature. Attraction of a piece of iron by a magnet, attraction between distant electric charges of opposite sign, have to be mediated by something. The virtual ...
2
votes
0answers
55 views

Is it possible to derive the effective potential of a given theory by only using the RGE equations?

I know that it is possible to derive the RGE equations from the effective potential by requiring that the first derivative with respect to the renormalization scale $\mu$ vanishes: $$ ...
1
vote
1answer
115 views

What kind of math is used in QFT? [duplicate]

What branch(es) of math are used in Quantum Field Theory? Or the question, by way of analogy: Tensor Calculus is to General Relativity as What is to Quantum Field Theory?
5
votes
1answer
550 views

A confusion from Weinberg's QFT text (a vanishing term in Lippmann-Schwinger equation)

I was reviewing the first few chapters of Weinberg Vol I and found a hole in my understanding in page 112, where he tried to show in the asymptotic past $t=−∞$, the in states coincide with a free ...
22
votes
9answers
3k views

Is the wave-particle duality a real duality?

I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
1
vote
1answer
27 views

Chiral-Projection operator in a basis different than the Weyl basis

I was pretty confident that things are simple, but unfortunately I must have missed something. We can always change between between the bases for Dirac spinors, using unitary transformation, because ...
6
votes
0answers
78 views

Is it possible to have fermions in Schwarzschild spacetime?

To my understanding Geroch proved that on 4-dimensional non-compact manifold a necessary and sufficient condition for a manifold to have a notion of spinors is to be parallelizabe .1 (General ...
4
votes
2answers
121 views

Path integral derivation of the state-operator correspondence in a CFT

Below, I paraphrase the path integral derivation of the state-operator correspondence in David Tong's notes on CFT (see pdf here). This is my interpretation of the text in that pdf, so please correct ...
1
vote
1answer
50 views

Photon and Wave

There are some aspects of light that can be easily demonstrated by using the concept of wave. However I really want to know what it would be like in term of photon point of view. So I have some ...
3
votes
2answers
92 views

What is the physical interpretation of a field operator

So far in our lecture we defined creation operators $a^{\dagger}_{n}$ in the following way, that we said: Somebody got you a antisymmetric or symmetric N- particle state and now $a^{\dagger}_{n}$ ...
0
votes
0answers
37 views

A question from Schwinger's particles, sources and fields monograph

My first question from his first volume. On page 254, he writes down the action expression: $$(3-10.1)W=\int (dx)[K\phi+K^{\mu}\phi_{\mu}+\mathcal{L}]$$ Where the lagrangian is: $$ ...
0
votes
1answer
58 views

Higher-order gauge coupling terms in the Lagrangian

In QFT, one works with Lagrangians that are invariant with respect to a certain symmetry. Out of this invariance, one is able to write down interaction terms at first order in the gauge couplings. The ...
1
vote
0answers
40 views

Proof that the effective action is the generating functional of one-particle-irreducible (1PI) correlation functions

In all text book and lecture notes that I have found, they write down the general statement \begin{equation} ...
1
vote
2answers
37 views

Are relative phases observable for identical particles but not for non-identical ones?

In quantum mechanics, amplitudes are represented by complex numbers $e^{i\phi}$, which have phase angles $\phi$. These phase angles are clearly not observable in absolute terms. If I have two ...
9
votes
1answer
106 views

Confusion about two definitions of anomalies

As I am currently studying for an exam about quantum field theory and string theory, I got confused about the notion of "anomalies" and how they are actually defined. Similar questions have already ...
1
vote
0answers
15 views

Upper bound to annihilation cross section into heavy particles

For a process in which two relativistic particles annihilate to produce two or more heavy(er) particles of mass $M$: Is it true that the cross section $\sigma_{ann}$ cannot be larger than ...
0
votes
1answer
81 views

Invariance under charge conjugation… Or not?

I have read some paper which says that the electroweak Lagrangian includes these terms like $\bar{\psi} \gamma_a\gamma_5\psi$ and $\bar{\psi} \gamma_a \psi$. They violate charge conjugation symmetry. ...
7
votes
3answers
2k views

How deep can my knowledge of particle physics go without the maths?

By no means do I have the mathematical background to understand most of the math used in elementary particle physics. My current knowledge is of all the elementary particles and how they interact ...
7
votes
1answer
143 views

2 Component Spinor Formalism

In Chapters 34-36 of the Srednicki QFT book, 2 component spinors and their combinations in Dirac and Majorana spinors are carefully constructed. Specifically, in equations 36.14 and 36.15 the ...
5
votes
3answers
104 views

Justification of not quantizing small extra dimensions

When dealing with extra dimensions ($ x ^\mu $ represents $ 4D $ spacetime and $ y $ the extra dimension) we use what's known as Kaluza-Klein decomposition (basically a Fourier transform), ...
2
votes
1answer
38 views

Differences the nonlinerarties

I want to comparison between oscillons based on non-linearities. Can someone elaborate it with the reason behind it : When the sinusoidal vibrations are of the correct amplitude and frequency and ...
3
votes
1answer
70 views

Are Matsubara states pure states?

