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)

1
vote
0answers
115 views

How do instantons look in real time/spacetime?

Instantons, as I understand it, are mathematical constructions in Eucledean spacetime. Does it imply that instantons do not exist in real spacetime or instanton tunneling effects are does not have ...
1
vote
0answers
75 views

How do I derive Feynman rules for vectors involving derivatives?

Suppose I have a term in the Lagrangian: $$\cal{L} \equiv (\partial_\mu B^+_\nu) B^{-\mu} A^\nu $$, where $B^\pm$ are charged massive vector particles and $A$ is photon. Now, how can we derive the ...
1
vote
0answers
35 views

Massless Dirac Field Chirality and CP

I have some very basic questions about Quantum Field Theory. So let's assume we have massless fermions. In 4 spacetime dimensions, due to the Group Structure of $SO(3,1)$ there exists the famous $\...
1
vote
0answers
92 views

Spin and polarization, QM vs QFT

On page 34 of A. Zee's book QFT in a Nutshell, he states: I expect you to remember the concept of polarization from your course on electromagnetism. A massive spin 1 particle has three degrees of ...
8
votes
1answer
118 views

Gauge group topology

The fundamental difference between spinors and tensors is that spinors are sensitive to the homotopy classes of paths through the rotation group $SO(3)$: \begin{equation} \pi_1(SO(3)) = \mathbb{Z}_2, ...
7
votes
3answers
1k views

Is a single photon always circularly polarized?

While trying to understand polarization in quantum field theory, I wondered how a single photon could go through a linear polarizer. I found a paper which asked "Is a single photon always circularly ...
0
votes
0answers
26 views

Kinetic Term Normalization in Quantum FIeld Theory

Say we are given an antisymmetric two-form field: $A_{\mu\nu}$. Its kinetic term in the Lagrangian should be of the form $$ \mathscr{L}_{kin} = a\int d^4x \ \partial_{[\mu}A_{\nu\rho]}\partial^{[...
0
votes
1answer
76 views

can we prove the momentum operator is time inpdependent without using creation and annihilation operator?

in free scalar field, the momentum operator is $$P=-\int d^3 x \pi \nabla \phi$$. If we write it with creation and annihilation operator, then we can get the apparently time independent form,$$P=\int ...
0
votes
1answer
81 views

How to separate an exponential with a Hamiltonian with both momentum and position operators?

Statement of exercise On a page 11 of A.Zee's book QFT in a Nutshell, he derives Dirac's formulation of the path integral formulation of QM for a free particle. This starts with the free particle ...
0
votes
0answers
67 views

Quadratic terms in QED lagrangian density

I recently learned that when we speak about a "free lagrangian", this actually means that the lagrangian is quadratic in the fields. When considering the Lagrangian density describing the coupling to ...
2
votes
0answers
68 views

$i\epsilon$ versus $2i \epsilon E_k$ in the propagator

The Fourier Transform of the propagator can be written as $$\tilde{\Delta}(k) = \frac{i}{k^2-m^2+i\epsilon} \tag{1} $$ which is then "factored" into $$ = \frac{i}{\left( k^0-E_k +i\...
31
votes
5answers
5k views
6
votes
0answers
279 views

Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
0
votes
1answer
59 views

Excitation source in 2D grid coupled harmonic oscillator

In A. Zee's Quantum field theory in a Nutshell, he describes the QFT analogy of a matress, a 2D grid of points $q_a$ connected by springs (first page of first chapter, $q_a$ is the vertical ...
2
votes
0answers
75 views

What is Hawking Hartle vacuum state and why does the following Euclidean path integral gives the wave functional of it?

I am studying the wave function of black hole via the paper by Sergey Solodukhkin, Entanglement entropy of black holes,arXiv:hep-th: 1104.3712. In the paper, equation (53) is as follows: $$\Psi[\psi_{-...
1
vote
0answers
99 views

Relation of field creation operators to path integral?

Applying two field creation operators to a vacuum I get: $$\hat{\psi}^\dagger(x)\hat{\psi}^\dagger(y)|0\rangle = (\hat{\phi}(x)\hat{\phi}(y) - s^{-1}(x-y)) |0\rangle$$ where the quantum field ...
1
vote
1answer
24 views

Lifting an analogy of a pond to question signals at natural or artificial boundaries in space-time [closed]

I conjured up an idea to lift an analogy into the language of QFT and GR. I thought up the universe as a pond with a liquid. If we imagine a liquid poured into some pond (sort of bang and inflation ...
1
vote
2answers
118 views

Wavefunction collapse and relativity [closed]

In classical QM, when I measure the wave function of a system, e.g. the position of an electron somewhere in a box, its wave function collapses instantaneously to some classical position. But how fast ...
1
vote
3answers
201 views

How many electrons are there – quantum-wise?

