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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Why do we consider Lagrangian densities in QFT?

My question is: Why do we consider Lagrangian densities in QFT (as opposed to Lagrangians as in classical mechanics)? Is it simply because of the following? We wish the theories to be Lorentz ...
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36 views

Exact meaning of locality and its implications on the formulation of a QFT

As far as I understand it, locality in physics is the statement that interactions can only occur between physical objects if the spacetime interval separating them is null or time-like. Thus, if the ...
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44 views

How to calculate the functional derivative of the functional integral

I study by myself with the QFT,in the page 197 of book of Lewish. Ryder(2nd edition), The author wrote that he take the functional derivative of equation 6.69: $$\frac ...
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30 views

Calculating OPE of Graviton Vertex Operator

Consider Exercise 2.8 in Polchinski's String Theory book. We are asked to compute the weight of $$f_{\mu \nu}:\partial X^{\mu} \bar{\partial}X^{\nu}e^{ik\cdot X}:$$ I have carried out the usual ...
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127 views

Commutation relations in QFT and the principle of locality

My question is, given two space-time points $x^{\mu}$ and $y^{\mu}$, if the events that occur at these points are simultaneous, i.e. $x^{0}=y^{0}$, are the two events necessarily space-like separated? ...
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37 views

Locality, unitarity & vacuum energy

I've read in a set of lecture notes that the requirement of locality and unitarity in QFT imply that the vacuum must have a non-zero energy associated with it (http://arxiv.org/pdf/1502.05296v1.pdf , ...
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28 views

Equivalent forms of four fermion operators?

In this paper a little below equation (15) it is said that the four fermion operator $(q^{\dagger}\bar{\sigma}_{\mu}q)(u^{\dagger}\bar{\sigma}^{\mu}u)$ where $q$ and $u$ are left chiral Weyl ...
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927 views

Do neutrinos refract?

The most benign of interactions is refraction. While neutrinos rarely interact with matter in a sense like the photoelectric effect, does that mean that they don't refract either?
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76 views

What does it mean by saying the generators of translations transform as vectors under the Lorentz Group?

The commutator of generators of Lorentz transformation and translation is as follow: $$[M^{\mu\nu},P^\sigma]=i(P^\mu\eta^{\nu\sigma}-P^\nu\eta^{\mu\sigma} )$$ Then from this we usually say that the ...
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142 views

Green's function for the Klein-Gordon equation diverging?

I'm trying to work out the propagator for the free scalar field theory (i.e., the Green's function for the Klein-Gordon equation). On pages 23 and 24 of Zee's Quantum Field Theory in a Nutshell (you ...
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65 views

Redefinitions of Lagrangians using EOM

I am trying to understand an statement of this paper. In section 2 this Lagrangian is introduced ...
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1answer
92 views

Two math methods apply the same loop integral lead different results! Why?

I tried to adopt the cut-off regulator to calculate a simple one-loop Feynman diagram in $\phi^4$-theory with two different math tricks. But in the end, I got two different results and was wondering ...
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51 views

How does the Higgs field relate to the Yang-Mills fields and gauge theories in general?

I asked this in astronomy How does the Higgs field relate to the Yang-Mills fields and gauge theories in general? but they suggested I ask it here. It is very confusing. Is there an easy ...
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30 views

Effect of orbifolding on gauge fields

A paper by Lalak et al, entitled "Soliton Solutions of M-theory on an orbifold", considers the brane solutions of 11 dimensional supergravity on a space of the form $R^{10} \times S^1/\mathbb{Z}_2$. ...
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43 views

How do the renormalization enter the actual amplitude calculation in QFT?

I have studied QFT from Peskin and Schroeder and from a few other books and lectures and I think I understand the procedure of renormalizing various parameters in the Lagrangian like mass, coupling ...
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22 views

Mass and wave function renormalization In chiral perturbation theory

Before I put forward my actual question, I think it will be useful to set the context in a clear way and that involves my understanding of a few very basic things of Chiral Perturbation Theory. ...
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43 views

Parity of $n$-photon system

The $C$-parity (charge conjugation) of an $n$-photon system is given by $(-1)^n$. If I'm not totally wrong, the intrinsic parity of a photon is $(-1)$. What is the parity $P$ of a system of $n$ ...
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73 views

Mathematician learning theoretical physics [duplicate]

EDIT: I was aware of the supposed duplicate. But I'm interested in a clear and focused path through the basics to advanced theoretical physics such as string theory - a path that avoids studying ...
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1answer
73 views

Is the Klein-Gordon Hamiltonian unbounded below?

