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 ...

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How do charged particles interact?

You'll have to forgive me if this question is too wrapped up in "classical" thinking. I've read that electrons and protons interact by trading photons, but this only raises more questions. What ...
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128 views

Transition amplitudes by functional methods in QFT

I am following section 9.2 in Peskin and Schroeder in which the Feynman rules are derived for scalar fields. They define (in eqn (9.14), page 282) the transition amplitude from $\vert\phi_a\rangle$ ...
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221 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 ...
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93 views

Symmetry factor and coupling constant in scalar field theory

I am just now starting my particles "education" so forgive me if this is elementary... Looking at interaction terms in a scalar field Lagrangian, I get: $$ ...
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49 views

Textbooks on algorithms for the perturbative calculation of High energy physics

For the perturbative calculation of High energy physics, I have known some packages such as FeynArts, FeynCalc, MadGraph, CompHEP, GiNaC, and so on. But I am wondering whether there exists a textbook ...
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95 views

Chiral anomalies

Recently I have read that there is contraction of chiral anomalies in SM. But people are working on chiral anomalies theory. So I have the question: what is the importance of development of the theory ...
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106 views

Is the ground state of a QFT always a pure state? And excited states are mixed?

I am studying entanglement entropy. It's fullfilled for any local quantum system that the entanglement entropy of a region $A$ in a highly mixed state is extensvie, $$ S_A \sim ...
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1answer
97 views

what physical quantity do real scalar field operators create/destroy?

Let $\phi(\textbf{x}) \neq \phi^\dagger(\textbf{x})$ be a complex scalar field, and let $\varphi(\textbf{x}) = \varphi^\dagger(\textbf{x})$ be a real scalar field. $\phi(\textbf{x})$ destroys a ...
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122 views

Massless integrals in dim-reg

Consider the massless divergent integral $$ \int dk^4 \frac{1}{k^2}, $$ which occurs in QFT. We can't regularize this integral with dim-reg; the continuation from the massive to the massless case is ...
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113 views

Unitarity and renormalizability

What is the difference between the unitarity of the theory and its renormalizability? Can we say that renormalizable theory is unitary after renormalization? The questions have arisen after I have ...
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1answer
70 views

Scattering theory textbooks

I am looking for a possibly extensive list of great textbooks on elastic and inelastic scattering of particles within quantum field theory. So far I am familiar with: Peskin and Schroeder: An ...
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881 views

Is the Standard Model consistent (UV complete)?

This is a question about the self-consistency of the Standard Model - which I believe is the same as asking whether it is UV complete - in other words, can it be used to predict experimental results ...
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166 views

Derivation of the full generator of the lorentz transformations

Let us study the subgroup of the Poincare group that leaves the point $x=0$ invariant, that is the Lorentz group. The action of an infinitesimal Lorentz transformation on a field $\Phi(0)$ is $L_{\mu ...
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104 views

Can quantum vacuum carry entropy?

So, we know that the state of quantum vacuum does carry energy, as it was measured in the Casimir effect. This energy comes from particles almost instantaneous creation and annihilation. Even if they ...
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1answer
250 views

Anomalously broken conformal symmetry

I'm trying to understand an argument made by Bardeen in On Naturalness in the Standard Model. The argument is about quadratic divergences in Standard Model. My notation is that the SM Higgs potential ...
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2answers
297 views

Determine if Theory is Unitary from Lagrangian

Question: Given a quantum theory specified with a Lagrangian and the degrees of freedom to be varied, what is the procedure to determine if the theory is unitary or not? Concrete example to aid ...
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1answer
100 views

When is quantum optics “correct”?

