Questions tagged [quantum-field-theory]

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 this tag for many-body quantum-mechanical problems and the theory of [tag:particle-physics]. Don’t combine with [tag:quantum-mechanics].

Filter by
Sorted by
Tagged with
2
votes
2answers
338 views

Are there any “Problems and Solutions” books or notes for advanced Quantum Field theory or/and String theory or/and Supersymmetry?

I was wondering whether or not there are any good resources of the type "Problems and Solutions" on String theory, on Supersymmetry and on advanced Quantum Field theory (separately). [I am aware ...
0
votes
0answers
15 views

Where to find a Path Integral treatment of 1D Quantum Heisenberg model or Quantum Spin Chain?

All: Where to find a Path Integral treatment of 1D Quantum Heisenberg model or Quantum Spin Chain? I would like to find a detailed calculation of path amplitude in such situation. I did some google ...
0
votes
0answers
8 views

Analytic Elements Haag Araki theory

Why the elements of a local von Neumann algebra cannot be analytic elements of the timelike translation?
1
vote
0answers
31 views

Why is Goldstone boson not observable in the non-Hermitian QFT?

I have recently stumble upon a paper on the spontaneous symmetry breaking of Non-Hermitian QFT arXiv:1808.00437. On page 8 (at the end of section 3) the author claims that one can not "observe" the ...
0
votes
1answer
24 views

Self-interaction of gauge bosons in electroweak theory

As one learns in QFT, in Yang-Mills theories non-Abelian gauge transformations give rise to self-interactions of the gauge fields in the quadratic field strength term. In QCD this produces the 3- and ...
1
vote
0answers
11 views

Simple question on Giamarchi's book

I have trouble from Eq.(2.62) to Eq.(2.63) in Giamarchi's "Quantum Physics in One Dimension". The book says as follows, but I think that some terms are missing. By straight computation of $\rho(r)\...
0
votes
0answers
24 views

(Giamarchi) Physical meaning of $\Psi^\dagger(r)\Psi^\dagger(r+a)$

I am currently reading Giamarchi's "Quantum Physics in One Dimension". The below is the part of the book: Question: 1. Eq. (2.72) of the book defines $$O_{SU}(r)=\Psi^\dagger(r)\Psi^\dagger(r+a)$$ ...
-1
votes
0answers
31 views

Can a field $\phi$ obey both the scalar relation and the fermi relation?

Let $L_{\text{scalar}}=\frac{1}{2}\eta^{\mu\nu}\partial_\mu \phi \partial_\nu \phi$ be the scalar lagrangian and $L_{\text{fermion}}=i\psi \gamma^u \partial_\mu \psi$ be the fermionic lagrangian. Can ...
2
votes
0answers
24 views

Supercurrent conservation for super-Yang-Mills in D=3,4,6,10 dimensions

I am following the book by Freedman and Van-Proeyen and this question is related to exercise 6.3. The supercurrent of a super Yang-Mills theory is given by $\mathcal{J}^{\mu} = \gamma^{\nu \rho} F^...
6
votes
2answers
101 views

Why do all fields in a QFT transform like *irreducible* representations of some group?

Emphasis is on the irreducible. I get what's special about them. But is there some principle that I'm missing, that says it can only be irreducible representations? Or is it just 'more beautiful' and ...
1
vote
1answer
483 views

Calculation of effective action

For a massless Dirac particle by integrating fermion degree of freedom in path integral, effective action is resulted for gauge field $$l(\psi,\bar\psi,A)=\bar\psi( \gamma^\mu (i \partial_\mu +A_\mu )...
3
votes
2answers
202 views

Quantizing Klein Gordon Field: Sign Problem

I'm trying to re-derive the Quantization of the Klein Gordon Field but I'm running into sign problems. My starting point is: $$ \phi(x,t) = \frac{1}{(\sqrt{2 \pi})^3} \int \tilde{\phi}(k,t) e^{i kx}...
1
vote
2answers
142 views

Initial values of creation/annihilation operators

I have a question about creation/annihilation operators. For example, if I have an evolution equation for annihilation operator of photon $$ \frac{da_k}{dt} = -i \omega_k a_k$$ I obviously obtain $$...
4
votes
2answers
393 views

What spinor field corresponds to a forwards moving positron?

When we search for spinor solutions to the Dirac equation, we consider the 'positive' and 'negative' frequency ansatzes $$ u(p)\, e^{-ip\cdot x} \quad \text{and} \quad v(p)\, e^{ip\cdot x} \,,$$ ...
0
votes
1answer
46 views

How can velocity and momentum be in opposite direction for antiparticles as given in the solutions of Klein Gordon Equation?