This question is about the Klein-Gordon Hamiltonian for simplicity, but the problem seems to remain when dealing with other fields (e.g. Dirac, photon...). One usually writes the Hamiltonian ...
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42 views

Where do negative powers of $f_\pi$ in the hadronic amplitudes come from?

According to Peskin and Scrhroeder the pion decay constant $f_\pi$ is defined via the following matrix element $$\left\langle0|j^{\mu5a}(x)|\pi^b(q)\right\rangle=-if_\pi \delta^{ab} q^\mu e^{-iqx}$$ ...
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16 views

heavy quark pair spin states

Apparently, heavy quark pair can have "axial-vector" spin state, "vector" spin state, and two different "tensor" spin states. Can anyone explain to me what they are and why this is the case? Thank ...
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29 views

Quantising the magnetic monopoles the make Maxwell symmetric

I don't believe this has already been asked, but I might be wrong; sorry. One can add a magnetic charge density/magnetic monopoles to Maxwell's equations to make the theory symmetric between the ...
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27 views

Fourier transformation and mode expansions [duplicate]

Sorry as this is a rather trivial question, but I'm stuck with a certain implication. I'm working on exercise 1.7 from Polchinski where we are given an open string with boundary conditions ...
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1answer
50 views

How to find the remaining subgroup after some Higgs field gets a VEV?

Say we have a group $G$ and a set of Higgs fields in a representation $R$ of $G$. One of the Higgs fields in $R$ gets a VEV, how can I determine the remaining subgroup after this symmetry breaking? ...
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27 views

renormalization subtraction point, scaling

When we use minimal subtraction scheme, for instance, we have a dependence of coupling on a scale $\mu$. Using the $\beta$ function, we can observe the behavior of the coupling at different scale ...
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36 views

QED renormalization: mass and dirac field

Why the mass renormalization $Z_m$ and the field renormalization $Z_\psi$ in QED (MS-renormalized) does not contribute to the beta function computation? From Ward identity, I know that $Z_A=Z_e^{-1}$, ...
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79 views

Degenaracy in mass of $8$ and $27$ reps of $SU(3)$ in Coleman's Aspects of Symmetry

In Coleman's Aspect of symmetry he proposes an amusing problem in the first chapter. It asks us to consider a set of eight pseudo-scalar fields transforming in the adjoint representation of $SU(3)$. ...
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87 views

Fourier transformation and commutators

Sorry as this is a rather trivial question, but I'm stuck with a certain implication. I'm working on exercise 1.7 from Polchinski where we are given an open string with boundary conditions ...
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0answers
47 views

(Super)Gauge Fixing in Supersymmetry

I have three questions about gauge fixing in supersymmetry, one is general and the other two explicit: Why gauge fixing seems not important in supersymmetry? By "not important" I mean gauge fixing ...
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1answer
39 views

Expanding free scalar field in terms of ladder operators

I'm having some difficulty with the finer points of expanding a field in terms of ladder operators. Note that this is not identical to the other related question I asked. From Peskin / Schroeder; ...
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1answer
74 views

Textbook on QFT in curved space-time via path integrals

I am looking for an introductory textbook on QFT in curved space-time via the path integral method. I want to understand the following: How to build a generic perturbative QFT in curved space-time ...
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74 views

Particle annihilation - mathematical description, equations governing it? [duplicate]

I was wondering about this and I would like to know an explanation why do particles and antiparticles annihilate? I would be interested in phenomenological, but most importantly mathematic explanation ...
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2answers
75 views

What is the algebraic form of the momentum eigenstate?

