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)

2
votes
1answer
208 views

How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum?

How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum? I used the Gordon Decomposition to split the Probability Current of the Dirac Field into its orbital current and ...
2
votes
3answers
169 views

Realistic interacting QFT construction

May I ask is it true that all the interacting 4 dimension qft couldn't be constructed and defined consistently and rigorously? If we are able to rigorously constructed lower dimension qft, what are ...
11
votes
2answers
381 views

Why are non-Abelian gauge theories Lorentz invariant quantum mechanically?

I seem to be missing something regarding why Yang-Mills theories are Lorentz invariant quantum mechanically. Start by considering QED. If we just study the physics of a massless $U(1)$ gauge field ...
0
votes
0answers
104 views

Epstein-Glaser causal perturbation theory

Why does causal perturbation theory in the sense of Epstein Glaser fall under algebraic QFT rather than heuristic QFT in renormalization?
9
votes
5answers
3k views

Chemical potential

This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at ...
2
votes
2answers
230 views

Finding wave-fuctions of a Dirac particle for given 4-momentum and spin 4-vector

I've been reading through various materials on relativistic quantum mechanics, but I find the lack of simple examples disturbing. I'm acquainted with the general form the solutions to the Dirac ...
3
votes
0answers
109 views

Effective field theories and gauge anomalies cancellation

Lets assume some theory which concludes sets of generations of fermions (lets call them $A$ and $B$). Fermions $A$ have some gauge group $G_{A}$ (for example, SM), while fermions $B$ are charged under ...
10
votes
7answers
747 views

Why regularization?

In quantum field theory when dealing with divergent integrals, particularly in calculating corrections to scattering amplitudes, what is often done to render the integrals convergent is to add a ...
10
votes
2answers
1k views

Bound states in QED

I am a beginner in QED and QFT. What is known (or expected to be) about bound states in QED? As far as I understand, in non-relativistic QM electron and positron can form a bound state. Should it be ...
10
votes
1answer
148 views

LSZ reduction vs adiabatic hypothesis in perburbative calculation of interacting fields

As far as I know, there are two ways of constructing the computational rules in perturbative field theory. The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free ...
1
vote
1answer
66 views

Is gauge invariance essential to a theory be renormalizable?

Let's consider a model of New Physics in which all operator have dimension smaller than four, but which breaks explicitly $SU(2)_L$ gauge symmetry. Is this model necessarily renormalizable? ...
1
vote
0answers
29 views

How can I prove that $\gamma^0$ is the parity operator for Dirac fields? [closed]

How can I prove that the parity operator on a Dirac field is $\gamma^0$? I was trying to prove it through Lorentz transformations but failed shortly.
1
vote
0answers
44 views

Why are the particles called irreps of Poincare group? [duplicate]

Why are particle excitations called irreducible representation of the Poincare group? It will be very helpful if someone can illustrate with one concrete example of a particle. EDIT : But how does ...
4
votes
1answer
262 views

Branch cuts in two-point function

The propagator of a QFT is known to have a branch cut as a function of the (complex) external momentum. The branch point (as done by, say, Peskin & Schroeder in eqn.7.19 section 7.1) is ...
4
votes
1answer
472 views

Traceless of stress-energy tensor in $d=2$

This is a question regarding Francesco, section 4.3.3. In this section, he considers the two-point function $$ S_{\mu\nu\rho\sigma}(x) = \left< T_{\mu\nu}(x) T_{\rho\sigma}(0)\right> $$ He then ...
12
votes
1answer
721 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, ...
1
vote
0answers
37 views

Pauli Villars Regularization

Consider the t-channel diagram of phi-4 one loop diagrams. Evaluated it is, with loop momenta p, $\frac{\lambda^2}{2}\displaystyle\int\frac{d^4p}{(2\pi)^4}\frac{1}{(p+q)^2-m^2}\frac{1}{p^2-m^2}$ If ...
6
votes
1answer
177 views

How do creation operators change with time in an interacting theory?

When studying the quantization of a field theory with free fields, the creation operators $a^\dagger(k)$ are independent of time. In an interacting theory, they are time-dependent, and therefore ...
1
vote
1answer
65 views

Equivalence principle for test fields

My question is very simple. We all know that, for a test particle(classical) in a gravitational field, the motion is only determined by the geodesic lines(let's forget about the initial conditions for ...
3
votes
1answer
1k views

Why/How is this Wick's theorem?