If you consider that a particle exists as a quantum field, could you say that all the particles' fields combine into one field for that particle type? Why could you then not say there is no specific ...
3
votes
1answer
312 views

Peskin Schroeder and the general solution to Callan-Symanzik Equation

I have a couple of questions regarding Peskin and Schroeder's derivation of the solution to the Callan-Symanzik equation. First of all, they claim that using $$\int_\lambda^\bar{\lambda}\frac{d\lambda'...
3
votes
0answers
171 views

Phase transitions, Landau Ginzburg theory and Symmetry reduction

On one side of critical temperature (usually for $T<T_{c}$), symmetry is reduced w.r.t the symmetry on the other (usually $T>T_{c}$) regime. I heard on the road (near a theoretical physics ...
0
votes
0answers
22 views

Symmetry of retarded R-current correlator in $\mathcal{N}=4$ Super Yang-Mills

The retarded correlator of the R-current $J_\mu$ of $\mathcal{N}=4$ Super Yang-Mills theory is $$ C_{\mu\nu}(x-y)=-i\theta(x^0-y^0)\langle[J_\mu(x),J_\nu(y)]\rangle. $$ In this paper in eq. (2.4), I ...
0
votes
1answer
76 views

Two Point Correlator

I have a problem to reproduce the following identity: \begin{equation} \Pi_{\mu\nu}(q^2) = i \int d^Dx e^{iqx} \langle 0 | T \{j_\mu(x) j_\nu(0) \} | 0 \rangle = (q_\mu q_\nu - g_{\mu\nu} q^2 ) \...
24
votes
1answer
2k views

Emergent symmetries

As we know, spontaneous symmetry breaking(SSB) is a very important concept in physics. Loosely speaking, zero temprature SSB says that the Hamiltonian of a quantum system has some symmetry, but the ...
9
votes
3answers
2k views

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are?

Can someone give a simple expose on Coleman Mandula theorem and what Mandelstam variables are? Coleman-Mandula is often cited as being the key theorem that leads us to consider Supersymmetry for ...
0
votes
0answers
29 views

What is therelation between nonlinear sigma model, complex projective group?

The O(N) nonlinear sigma model has topological solitons only when N=3 in the planar geometry. There exists a generalization of the O(3) sigma model so that the new model possess topological solitons ...
4
votes
1answer
105 views

Are quantum “virtual negative-energy particles” the same as “negative energy density” in EFEs?

Question is fairly straightforward. Quantum theory describes negative energy in the form of the Casimir effect and virtual negative energy particles. In the Einstein field equations, negative energy ...
0
votes
1answer
84 views

Is it possible to understand physics and make new discoveries using computer simulation? [closed]

I'm a computer science major and I want to learn Physics. I can create computer simulations of any type. I'm not good at math that is required to learn QFT or GR,but I'm thinking is it possible to ...
0
votes
0answers
30 views

What is the interpretation of coefficients in path integral

Say we want the amplitude for particles starting at x,y with distribution f(x,y) and ending up at w,z with distribution w,z. Given a functionals: $F[\phi] = \int f(x,y)\phi(x,t)\phi(y,t) dx^3 dy^3$ ...
5
votes
1answer
246 views

Scattering Amplitudes from Feynman Diagrams (Spinor Helicity Formalism)

$\require{cancel}$ I am trying to do an exercise from Scattering Amplitudes By Elvang (Exercise 2.9) which states: Show that $A_5(f^-\bar{f}^-\phi\phi\phi) = g^3\frac{[12][34]^2}{[13][14][23][24]} ...
2
votes
1answer
91 views

Spin sums in cross sections. Summing amplitudes or probabilities?

The context: I'm calculating the cross section for a scalar particle to decay into a fermion-antifermion pair in Yukawa theory, at tree level. In doing this, when calculating the amplitude from ...
1
vote
0answers
40 views

What is the current theory underlying the concept of fields? [duplicate]

When I went to school I was specifically told that fields are material (they occupy some region in space, and they "exist" there) and continuous. Recently, studying quantum physics I came across the ...
2
votes
0answers
75 views

Isn't is far more likely that general relativity, and not QFT, is “wrong?” [duplicate]

At the risk/certainty of both sounding super ignorant and talking out of my arse, I have always wondered why there is some big mystery about why there are contradictions between the predictions ...
0
votes
0answers
81 views

Dirac Delta in Field Theory

We start with a function $${\Delta(x) = \displaystyle \int \dfrac{d^3k}{(2\pi)^3 2k^0}}\left( e^{ik^\mu x_\mu} - e^{-ik^\mu x_\mu} \right).$$ It is obvious to me that for $t = 0$ the above expression ...
9
votes
1answer
1k views

What is the difference between quantum fluctuations and thermal fluctuations?