This is given in Greiner, Relativistic Quantum Mechanics For a free particle solution and antiparticle solution with momentum $\vec{p}$ the current is given by $e\frac{c^2\vec{p}}{E_p}$. The current ...
1
vote
1answer
118 views

Why coupling constants with negative mass dimensions lead to non-renormalizable theories?

can somebody explain or point to the relating mathematics showing Why coupling constants with negative mass dimensions lead to non-renormalizable theories?
5
votes
1answer
65 views

SUSY Loop diagrams from a categorical viewpoint

In the paper "A Prehistory of $n$-Categorical Physics" J. Baez and A. Lauda give an account of the use of category theory throughout physics. In section “Penrose (1971)” starting from page 25 they ...
0
votes
1answer
118 views

Simple explanation of a particular diagrams of Feynman [closed]

In relation to this question posed on the website TeX.SE. I am curious to know the use in Physics of green functions about the signs of feynman diagrams with fermionic fields. I have not understood ...
4
votes
0answers
74 views

The spinor metric, basic spinor calculations and spinor indices

I'm currently reading the textbook "Finite Quantum Electrodynamics" by Günter Scharf, but I find myself stuck already on page 24. Background Scharf introduces the index-raising symbol (spinor metric)...
4
votes
0answers
150 views

What's the space of eigenvalues/field configurations for a fermion?

In the Schrödinger picture of quantum field theory, the field eigenstates of a real scalar field $\hat\phi(\mathbf x)$ with $\mathbf x \in\mathbb R^3$ are the states $\hat\phi(\mathbf x)|\Phi\rangle=\...
3
votes
0answers
61 views

What's the momentum-space vacuum wave-functional of a fermion?

In the Schrödinger picture, the field eigenstates of a real scalar field $\hat\phi(\mathbf x)$ with $\mathbf x \in\mathbb R^3$ are the states $\hat\phi(\mathbf x)|\Phi\rangle=\Phi(\mathbf x)|\Phi\...
0
votes
0answers
35 views

Constraints in path integral and the Lagrange multiplier

I was reading some references on the slave-particle approach to the Kondo problem and Anderson model. It is known that the slave-particle is introduced in the large Hubbard $U$ limit of the system so ...
1
vote
2answers
56 views

How does the underlying symmetry of QCD imply the allowance of a 4-gluon vertex?

Quantum chromodynamics allows for a four-gluon vertex such as this, in a diagram Such a vertex would never be allowed in quantum electrodynamics, which has an underlying U(1) gauge symmetry. I know ...
3
votes
1answer
95 views

The central charge and normal ordering

This question is about how the normal ordering in the energy momentum tensor for a free field is consistent with a non-vanishing vacuum expectation value implied by the transformation rules for a CFT. ...
1
vote
1answer
37 views

Some counting of field degrees of freedom for a classical spin-1/2 Dirac field

A classical real scalar field admits a decomposition $$\phi(x)\sim a_pe^{-ip\cdot x}+a_p^*e^{+ip\cdot x}$$ which tells that at each $x$, there exists a real number i.e., one degree of freedom at each ...
1
vote
1answer
27 views

Holographic entanglement entropy (Thermal case)

I'm trying to calculate the entanglement entropy in CFT2/AdS3 in the thermal case for a finite interval (-a,a). I'm reading the paper of Takayanagi and Rangamani (2016): https://arxiv.org/pdf/1609....
2
votes
1answer
209 views

Why bound states in QFT have higher mass than single particle states?

In standard textbooks in QFT while discussing e.g. the Kallen-Lehmann formula (see e.g. Section 7.1 in the Peskin-Schroeder book) it is always assumed that bound states of two or more particles have ...
2
votes
1answer
241 views

Definition of one-particle irreducible diagrams

Text books often defines one-Particle Irreducible diagram (1PI diagram) as a connected diagram which does not fall into two pieces if you cut one internal line. Is this internal line the full ...
0
votes
1answer
54 views

Breaking down QFT into a single multiparticle equation of state

I'm trying to fit QFT into a familiar mathematical framework: Newtonian Mechanics (Single Particle): We have a set of particles $X$ whose locations at given moment in time is $\hat{X}(t)$ and whose ...
5
votes
1answer
101 views

Does energy conservation apply to Casimir effect?

If you cancel out some quantum field modes using two 'Casimir' plates you decrease the average energy density in the region and gain potential energy in Casimir force approximately proportional to the ...
0
votes
0answers
35 views

How can energy be negative for antiparticles in the solutions of Klein Gordon equation?

Although similar questions have been asked before I'm still confused. This is from Greiner, Relativistic Quantum Mechanics $E^2=c^2\sqrt{\vec{p}^2+m_0^2c^2}$ Consequently, there exist two possible ...
3
votes
2answers
251 views

Inverse Square Law in $D$ dimensions (two cases)

I am reading A. Zee "Quantum Field Theory in a Nutshell" and I have solved the problem about inverse square law in $D$ dimensions. Unfortunately, I have been confused with some results. Let me desribe ...
1
vote
0answers
37 views

Intuitive explanation of superficial degree of divergence

Consider $\varphi^p$ theory in dimension $D$. For a Feyman diagram $\Gamma$ one can introduce the superficial degree of divergence $deg(\Gamma)$. It is defined as $DL-2I$ where $I$ is the number of ...
0
votes
0answers
16 views

Why does the phenomenon of localized energy producing particles and antiparticles lead to the creation of an infinite number of particles?