What is the regime under which we may consider quantum optics description of light a good approximation of a more correct theory such as QED? By quantum optics I mean describing the electromagnetic ...
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541 views

Intuition for Path Integrals and How to Evaluate Them

I'm just starting to come across path integrals in quantum field theory, and want to get the right intuition for the them from the start. The amplitude for propagation from $x_a$ to $x_b$ is typically ...
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0answers
94 views

Anomalies in QFT books

Why in most QFT books when author discusses of non-invariance of measure of path integral (massless fermions interact with gauge fields) $$ \int D\bar{\Psi} D\Psi \to |\Psi \to U\Psi , \quad ...
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1answer
52 views

Typical form of the beta function of the renormalization group

Why in "typical" cases (according to some non-English text I read), does the $\beta$-function have the form $$ \beta (g) = ag^{2} + bg^{3} + O(g^{4})\ ? $$ I.e., why are there no linear or logarithmic ...
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1answer
230 views

Time-ordered operator in Srednicki

On page 51 Srednicki states, "Note that the operators are in time order...we can insert $T$ without changing anything". This I agree with. But then on the next paragraph he states "The time order ...
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120 views

Level quantization of 7d $SO(N)$ Chern-Simons action

In 3d, one can write down the $SO(N)$ Chern-Simons action to be $$S(A)=\frac{k}{192\pi}\int_{M}\text{Tr}(A d A +\frac{2}{3}A^3),$$ where $A$ is an $SO(N)$ connection. The level quantization can be ...
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30 views

Invisible stars due to finite photons [duplicate]

When we study black body radiation, we often make calculations assuming a continuum of radiation with some amount of flux. In reality, there is a very very large number of photons being emit per unit ...
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4answers
151 views

Nature of Fields in QFT

I'm not exactly an expert in quantum physics, but this seems to be a simple question, and I can't find an answer anywhere! There are specific types of fields used in physics: scalar fields (i.e. as ...
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How to derive the scale factor for special conformal transformation? [closed]

By definition a conformal transformation of the coordinates is an invertible mapping $x\rightarrow x'$ which leaves the metric invariant upto a scale factor: \begin{equation} g_{\mu\nu}'(x') = ...
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1answer
108 views

Graph Theory and Feynman Integrals

In Vladimir A. Smirnov's book Analytic Tools for Feynman Integrals, Section 2.3, the alpha representation of general Feynman integral takes the form $$ F_{\Gamma}(q_1,\ldots,q_n;d) = ...
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Mathematical Prerequisites for QFT [closed]

I am curious about which areas of mathematics one should be comfortable with before learning QFT. I am familiar with the "learn-it-as-you-go" approach often advocated in physics, but would like to ...
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1answer
107 views

In QFT, why do fermions have to anticommute in order to insure causality?

I have seen this question and I believe I understand the answer to it. However, AFAIK, only for bosons the causality condition is a vanishing commutator. For fermions we expect the anticommutator ...
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An electron is an excitation of the electron field. So when we observe a higgs boson that means we've excited the higgs field?

See this related question: If particles are excitations what are their fields? I ask this question because, according to a lecture, the higgs boson was frozen into a "matrix" at some point before ...
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1answer
58 views

Ambiguous points in spontaneous symmetry breaking of discrete symmetry

For a discrete symmetry: At the minimum value of the potential, $V$, in the Lagrangian density, why do we take $\phi= \langle v\rangle + \eta$? Aren't we deliberately breaking the symmetry? If we ...
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1answer
90 views

How does string theory describe classical gravity theory, and QFT? [closed]

I am learning string theory, as I understand, gravitons exist as modes in string excitations, and also other particles. It gave me this picture: a lot of strings fulling in the spacetime, excitations ...
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2answers
83 views

Is it possible to create matter from space?

Like could maybe fluctuate the space some how and make the virtual paricles turn into normal matter
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1answer
71 views

change of variable in a 2-loop integral

given the 2 loop integral $$ \int dq_{1} \int dq_{2}F(q1,q2) $$ (1) then in dimension D=4 our integral will be a 8-dimensional integral so why can not make a change of variable to 8-dimensional ...
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57 views

What's the value of the coupling constant in interacting field theories?

Consider this Lagrangian : $L = \frac{1}{2}(\partial_\mu \Phi)^2 - \frac{M^2}{2}\Phi^2 +\frac{1}{2}(\partial_\mu \phi)^2 -\frac{m^2}{2} \phi^2 -\mu\Phi\phi^2$ Its interaction term is given by : ...
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What equation describes the wavefunction of a single photon?