Start with a simple scalar field Lagrangian $\mathcal{L}(\phi)$ at zero temperature $T = 0$, which has a hidden symmetry and spontaneously break it. By the standard procedure a field $\phi$ is ...
3
votes
3answers
169 views

Are field theories special?

Our best descriptions of the microscopic world, that satisfy many fundamental requirements (as we know them today), are field theories. Is there something fundamental about field interactions, or are ...
1
vote
1answer
80 views

Boosting massless particles

How does one calculate the boost matrix to go from a photon of (standard) four-momentum $k^\mu = (k,0,0,k)$ to $p^\mu = (p,0,0,p)$? (in terms of $|p|/|k|$) Weinberg in his Quantum Field Theory Vol.1 ...
1
vote
1answer
102 views

Wightman axioms. Are test functions injectively mapped to operators

In AQFT test functions f are mapped to operators $\phi(f)$. This operator is said to obey a Klein Gordon equation KG ($\phi(f)$) = 0 if $\phi(KG(f))$ = 0. This means that if the map is injective it ...
0
votes
1answer
82 views

A derivation in Schwinger's proper time approach

I have a question in derivation of Schwinger's proper time method in chapter 2.1 of http://link.springer.com/book/10.1007%2F3-540-45585-X from Eq.(2.20)-Eq.(2.23) to the classical action expression ...
2
votes
2answers
139 views

Simulation of everyday life based on standard model [closed]

If I were to model the standard model, say on a super powered computer (which does not necessarily have to exist in the real world), would I get molecules, chemistry, life? I want to understand the ...
8
votes
3answers
933 views

What is meant by a “c-number”?

In Chapter 2 of David Tong's QFT notes, he uses the term "c-number" without ever defining it. Here is the first place. However, it's easy to check by direct substitution that the left-hand side ...
1
vote
1answer
88 views

Why are the odd point green functions in free field theory zero?

I don't understand why the $(N=\mathrm{odd})$-point Green functions calculated in free field theory are identically zero. Is it because the Green functions are odd? If so, then how do I prove it? Is ...
2
votes
1answer
75 views

What is the interpretation of a wave function of the Universe in Hawking's no boundary proposal?

In the path integral formalism we have an in state $\Psi_{in}[\phi]$ and and out state and we find the amplitude for going from one to the other: $$\Delta[\Psi_{in},\Psi_{out}] = \int \Psi_{in}[\phi]...
1
vote
2answers
104 views

Baryogenesis via Leptogenesis

Baryon number is directly violated through electroweak anomaly and so does the Lepton number, for each transition from one vacuum to another. The two violations are of equal amount $\Delta B=\Delta L=...
2
votes
0answers
98 views

Schwinger-Dyson equation from the Heisenberg formalism?

All the derivations of the Schwinger-Dyson equation I can find are done using either the path integral formalism, or for the oldest papers, Schwinger's own quantum action principle formalism, which, ...
7
votes
2answers
418 views

Complex coordinates in CFT

The Setup: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric $ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$. It seems to me that ...
9
votes
3answers
3k views

Why do neutrino oscillations imply nonzero neutrino masses?

Neutrinos can pass from one family to another (that is, change in flavor) in a process known as neutrino oscillation. The oscillation between the different families occurs randomly, and the likelihood ...
4
votes
0answers
180 views

Scattering, Perturbation and asymptotic states in LSZ reduction formula

I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix ...
1
vote
0answers
30 views

Phase-space average equal to the quantum mechanical average in the early universe

I was reading Mukhanov's book of cosmology http://www.amazon.com/Physical-Foundations-Cosmology-Viatcheslav-Mukhanov/dp/0521563984 , specifically about symmetry restoration in the early universe ...
9
votes
2answers
465 views

What is the algebraic property that corresponds to a topological term?

Warning: This question will be fairly ill-posed. I have spent a lot of time trying to make it better posed without success, so please bear with me. A single $SU(2)$ spin may be represented by the $0+...