Penrose says the following (paraphrased) in "Road to Reality" on pg 611 of the first American edition A particle and anti particle may combine to produce energy, as given by general relativity. ...
0
votes
0answers
29 views

Quintessential models for dark energy

Following Sean Carroll here There are good reasons to consider dynamical dark energy as an alternative to an honest cosmological constant. First, a dynamical energy density can be evolving slowly ...
2
votes
2answers
162 views

OPE double-contractions between $T$ and $e^{ikX}$

I am reading David Tong's lecture notes chapter 4 http://www.damtp.cam.ac.uk/user/tong/string.html On the top of page 82 in the eq. before eq. (4.27), we are computing the OPE between $T$ and $e^{ikX}...
1
vote
2answers
567 views

Annihilation and Creation Operators in QFT

I have following question about creation and annihilation operators in QFT: The Klein-Gordon field is introduced as continuous interference of plane waves $\mathrm{e}^{i(\omega_kt-\vec{k}\cdot\vec{x})...
0
votes
0answers
52 views

Thermal average of fermionic operators in QFT

Consider the following expression of a thermal average involving fermionic operators \begin{equation} \sum_{\nu, \nu', \sigma, \sigma'}\langle c_{\nu,\sigma}^{\dagger}(t)c_{\nu',\sigma'}\rangle, \end{...
0
votes
1answer
81 views

A question in imaginary time Green's function

I am learning many-body quantum field theory with Bruus and Flensberg's Introduction to Many-body Quantum Theory in Condensed Matter Physics, there is a derivation that confuses me a lot. To add ...
2
votes
1answer
332 views

Decay of a scalar Particle-Symmetry factors

Consider the Lagrangian $$\mathcal{L} = \dfrac{1}{2} (\partial_{\mu}\phi_{1})^2 + \dfrac{1}{2}(\partial_{\mu}\chi)^2 - \dfrac{M_1^2}{2}\phi_{1}^2 -\dfrac{M^2_\chi}{2} \chi^2 - \dfrac{\mu_\chi}{2} \...
1
vote
1answer
186 views

Why do not renormalization group equations explicitly depend on cutoff?

Suppose $g$ is the parameter set and $\Lambda\equiv\Lambda_0e^{-t}$ the momentum cutoff, then usually one finds the renormalization group equations to take the form $$\frac{dg(t)}{dt}=\beta(g).$$ My ...
0
votes
1answer
163 views

Commutation of currents in QED

In an outline of a proof of the Ward identities in QED, the authors Green, Schwarz, and Witten in their book "Superstring theory", vol. I, Section 1.5.1, claim that in the QED the electromagnetic ...
6
votes
1answer
287 views

Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
7
votes
1answer
2k views

First quantization vs second quantization

What is the difference between first quantization and second quantization and where does the name second quantization come from?
1
vote
0answers
28 views

Incompatible equations of motion in non-Hermitian (PT-symmetric) model

There is an interesting paper on Goldstone theorem of non-Hermitian QFT. arXiv:1808.00437. On page page 8-9 equation (36)-(38), author says that having equations of motion that are NOT complex ...
1
vote
0answers
46 views

High Temperature Expansions and Cumulants

In this paper the authors perform a high-temperature expansion of the correlation functions for a Heisenberg model on a lattice. Starting from $$\left<\mathbf{S}_i\cdot\mathbf{S}_j\right>_\beta ...
0
votes
0answers
26 views

Vacuum restructuring for superconductivity

I have posted several questions about superconductivity recently and all of them are related to vertex function but these questions were incorrect. I have found the following statement in book ...
2
votes
1answer
76 views

Feynman Parameters vs Passarino-Veltman reduction

I have computed the following one-loop integral: $$\int \frac{d^dp}{(2\pi)^d} \frac{p^{\mu}p^{\nu}}{(p+k)^2p^2}.$$ Using both Feynman Parameters and the Passarino-Veltman reduction. However, while I ...
3
votes
1answer
106 views

Mass of the fields in quantum field theory

I understand that if I have an action $$S=\int \phi(\Box + m^2 )\phi$$ Then the field $\phi$ has mass $m$ since this is the pole of the propagator of $\phi$. Now If I have an action $$S=\int \phi_1 \...
1
vote
1answer
30 views

Can one have $\mathcal{PT}$-symmetry in a QFT theory proportional to an imaginary field?

There is a lot of fuss nowadays around $\mathcal{PT}$-symmetry in non-relativistic quantum mechanics. Recently I came across this paper where the authors generalize the non-relativictic Hamiltonian $$...