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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The $T\rightarrow \infty $ limit in quantum field theory

I am new to quantum field theory. Prior to this, I have been using quantum mechanics for a few years. I am reading the book by A. Zee, ''quantum field theory in a nutshell'', 2nd Ed.. On page 18, ...
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1answer
71 views

What gives a particle its identity?

A lot of very smart people have stitched together the standard model, and I accept it. I don't understand it, but I assume there should be a mechanism of sorts that gives a particle some fundamental ...
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2answers
597 views

Quantum entanglement definition [closed]

How can we define Quantum entanglement (in QFT)? What are the known mathematical settings and special physical (or logical) conditions of QE applied to Quantum computing?
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1answer
69 views

Operator formalism in QFT in Euclidean space-time

In QFT there are two very useful general approaches to study quantum fields (on the Minkowski space-time): path integrals and operator formalism. Sometimes they give the same results, sometimes one ...
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67 views

S-matrix and derivative interaction

I just read in some lecture notes that formally we can write the S Matrix as: $$S=T(e^{-\int_{-\infty}^{+\infty} H_{int}dt}) $$ Where $T$ is the normal product and $H_{int}$ is in the interaction ...
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20 views

Construct recurrence relation for the temporal evolution of a Master equation

Say that we have a system evolving over discrete timesteps. The quantity we are interested is X and is given by a distribution $P_X$. This distribution is evolving temporally, and we have a ...
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0answers
64 views

Path integral (sum over paths where $v>c$) [closed]

The path integral formalism is used to get for example the propagator of particles. In this formalism we integrate over all mathematically possible paths (and weight them with the non-relativistic ...
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25 views

Superficial degree of divergence for scalar theories

I have a few questions regarding the derivation of the degree of divergence for feynman diagrams. The result is $$D = [g_E] - \sum_{n=3}^{\infty} V_n [g_n]$$ (following notation in Srednicki, $P118$) ...
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34 views

What is quantum foam?

Can someone please explain me what quantum foam is? Is it the space-time fabric or just any other field? Also please explain this image
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15 views

Deep Inelastic Scattering - electromagnetic current

When one tries to compute the deep inelastic scattering for the process: where $l$ is a lepton with incoming momentum $k$ and outgoing $k'$, $h$ is an hadron with momentum $P$, $q$ denotes some ...
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1answer
85 views

Spontaneous symmetry breaking of a spinor / vector field [duplicate]

Why does SSB deal only with scalar fields and not with fermion or vector fields? My professor told me that it's closely related to the Lorentz invariance of the theory, but I don't understand at all ...
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1answer
98 views

What does it mean by “infinities” when dealing with QFT? [closed]

I found this PDF online here while browsing Nobel Prize winner contributions, which explains a bit about renormalization (a concept for which Kenneth G. Wilson won the Nobel). However I was somewhat ...
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1answer
47 views

Fine structure constant and unit conversion [closed]

In a paper I'm reading, the author writes down the following formula: $$\Gamma=\dfrac{\alpha^2}{576\pi^3}\dfrac{\left(4+z\right)^2}{z}\dfrac{m^5}{m^2_\pi f_\pi^2}$$ $\Gamma$ is a function of $m$ (in ...
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28 views

Transverse and longitudinal random forces

I am trying to read following article: http://arxiv.org/pdf/1410.1262v1.pdf According to the equation (2.10) and (2.11), the random force is defined as $ \langle f_i(x) \ f_j(x) \rangle = ...
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0answers
44 views

Entanglement in Quantum field theory [duplicate]

How is entanglement represented in a field theory? For instance how can I represent a maximally entangled state such as a Bell state? Would such an approach also apply in a Conformal field theory ...
1
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1answer
70 views

Time-ordered product of two normal-ordered products of fields

Suppose you have a scalar field theory with field operators $\phi(x)=\phi(x)_+ + \phi(x)_- $ that can be decomposed into terms of annihilation and destruction operators. Let $$ D(x-y) = ...
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1answer
56 views

Coulomb law and photons

When we consider process like $e^- e^- \to e^- e^-$ in QED, we see that from exchanges of one photon (tree-level diagrams) one can obtain Coulomb's law, while loop-diagrams give quantum corrections ...
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1answer
34 views

Differential cross-section for a 2-particle process in the LAB frame

This should really be a straightforward calculation, but somehow, I keep confusing myself and failing over and over again. I did the calculation so many times that I don't even know what I'm looking ...
3
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1answer
126 views

How do (and don’t) particles emerge from fields?

