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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Can we express QFT in R^8 where the spacetime can be embedded in?

A smooth, 4-dimensional manifold can be embedded in $R^8$. Isn't it a natural selection of space for QFT when we try to extend QFT with gravity?
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1answer
39 views

Solving linear equations for the groundstate of a quadratic field theory

I have successfully solved a field theory quadratic in fermonic creation and annihilation operators via Bogolyubov transformation to a diagonal field theory. I now want to extract the groundstate of ...
0
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57 views

Definition of anomalous symmetry in Hamiltonian formalism

In the Lagrangian path-integral formulation of QFT, an anomalous symmetry is defined to be a symmetry of the action which is not a symmetry of the measure of the path integral, and therefore not a ...
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0answers
69 views

How to arrive at the Dirac Equation from Poincare Algebra?

For the case of Galilean group, the time translation is given by the generator $H$. Hence, $$\mid\psi(t)\rangle\to \mid\psi(t+s)\rangle =e^{-iHs}\mid\psi(t)\rangle$$ Which immediately is the ...
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0answers
48 views

Physical side of TQFT

How would one go about understanding the physical side of TQFTs? What are the best introductory resources? I know Atiyah axioms but I don't know any QFT.
2
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1answer
97 views

Calculating the boundary modes in Kitaev Chain

In section 2 of the paper, 'Unpaired Majorana Fermions in Quantum Wires', equation (14), the following transformation: \begin{equation} b^{'} = \sum_{j} (\alpha_+ ^{'} x_+ ^{j} + \alpha_- ^{'} x_- ^{...
6
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90 views

In QED/Yang Mills, why do fermions contribute 4 times as much as scalars to vacuum polarization?

Consider a Yang-Mills theory in $4D$ over a gauge group $G$ $$ \mathcal{L} = - \frac{1}{4} F^{a\mu\nu}F_{\mu\nu}^a + \bar \psi i D_\mu \gamma^\mu \psi + (D_\mu \phi)^\dagger D^\mu \phi $$ where $\...
2
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0answers
45 views

Noether charge in light-cone coordinates (1+1D)

I have read in this article http://arxiv.org/abs/1107.2917 that the noether charge (in 1+1 D) $$ Q= \int dx \; q_t$$ could be written in terms of lightcone coordinates $x^\pm = t\pm x$ as $$Q=\int dx^...
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3answers
57 views

Time dependence of canonical variables

As far as I understand it, at least in scalar QFT, the canonical variables are the field operator $\hat{\phi}(x)$ and its conjugate momentum $\hat{\pi}_{\phi}(x)=\frac{\partial\mathcal{L}}{\partial\...
10
votes
2answers
314 views

How to count the number of cubic tree-level Feynman diagrams at $n$ points?

I'm following this paper: arXiv:0805.3993 [hep-ph] where it's said that the total number of distinct tree-level diagrams at $n$-points with cubic vertices only is $(2n-5)!!$ I want to know where this ...
1
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1answer
48 views

Reason behind choosing the invariant states for an operator which commutes with an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
1
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1answer
54 views

Central charges in 2D CFT and Virasoro algebra

Suppose we quantize some classical CFT algebra given by generators which satisfy $$[l_n,l_m]=(n-m)l_{n+m},$$ $$[\overline{l}_n,\overline{l}_m]=(n-m)\overline{l}_{n+m},$$ $$[l_n,\overline{l}_m]=0.$$ ...
1
vote
1answer
90 views

Virtual particles in EM interaction and Weak interaction

I know that a real electron has a probability (which depends on the intensity of the EM force) of emitting a photon, changing his 4-momentum. The photon should be virtual. Now, my teacher says that ...
0
votes
1answer
57 views

Renormalization group invariant objects of a quantum field theory

Consider an arbitrary QFT with $g_b$ as the bare coupling constant. After dimensional regularization, is $g_b \mu^\epsilon$ a renormalization group invariant object of the theory? In other words, is ...
4
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2answers
93 views

Partition function and coherent state path integral

I have been working through the derivation of the partition function expressed as a path integral in terms of coherent states, following the many-body condensed-matter field theory books of Altland &...
3
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1answer
77 views

Feynman propagator for photons and the actual propagation of photons

Reading some books of quantum field theory (c.f. LH Ryder. 'Quantum Field Theory') it seems that the concept of path integrals in quantum mechanics may be extended to the field theory using the ...
8
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0answers
115 views

$\phi^4$ theory kinks as fermions?