Let $\phi$ be a scalar field and then I see the following expression for the square of the normal ordered version of $\phi^2(x)$. $$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 $$ ...
4
votes
2answers
200 views

Why does the non-linearity of the string action prohibit stretching due to strong excitations?

From 't Hooft's String Theory lecture notes on page 8 (paraphrased): To understand hadronic particles as excited states of strings, we have to study the dynamical properties of these strings, and ...
0
votes
1answer
29 views

Higgs mass and EW precision tests

I'm trying to understand how the Higgs mass can influence EW precision tests. In order to do that I'm using the following document (section 4.3): http://arxiv.org/pdf/0706.0684v1.pdf There are a ...
3
votes
1answer
274 views

Energy eigeinstates written in the field operator eigenstates basis

For an harmonic oscillator we can write the Hamiltonian eigenvalues in the basis of the amplitude eigenvalues : for example the ground state is a gaussian : $⟨x|0⟩=a.e^{-b.x^{2}}$. I was wondering ...
4
votes
1answer
204 views

Feynman rule for deriative interaction: an example

Consider a theory for a finite number of real scalar fields $\phi _i$ with interaction terms of the form $$ -\lambda _{ijk}\phi _i\partial _\mu \phi _j\partial ^\mu \phi _k, $$ with the sum over ...
8
votes
7answers
1k views

Why do physicists believe that particles are pointlike?

String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories. So why is it that it's popular ...
7
votes
2answers
137 views

Expectation values of interacting fields

I was motivated to ask this question by the equality claimed in equation 10.3.3 of Weinberg's volume 1 of QFT books. My interpretation of that, If $O_s$ is a quantum field of spin $s$, $\psi_s$ is ...
1
vote
1answer
55 views

Gordon decomposition of Dirac current for massless electron?

We know Gordon decomposition of Dirac current is applicable only for massive (nonzero mass) Dirac particles. Is there an analog for massless Dirac particles? (I have made an attempt to answer ...
3
votes
1answer
134 views

Group theoretic way to find charges after SSB

I was wondering what is the group theoretic way to find the resulting charges of matter fields after a scalar field is given a vev. In the case of the EW symmetry breaking, one can directly read the ...
1
vote
2answers
119 views

Simplifying effect of a hidden Weyl symmetry in a QFT on curved spacetime

We consider AdS$_{d+1}$ in Poincaré coordinates: $$ ds^2=\frac{1}{z^2}\left(-dt^2+dz^2+dx_{d-1}^2\right), $$ where we set the AdS radius to unity. We study a scalar in this background with action $$ ...
2
votes
1answer
129 views

Massless boson in 2D and its (retarded) propagator

I have the retarded propagator for a free scalar field in 1+1 dimensions. Inside the light cone, this looks like $J_0(m \sqrt(t^2-x^2))$, J being a Bessel function. When I take the massless limit, ...
1
vote
1answer
59 views

Why does Srednicki insist on $\phi$ having zero VEV?

Let $\phi$ be a scalar field in an interacting theory ($\phi^3$ or $\phi^4$, for example). If $|0\rangle$ is the vacuum of the interacting theory and $P^\mu$ is the four-momentum operator, we have ...
5
votes
2answers
247 views

Secondary constraints leads to the value of lagrange multiplier

From Lagrangian I got two primary constraint $\phi_i$ and $\phi$. And my Hamiltonian in presence of the constraints becomes- $$H_p=p\dot q-L+\lambda_i\phi_i+\lambda\phi$$ here the $\lambda_i$ and ...
1
vote
1answer
48 views

Scalar Yukawa theory derivation

I am using Tong's notes for QFT, and on page 59 there is a derivation for the scattering amplitude of $\psi\psi \rightarrow \psi\psi$ in Scalar Yukawa theory. It goes from here: $$\langle ...
-8
votes
1answer
140 views

How to mathematically describe a spin-0 particle [closed]

I don't know all the technical things like Eigenstates. I want to know, mathematically written out for beginners, how to make a quantum field theory of a scalar boson. To spare confusion- I understand ...
1
vote
0answers
79 views

Why switching from Heisenberg picture to Interaction does not change the (Lorentz) transformation law of fields?