I am aware of the following field- and particle-like notions: QFT particle, a unit of excitation in (the Fock space of) a QFT; SR field, an extremal $A = A(\mathbf x)$ of a Lorentz-invariant action; ...
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33 views

Wick contraction in proton-pion production

Proton-pion production $\gamma + p \rightarrow \pi^0 + p$ occurs through the interaction hamiltonian $$\mathcal H_{int} = ig \bar \psi^{(p)} \gamma_5 \psi^{(p)} \phi + e \bar \psi^{(p)} \gamma_{\mu} ...
3
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1answer
66 views

Limits used to find non-rel limit of the Klein-Gordon equation

I just have a question regarding assessing the non-relativistic limit of the Klein-Gordon equation. In the book I'm following (Quantum Mechanics by Bransden & Joachain) they use the limits (Chpt. ...
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2answers
129 views

Are the path integral formalism and the operator formalism inequivalent?

Abstract The definition of the propagator $\Delta(x)$ in the path integral formalism (PI) is different from the definition in the operator formalism (OF). In general the definitions agree, but it is ...
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1answer
36 views

Placement of indices in canonical commutation relations of coordinates and conjugate momenta as well as fields and conjugate momenta

The canonical commutation relations between generalised coordinates $q_a$ and their conjugate momenta $p^a$ are given by $[q_a,q_b]=[p^a,p^b]=0$ $[q_a,p^b]=i\delta^b_a$. Furthermore, the canonical ...
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70 views

Is it possible to do a path integral between two boundaries analytically on a quantum lattice?

I have been trying to perform some path integral between two boundaries for a massless scalar field $$\int_{\varphi(t_a, \vec{x})}^{\varphi(t_b, \vec{x})} \mathcal{D}\varphi(x)e^{iS[\varphi(x)]}$$ ...
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1answer
78 views

Where does the matching condition for $U(1)$ subgroups come from in unified models?

The matching conditions for a breaking $G \rightarrow \prod_i G_i$ are $$\omega_G-\frac{C_2(G)(\mu)}{12 \pi}=\omega_{G_i}-\frac{C_2(G_i)(\mu)}{12 \pi} ,$$ where $C_2(g)$ denotes the quadratic ...
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27 views

Perturbation expansion of effective action

Chapter 11.4 of Peskin & Schroeder's book discussed the computation of effective action, but I don't understand some details of derivation. The book first split the Lagrangian into normal ones and ...
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0answers
95 views

Two-point function of a free massless scalar field in Euclidean space-time

Let $\phi(x)$ be a free massless scalar field on $d$-dimesnional space-time with Euclidean metric. I am interested in the operator formalism, i.e. $\phi(x)$ is an operator satisfying $\Delta \phi=0$ ...
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1answer
42 views

Crossing Symmetry in Bhabha scattering and Moller scattering

Given the amplitude for a particular process, it may be possible to obtain the amplitude for another similar process by a so called crossing symmetry. I know there is a $s \leftrightarrow u$ crossing ...
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1answer
309 views

Why can't a real scalar couple to the electromagnetic field?

If we have a complex scalar $\phi$ we know that the gauge-invariant interaction with $A$ is given by $A^\mu J_\mu$, where $J$ is the Noether current of the $U(1)$ symmetry of the Lagrangian $$ ...
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1answer
33 views

Estimate mass of exchange boson by decay time

I have made a rough estimate that the minimum lifetime $\tau$ of the proton must be $10^{23} \, \mathrm{s}$. From this I would like to estimate the mass of the X boson which would mediate this decay ...
5
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1answer
64 views

Supersymmetric background and fermion variations

I'm trying to understand some basic questions about supersymmetric theories in curved backgrounds and supergravity. If I understand it correctly, there's a condition for a background to preserve SUSY, ...
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47 views

Connection between statistical and quantum mechanics

I am aware of Gibbs measures, given the energy (Hamiltonian) of an arrangement, one can determine the frequency of the arrangement. Plug the energy level in the Boltzman equation and there you go. I ...
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20 views

Renormalization Point for Coulomb Potential?

In Introduction to Quantum Field Theory by Matthew Schwartz at page 177 he explains that we use the renormalization point $p_0=0$ in order to derive Eq. 17.54: \begin{equation} \tilde{V}(p)= ...
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40 views

What's the connection between the pole contours of propagators and their causality?

Wikipedia distinguishes between three kinds of propagators for a scalar field: The Retarded propagator's contours have $\mathrm{Im}(k^0)>0$ on both poles, so its limit is completely in the first ...
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0answers
37 views

Physical poles in QFT scattering amplitudes?