In 1+1 dimensions there is duality between models of fermions and bosons called bosonization (or fermionization). For instance the sine-Gordon theory $$\mathcal{L}= \frac{1}{2}\partial_\mu \phi \...
3
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0answers
71 views

Dimensional Reduction for scalar fields

The main motivation for this question is the paper "Supersymmetric Yang-Mills Theories" by Brink, Schwarz and Scherk where they use dimensional reduction to go from Yang-Mills in $D=4$ to $D=2$. But ...
2
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1answer
51 views

Is there scale invariance in the region of QCD aymptotic freedom?

It is said that in the deep inelastic scattering, scale invariance emerges. In the scattering of electrons off protons, this reflects the asymptotic freedom. Now I got a question. Normally, a system ...
1
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1answer
64 views

Kitaev Chain Spectrum (Unpaired Majorana Fermions in quantum wires) [closed]

How does one arrive at the spectrum equation(13): $$\epsilon (q)=\pm \sqrt{(2w \cos q +\mu)^2+4\cdot \mid {\Delta} \mid^2 \sin ^{2} q}$$ from the initial Hamiltonian. Also, shouldn't (12) in the ...
1
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0answers
59 views

Are virtual particles experimentally verifiable? [duplicate]

If not, why do we include such a description for force interactions? It seems to me that physics implements virtual particles as a means to do calculations. If this is the case, what is the ...
2
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0answers
46 views

Stratonovich integral in quantum field theory

I'm reading a paper on Wick renormalization and there are a couple of things that are not that clear to me. The paper ends with the following sentence: In Euclidean quantum field theory, the ...
2
votes
1answer
74 views

Why does $\prod^n_{j=1}\sigma^{(j)}_x$ commute with this adiabatic Hamiltonian? [closed]

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. The adiabatic Hamiltonian is defined as $$...
3
votes
1answer
47 views

How is information encoded in the Cosmological Horizon?

It is my understanding, according to the "Holographic Universe Theory", that multi-dimensional volume somehow emerges from a two-dimensional surface called the "Cosmological Horizon". And all three-...
5
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1answer
121 views

conformal symmetry vs time ordering

In Quantum field theories we generally calculate time ordered correlation functions. But it seems that in a conformal field theory I can use conformal symmetry to destroy time ordering. Let me look ...
2
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0answers
50 views

Do the Cutkosky rules imply (perturbative) unitarity?

In most standard textbooks on relativistic QFT, the Cutksoky rules are presented as a consequence of unitarity of the S-Matrix. However, at least for scalar field theories, it appears that the ...
0
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1answer
80 views

Number of degrees of freedom in the Standard Model Lagrangian

Consider a Lagrangian $L$ which depends on a number of fields $F_1$, $\cdots$, $F_N$ and their (spacetime) derivatives. Each of those fields $F_n$ is valued in $\mathbb{R}^{k_n}$. Is the Standard ...
3
votes
1answer
76 views

Fluctuation-dissipation theorem in QFT

If I understand correctly, the fluctuation-dissipation theorem (fdt) in QFT technically arises because of $\pm i\epsilon$ - infinitesimally small summand in the denominator of spectral representation ...
2
votes
1answer
86 views

What is the correlation between QFT and thermodynamics?

This may be a naive question. In physics many processes are symmetric, except a few involving entropy, or the arrow of time. Another one has to do with heat generation. We can generate heat, or energy ...
0
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1answer
64 views

Definition of the S-matrix

when I think about scattering process I reach to slightly another definition to the S-matrix. because I understand my reasoning I hope someone could refine it to a correct one so that I can have a ...
3
votes
1answer
57 views

$W^{++}$ / $W^{--}$ Bosons in theory and experiment

I wonder whether there is any theoretical interest in and/or experimental search for double charged bosons, probably to be called $W^{++}$ and $W^{--}$. The latter would obviously turn an electron ...
2
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0answers
43 views

Integrating out heavy fields while preserving symmetries

The basic a-b-c for integrating out heavy fields what one learns when making the example of Fermi theory, is that if you have a Lagrangian $L= -\frac{1}{4}F^{\mu\nu}F_{\mu\nu}+\frac{1}{2}M^2 V^\mu V_\...
0
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1answer
51 views

Scattering in Schrödinger picture [closed]

If we look at a scattering process in the Schrödinger picture for a Hamiltonian $H = H_0(t) + V(t)$ where $H$ is independent of time (because we examine a theoretical situation after accelerating ...
0
votes
1answer
50 views

Are pure Dirac fermions (electrons, quarks, …) allowed to have effective Majorana mass?