The Schrödinger equation describes the quantum mechanics of a single massive non-relativistic particle. The Dirac equation governs a single massive relativistic spin-½ particle. The photon is a ...
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1answer
82 views

Moduli spaces in string theory vs. soliton theory

In both string theory and soliton theory, moduli spaces are frequently used. As far as I known, for soliton theory, moduli spaces are something like collective coordinates for solitons, and for ...
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2answers
102 views

Lorentz symmetry and Noether's theorem

I'm trying to overcome some misunderstanding that I have in Noether's theorem. There is formula in David Gross's Lectures on QFT for Noether's theorem: ...
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1answer
36 views

Difference between Veneziano amplitude and Virasoro shapiro amplitude

I have been study about Veneziano amplitude and Virasoro Shapiro amplitude. I want to summarize this two amplitude in the following way, please check that i am understand them properly. Veneziano ...
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2answers
98 views

Does one really need classical physics in order to understand quantum physics? [closed]

I want to start studying quantum mechanics, and then move to quantum field theory. I have a strong mathematical background, and I think this aspect of quantum physics won't be a problem to me. Though, ...
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2answers
116 views

LHC data and mathematics of QFT

I'm reading Frederic's Paugam Towards the Mathematics of Quantum Field Theory, an advanced theoretical physics book. I would like to know how I could apply the theories in this book. For example, ...
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2answers
71 views

Converting two component product to four component notation

Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry, \begin{equation} \chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta ...
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64 views

Understanding the effective low-energy Lagrangian for hadrons

My course in Higgs Physics is discussing a two-nucleon low-energy effective theory of hadron interaction. With $\psi=(p,n)$, the pion is defined as $\vec{\pi}= i \bar{\psi}\vec{\tau} \gamma_5 ...
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1answer
184 views

Fundamental representation in quantum field theory

In QFT we associate to each Gauge theory a continuous group of local transformations (a Gauge group), and then we require\define fermion fields to be irreducible representations belonging to the ...
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1answer
92 views

Why doesn't the photon have mass? The Higgs mechanism and pre-electroweak epoch

1) When electroweak separation occurred, 'why' wasn't the photon 'given' mass like the W and Z bosons? i.e why don't photos interact with the higg's field? 2a) How well is the higg's mechanism ...
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1answer
61 views

Scalar Particles, Flavor Changing Processes and Gauge Symmetries

Let's consider an extended version of the Standard Model (SM) with a new Yukawa operator of the form $$ \sum_\ell g_\ell\bar{\ell}\ell \phi ,$$ where $\ell$ is any lepton of the SM and $\phi$ is a new ...
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2answers
76 views

What is the reason for the $ i \tau_2 $ - factor in the higgs coupling with up-type quarks?

The quark mass term in the Standard Model Lagrangian looks like this: $$ L = - \lambda_d \bar{Q}\phi d_R - \lambda_u \bar{Q} i \tau_2 \phi^* u_R $$ What is the reason for the $ i \tau_2 $ - ...
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1answer
120 views

Free Field theory to Interacting Field theory

Free field theory: Why is it said that different Fourier modes in case of a free field (say, real Klein-Gordon field) are independent of each other? Interacting field theory: How exactly does the ...
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1answer
236 views

Gauge fermions versus gauge bosons

Why are all the interactions particle of a gauge theory bosons. Are fermionic gauge particle fields somehow forbidden by the theory ?
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51 views

Why does the state space contain states with negative norm and what would be an example?

My lecture script of Quantum Field Theory states that " the state space contains states with negative norm ". Why does it have to be like this and what would be an example fo such a state?
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For a particle to have physical mass, is it always necessary to have a mass term in the lagrangian?

Since the self-energy adds to the bare mass defined in the Lagrangian, is it possible to create a physical particle mass from the self-energy alone, with no mass terms occuring in the Lagrangian? On ...