In his book, The theory of quantum fields, Weinberg builds the most general interacting picture (i.e. free) field by listing all possible Poincarè representation. These fields change so that, if we ...
5
votes
1answer
294 views

Determinant for a coupled fluctuation Lagrangian

Lets consider a bosonic physical system in variables $t, x$ and $y(x)$ ($x$ dependent) with a classical Lagrangian $L$. To first order in fluctuations $x \to x+\xi_1$ and $y \to y+\xi_2$ the ...
1
vote
1answer
73 views

using tetrads to glue local currents into global currents

According to John Baez it is possible to take a locally conserved tensor $\nabla_\mu\: T^{\mu\nu}(x)=0\ \ \ \ \ \mbox{(locally)}$ and convert it to a globally conserved tensor by "patching" ...
2
votes
1answer
64 views

How can one prove that there cannot exist a conformal primary, in the case of free field theory, that doesn't saturate the unitarity bound?

In free field theory, the full list of conformal primaries, is given by the Twist-2 operators. These have $\Delta = l+2$, which is also the saturation condition for the unitarity bound for $l \neq 0$. ...
3
votes
1answer
119 views

Quantizing highly nonlinear field-theories?

I'm wondering how to go about quantizing a classical field theory which looks nothing like a free field theory plus a perturbation term. Suppose for concreteness I have the classical hamiltonian $ ...
8
votes
3answers
236 views

Problem understanding the symmetry factor in a feynman diagram

I am trying to understand a $1/2$ in the symmetry factor of the "cactus" diagram that appears in the bottom of page 92 In Peskin's book. This is the diagram in question (notice that we are in $\phi^4$ ...
0
votes
0answers
21 views

Problem in the derivation of the Ward identities

This is a follow up to my previous Phys.SE question. The last equation in that question is $$-a\frac{1}{k^2+i\eta}k^{\lambda}i\Pi_{\lambda\rho}(k)iD^{\rho\nu}(k)=0$$ which we can further simplify as ...
2
votes
2answers
91 views

Is this symmetry factor in Peskin wrong?

I am trying to compute the symmetry factor of a Feynman diagram in $\phi^4$ but i do not get the result Peskin Claims. This is the diagram I am considering ...
4
votes
1answer
196 views

Is the exact form of the Higgs potential known?

Usually the Higgs potential is given as $$ \frac{1}{2}\mu^2\phi^2 - \frac{1}{4}\lambda^2\phi^4 $$ but I never quite understood if this just serves to give us an idea of how symmetry breaking works, or ...
5
votes
2answers
477 views

Teach me Wick's theorem the honest way

Generally speaking the average guy marginally acquainted with quantum field theory or advanced combinatorics describes Wick's theorem as some sort of correspondence between higher order differential ...
8
votes
2answers
263 views

The poles of Feynman propagator in position space

This question maybe related to Feynman Propagator in Position Space through Schwinger Parameter. The Feynman propagator is defined as: $$ G_F(x,y) = \lim_{\epsilon \to 0} \frac{1}{(2 \pi)^4} \int d^4p ...
0
votes
1answer
57 views

Topological entanglement entropy in transverse quantum Ising model?

I have seen from literature that the $Z_2$ lattice gauge theory in 2d could be mapped into a quantum Ising model with gauge constraints on the Hilbert space by dual transformation. The deconfined ...
2
votes
1answer
90 views

Proper way to quantize the string in the light-cone gauge

In many books like Polchinski and Green-Schwarz-Witten the light cone quantization is carried out in a fast way. They just use the virasoro constraint in the light-cone gauge to get the ligh-cone ...
2
votes
3answers
97 views

Why are complex fields in the Lagrangian?

I know that a complex field has twice the number of degrees of freedom of a real field, and that fields (in QFT) aren't observables so we don't really care if they are real. But why the need for ...
-1
votes
0answers
58 views

Why can't I use Bloch's Theorem in Lattice QFT?

Let's take a really simple example: given a typical hamiltonian for a quantum field on a 1D lattice $X=\{0,\cdots,Na\}\subset \mathbb{S}^1$: $$H=\sum_{x\in X} ...
0
votes
1answer
94 views

Scale invariance in QFT?

I was reading the following paper http://arxiv.org/abs/hep-ph/0703260 for Georgi and I have a conceptual question about it. Howard Georgi was talking about this Unparticle Physics theory and at the ...