Charged particles such as electrons and quarks are not allowed to have a hard Majorana mass (see here). With 'hard' I mean an explicit mass term in the Lagrangian which would break the corresponding ...
2
votes
1answer
93 views

Why is Wick contraction a $c$-number?

It is mentioned in Fetter's Quantum Theory of Many-Particle Systems (in contraction part of section 8 Wick's Theorem), that: contractions are c numbers in the occupation-number Hilbert space, not ...
1
vote
1answer
42 views

Why do quasi-free states satisfy the positivity condition?

In LQFT, a state, $\omega$, is a linear map $\omega:A=:CCR({\cal{S}},\Omega)\rightarrow \mathbb{C}$ satisfying: $\omega(aa^{*})\geq 0$ for all $a\in A$. $\omega(I)=1$ where $I$ denotes the identity ...
5
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0answers
69 views

The relation between anomalous dimensions and renormalization constants

I am trying to understand the general strategy and technical details of calculating $\beta$-function at higher orders. $\beta$-function is the anomalous dimension of the coupling constant and there is ...
0
votes
0answers
27 views

Polarized Moller scattering cross section

When doing a computation of scattering cross sections of particles with spin, one usually averages over the initial spins and sums over the final ones. I'm a bit puzzled as to how to do the ...
4
votes
2answers
136 views

Why do we learn only two computations, cross sections and decay rates, in such a fundamental theory as QFT?

When I learned Newtonian mechanics I found a vast variety of computations that I could do and that was so interesting. And it was so when I learned Maxwell theory. When I started learning QFT I hoped ...
1
vote
1answer
34 views

Is the time ordering in Dyson series either 1 or -1?

Because I think to make it a unitary operator, the norm of the unitary operator should be one. But I did not see any claim about the value of time ordering in Dyson series.
-2
votes
1answer
43 views

Why we have to sum in all final states of hadrons?

Correct if I am wrong. In deep inelastic scattering have to sum in all final sates hadrons because we do not want to detect the hadrons. All we want to detect is the electron. Am I right?
0
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0answers
27 views

Heisenberg uncertainity principle is valid in the case of QFT? [duplicate]

The Heisenberg uncertainty principle is valid (or taken into account) in the case of QFT?
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0answers
24 views

Can charged scalar have non zero vev?

In Higgs-Kibble mechanism, if we consider a SU[2]_L doublet of complex scalar fields, then one of them is charged and the other neutral. Why does the neutral field acquire vev and not the charged one?
-2
votes
1answer
69 views

Is there one wavefunction per field? [closed]

Is the big picture of quantum field theory that: There are fields (EM, electron, Higgs, gravity, etc.) A field can be described by a wavefunction indicating the probability density of 1 or more '...
0
votes
0answers
22 views

What is the most essential theoritical constrains should be imposed on arbitrary potential's parameters?

I'm little confused about the unitarity and perturbativity constrains which imposed on a potential's parameters, like 2HD potential. Look for example: [arXiv:1507.03618v3 [hep-ph]] First, I'd like to ...
7
votes
2answers
64 views

bare Phonon and Symmetry Breaking

In condensed matter physics, the phonon is considered as a quasiparticle which is a result of the quantization of lattice vibrations. In many textbooks on solid state physics, it can be done if we ...
3
votes
0answers
55 views

Higgs mechanism in quantum GLSM

My question is regarding the following Gauged Linear Sigma Model (GLSM) in two dimensions. $$\tag{1} S=\int d^2x\Big(-D_{\mu}\overline{\phi} D^{\mu}\phi +\frac{D^2}{2e'^2} +D(|\phi|^2-r)\Big).$$ ...
2
votes
0answers
55 views

Sudakov double logarithm

I have calculated a few NLO corrections in QED and in the final result the Sudakov double logarithms have always canceled. So I thought that they have no physical meaning. On the other hand I have ...
4
votes
1answer
71 views

Non-abelian current commutators

There many articles, in which non-abelian current commutators are computed. The general result is that quantum corrections lead to additional term in commutator $$[J^a_\mu (x), J^b_\nu (y)] \delta (x^...
4
votes
1answer
96 views

Photons are self-conjugate but neutrinos may or may not: why is that?

Caution: This may be a very naive question but I find it confusing. Moreover, I believe this question is based on potential misconception. I would like it to be clarified. Although the neutrinos are ...