I'm asking this in the context of trying to verify the equation $a^{\dagger}_{p} \vert 0 \rangle = \frac{1}{\sqrt{2\omega_p}} \vert p \rangle$. So far I have calculated $\vert 0 \rangle = ...
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43 views

Clarification on Use of Counterterms in Renormalized Perturbation Theory

In renormalized perturbation theory, it's unclear to me how exactly we add the necessary counter-terms. Do we: Draw all possible diagrams, including the diagrams of the counter-terms to some order ...
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1answer
80 views

Field expansion in Peskin & Schroeder

Peskin and Schroeder state something which I'm not fully understanding. More specificially I think it's just phrased in a way I'm not understanding. In the Schrodinger picture we can expand the real ...
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1answer
40 views

What do we take the functional determinant of in computing th effective action in the Background field method?

I have some schematic notes on computing the effective action and I would like someone to help me fill the gaps. We start with \begin{equation*} \int{}\mathcal{D}\phi\,e^{-iS[\phi]} \end{equation*} ...
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1answer
66 views

Non-relativistic limit of complex scalar field Lagrangian

I am trying to derive the non-relativistic Lagrangian for a complex scalar field from taking the non-relativistic limit of the complex scalar field Lagrangian. I am following the steps in "QFT for ...
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2answers
135 views

In QFT how do you write down the most general interactions?

This past year I took a QFT class and I now feel comfortable solving scattering problems, but I am still a bit perplexed by how physicists write down a Lagrangian in the first place. In particular, ...
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1answer
72 views

A trace formula of two noncommutative operators

In many cases of quantum many-body problems, the Hamiltonian $H$ can always be divided into two parts, i.e. $H_0$ and $H'$. In this occasion, one can systemically calculate the partition function ...
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24 views

Plane wave solutions of the Majorana equation

Let u(p) and v(p) be the plane wave solutions of the Dirac equation with positive respectively negative energy. In case of a solution of the Majorana equation the charge-conjugated solution is ...
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51 views

Choice of framing in Gravitational Chern-Simons

I was trying to understand formula(2.21) in Witten's paper "Quantum Field Theory and Jones Polynomial"(link: https://projecteuclid.org/euclid.cmp/1104178138) (Page 360). There, it was mentioned, the ...
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1answer
92 views

Doubts with basic renormalization

When we renormalize to obtain the physical mass, the $\Lambda$ dependence of the physical mass is removed by introducing the counterterms in the Lagrangian. So whether we put ...
2
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2answers
128 views

Gaussian integral on a Riemannian manifold

How do I estimate the Gaussian integral $\int d^nx \sqrt{g(x)}~e^{-x^2} $ on a Riemannian manifold $(M,g=det~g_{\mu\nu})$? I've tried to consider $\sqrt{g(x)}$ as an analytic function and expanded it. ...
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0answers
37 views

Dynamics and kinematics of quantum field theory

What is the difference between dynamics and kinematics of quantum field theory? I read that in QFT there is no possibility to keep the two things distinct because of a problem with the separability of ...
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1answer
32 views

Spin magnetic moment direction of a particle

Is the spin magnetic moment of a fundamental particle like an electron always aligned along the direction of the spin angular momentum (meaning that the magnetic moment and the spin operators have the ...
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2answers
108 views

Uncertainty principle in quantum field theory

Can the uncertainty principle be derived in quantum field theory? If yes, does is have a different interpretation than quantum mechanics because the coordinates $x_i$ are now parameters and not ...
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1answer
45 views

Why is cut-off regularization is not Lorentz invariant?

Why is it said that the cut-off regularization is not a Lorentz invariant regularization method?
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58 views

Violation of unitarity: meaning and consequences

What is meant by unitarity and violation of unitarity of a QFT? For example, Fermi theory of beta decay is said to violate unitarity. How does violation of unitarity make a theory sick?
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64 views

$\phi^4$ theory two-loop contributions

Wherever I see calculations of two-loop contributions to the $\phi^4$ propagator (such as Peskin, page 328, on the bottom), only the sunset diagram (aka the Saturn diagram) is considered, but not, ...
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A question about a consequence of symmetry in $\phi^4$ theory

Why does the symmetry $\phi→-\phi$ mean that an amplitude can be written as $\alpha+\beta p^2+\gamma p^4+...$ without the odd terms in $p$? I understand that, due to this symmetry, any diagram in ...