Generally in a non-interacting QFT one can solve the Klein-Gordon equation to get a (complete) set of states $\frac{e^{i\omega_k t-ikx}}{\sqrt{2\omega_k}}$. It is not clear to me how to construct the ...
3
votes
2answers
85 views

Scalar operators In Quantum Field Theory

I am trying to learn Quantum Field Theory and I am stuck in a basic point. What is the definition of a scalar operator in QFT? That is, how does it transform under a Poincare transformation? Why do ...
2
votes
2answers
155 views

masslessness of Goldstone boson, Effective action, and functional-integral measure

I have difficulty in understanding the path-integral formalism of SSB, and that of Effective Action. Let's say a complex scalar field theory has the global $U(1)$ SSB, $$L(\phi)=(\partial^\mu ...
0
votes
1answer
86 views

Do physicists use agent based models?

I am hoping that this is a simple and specific question. I just wanted to know whether physicists from any branch of physics use agent based models as a tool in their research? If so, then in which ...
0
votes
1answer
70 views

Vector bosons: polar vectors or axial vectors?

The $W$ and $Z$ bosons are known as vector bosons, because they have non-zero spin. How do we know whether they are axial or polar vectors? Context: I am reading about a technique called Operator ...
3
votes
2answers
380 views

Density operator in second quantization

I would want to understand why the density operator in second quantization takes the form: $$\rho_\sigma(\mathbf{r})=\Psi_\sigma^\dagger(\mathbf{r})\Psi_\sigma(\mathbf{r})?$$ Is this a definition or ...
4
votes
1answer
123 views

Second derivative of dirac delta expression

I have come across the expression $$ \int f(x) \delta(x-a) \delta''(x-a) \mathrm dx$$ where the prime represents the derivative. Usually with derivatives of the delta distribution I'd partially ...
2
votes
4answers
314 views

Bogoliubov transformation with a slight twist

Given a Hamiltonian of the form $H=\sum_k \begin{pmatrix}a_k^\dagger & b_k^\dagger \end{pmatrix} \begin{pmatrix}\omega_0 & \Omega f_k \\ \Omega f_k^* & \omega_0\end{pmatrix} ...
3
votes
0answers
114 views

Is everything made of space? [closed]

I had been studying quantum field theory for a while now, and how there had been many efforts in physics to finally create a "Theory of Everything" (TOE). But while I was learning about all this, I ...
1
vote
0answers
49 views

One loop correction to $F^2$ in massless QED, question from Peskin & Schroeder

In Peskin & Schroeder chapter 19, about trace anomaly in massless QED, the trace of $\Theta^{\mu\nu}$ is given by $$ {\Theta^\mu} _\mu =-\frac{4-d}{4} (F_{\lambda\sigma})^2 + (1-d) \bar{\psi} i ...
5
votes
2answers
88 views

Gross-Neveu model analytic solution [closed]

I need to find an analytic solution via asymptotic expansion for the following system of equations: \begin{align} & i(u_t+u_x) + v = 0 \\ & i(v_t-v_x) + u = 0 \end{align} \begin{equation} ...
3
votes
2answers
70 views

What makes a one particle state?

I'm trying to understand free particle states in quantum field theory but I'm having trouble with one thing: what exactly defines a one particle state? For example, we can define a 'plane wave' as a ...
0
votes
0answers
39 views

Polarization sum rule for Rarita-Schwinger field

There are Rarita-Schwinger equations: $$ \tag 1 (p\!\!\!/ - m)\psi_{\mu} = 0, \quad \gamma_{\mu}\psi^{\mu} = 0, \quad i\partial_{\mu}\psi^{\mu} = 0. $$ So the polarization sum $D_{\mu \nu}(p) = ...
1
vote
0answers
32 views

classical and quantum correlation functions

Quantum Field, quantum fluctuation even with no temperature In QFT, the correlation function $<0|\hat{\phi} (x)\hat{\phi} (y)|0>$ describes the fluctuation correlations of vacuum state ...
11
votes
2answers
263 views

Proof of Loss of Lorentz Invariance in Finite Temperature Quantum Field Theory

In the standard quantum field theory we always take the vacuum to be a invariant under Lorentz transformation. For simple cases, at least for free fields, is very simple to actually prove this. Now ...
6
votes
1answer
51 views

Incoherent assumption of the parton model

Consider the scattering process $ep\rightarrow eX$, in the frame of an ultra-relativistic electron, the partons inside the proton are "frozen," and since the time scale of strong interaction is much ...
2
votes
2answers
78 views

What is the physical meaning of $a_{\vec{p}} \! \mid \! 0 \rangle$

$a^\dagger_{\vec{p}} \! \mid \! 0 \rangle = \mid \! p \rangle$ is interpreted as a creation of a particle with momentum $p$ from the vacuum. $a_{\vec{p}} \! \mid \! p \rangle = \mid \! 0 \rangle$ is ...