In QFT, for instance in $\phi^3$ theory, the scattering amplitudes are said to be constrained to feature so called "physical poles" only. Consider generalized Mandelstam variables ...
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1answer
42 views

$e^-e^-\rightarrow e^-e^-$ scattering relative negative sign quick computation

In the QED scattering process $e^-e^-\rightarrow e^-e^-$ there are two possible diagrams in the tree level. If I label the momenta I have, $$e^-(k_1)\quad e^-(k_2)\quad \longrightarrow \quad ...
3
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0answers
36 views

Some questions about QCD [closed]

About QCD, I have two questions. I know I should propose one question one time, but they are actually two steps of the same question: Non-perturbative aspects of QCD. 1, Why do we need to solve QCD ...
6
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2answers
67 views

SHO in QM and Klein Gordon field in 1+0D QFT

The SHO in QM with mass $m=1$ has action $$ S[x] = \int dt \frac{1}{2} \dot x^2 + \frac{1}{2}\omega^2 x^2 $$ by integration by parts we see this is the same as 1 dim Klein Gordon QFT action with ...
3
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1answer
131 views

Why don't we observe spontaneous symmetry restoration in nature?

Why do we always observe spontaneous symmetry breaking in nature and not restoration? Does there exist some argument with the 2nd law of thermodynamics and the entropy of the universe increasing? If ...
5
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1answer
74 views

What is a slow-roll field?

I am studying inflation reading this article http://lanl.arxiv.org/abs/hep-ph/0406191 and in section 3 it states: This inflaton field may evolve slowly down its effective potential, or not. While ...
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1answer
54 views

Global Anomaly and Ward Identity

This question is a continuation of the answer posted for this question about anomalies. What happens to the Ward identity corresponding to a global symmetry if that symmetry is anomalous? I mean, is ...
1
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1answer
42 views

Structure of Mass Renormalisation

I'm currently working on the renormalisation part in Peskin, Schroeder QFT. There it is stated that non-logarithmic UV divergences give a mass renormalisation and thus are forbidden, e.g. for the ...
2
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1answer
77 views

Is a Weyl fermion its own antiparticle?

Majorana fermions are their own antiparticles, and Weyl fermions are just Majorana fermions without mass. However, I haven't been able to find any source that says whether a Weyl fermion is its own ...
4
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1answer
161 views

Two conflicting definitions of chirality

Consider a Majorana fermion embedded in a Dirac spinor, $$\psi = \begin{pmatrix} \psi_L \\ i \sigma_2 \psi_L^* \end{pmatrix}.$$ The Majorana fermion $\psi_L$ is left-chiral, i.e. it transforms in the ...
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0answers
21 views

Is absorption probality modulated by interferance instanteneous or retarded effect?

Let say the absorption probability at some atom 1 location is modulated by photo ionized electron wave (ionized from 1) that scatters by neighboring atom 2 and returns to the 1. (Around the absorption ...
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35 views

How to represent the spherical wave by using Fock basis?

Suppose I have two particles with opposite momentum: $$ |\psi \rangle_{\mathbf k} = |\mathbf k; -\mathbf k\rangle ,\quad |\mathbf k| = M $$ I want to represent the spherical symmetric distribution of ...
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2answers
60 views

Commutation Relations in Second Quantization

I understand that if I have the field operators $\psi(r)$ and $\psi^\dagger(r)$, then I have the canonical commutation relation (in the boson case) $$[ \psi(r) , \psi^\dagger(r')]=\delta(r-r').$$ My ...
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1answer
219 views

Are there negative energy states in QED?

I was reading Weinberg I, when I came upon the following statement$^1$ (slightly edited by me): \begin{align} (\not p+m)u=ie\not A\\ (\not p-m)v=ie\not A \tag{1} \end{align} The minus sign on ...
2
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1answer
35 views

Computation of theta-term from triangle diagram

The chiral $U(1)$ anomaly in QCD can be calculated exactly by one-loop Feynman diagrams, for example by the famous triangle diagram. I am currently performing the computation to get a better ...
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0answers
26 views

Spontaneous symmetry breaking of scalar multiplet theory

Consider a theory with two multiplets of real scalar fields $\phi_i$ and $\epsilon_i$, where $i$ runs from $1$ to $N$. The Lagrangian is given by: $$\mathcal L = \frac{1}{2} (\partial_{\mu} \phi_i) ...