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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Euler-Lagrange Equation in Quantum Field Theory

The quantum fields are operator valued distributions. In some sloppy books like Peskin and Schroeder the Euler-Lagrange equation are used to get the equations of motion. What does it mean to take a ...
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Construction of Primaries of WZWN CFT

Is it possible to construct primaries of $SU(2)_{k+1}$ by using primaries of lower levels?. E.g. If I have a primary of $SU(2)_2$, let's say $\Phi^{(1/2)}$, the field with spin $1/2$ and another ...
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63 views

One particle states in an interacting theory

Question: What is the general definition of one particle states $|\vec p\rangle$ in an interacting QFT? By general I mean non-perturbative and non-asymptotic. Context. 1) For example, in Weigand'...
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Are strings in string theory actually little black holes? [on hold]

I sometimes read that strings in string theory are actually little black holes, or can be interpreted that way. Is this true? How is that consistent with that the particle that a string represents ...
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What is the difference between worldsheet supersymmetry and spacetime supersymmetry?

What is the difference between worldsheet supersymmetry and spacetime supersymmetry? For worldline formulation of fermions quantum mechanics, there is a supersymmetry. But the corresponding spacetime ...
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Virtual Particles in QCD Vacuum [on hold]

I would like to ask what are the virtual particles in the QCD vacuum. Are they QCD bound states or they are just quarks? In fact, I am puzzled by the logics explained in Peskin and Schroeder book, ...
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1answer
64 views

R-matrix and S-matrix in QFT

In the study of quantum field theory, one may encounter S-matrix a lot. Recently, in the study of integrability, I encountered R-matrix formulation which I am not familiar with. First of all, the S-...
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45 views

If you reverse the development of all fields, is time moving backwards? [on hold]

Imagine that the development of all physical fields is reversed, and the expansion of space also. Does time go back?
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41 views

Vacuum persistance amplitude

E. Fradkin's Field Theories in Condensed Matter Physics formulas 3.57 and 3.58: I feel really sad about it, but all my tries of getting from formula $$ Z = \operatorname{tr} \hat{T} \prod_{j=1}^{...
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Are there Gauge fields that are not 4-vectors?

In my understanding Gauge fields are fields that have some kind of redundancy, i.e. a transformation that does not change the physical state. As far as I can see all the Gauge fields in the Standard ...
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What is the meaning of the size of an elementary particle in QFT? What is the meaning of a point particle? [duplicate]

I have often seen people refer to the size of a particle being at most a given value, or a particle being a point particle, in the context of quantum field theory. Examples are the Wikipedia entry on ...
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Multi-Cut Matrix Models

I have a question pertaining specifically to a one-matrix model with a multi-cut solution. The standard procedure is to take a polynomial superpotential $W(x)$. In the classical limit (analogous to $...
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Does Feynman parametrization commute with derivative?

Let $I = \int \frac{d^4k}{(2\pi)^4} \frac{(p+k)\cdot\gamma}{(p+k)^2-m^2+i\epsilon} \frac{1}{k^2+i\epsilon}$ I would like to do two operations on the integral, namely Feynman parametrization and $\...
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61 views

Such a huge mass for Higgs boson? And how can it, as a quantum, decay?

With a mass of 126GeV/c2 Higgs boson would have a mass slightly greater than a caesium atom. Isn't it too much? Wouldn't be in this way the ubiquitous Higgs field so dense to cause problems for the ...
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Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
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2answers
53 views

Does QFT modifies Quantum Mechanics? [duplicate]

The basis of Quantum Mechanics is contained in the postulates which tell us how to describe quantum systems (below I disconsider possibly degenerate spectra just for simplicity): To describe a ...
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1answer
51 views

How to define the distance between two points in a conformal transformed space?

Consider a particular conformal transformation $x^\mu\rightarrow x'^\mu$, and the metric of a flat space transforms in the following way, $$\eta_{\mu\nu}\rightarrow g'_{\mu\nu}=\Lambda^2(x)\eta_{\mu\...
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Is it possible in this Universe to communicate a bit of information with energy that scales sub-linearly with distance?

If we look at all the ways that people do communicate information, they all seem to have a cost "at least linear in distance." For example, communicating over a wire has attenutation, so the energy ...
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Is the usage of the Fock space a postulate in QFT?

In this question, when I write Fock space, I mean "the direct sum of the symmetric or antisymmetric tensors in the tensor powers of a single-particle Hilbert space H", as it is described by Wikipedia. ...
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Experimental observation of non-perturbative effects

Many quantum field theories come with non-perturbative objects such as solitons and instantons, and non-perturbative effects such as the Schwinger effect. However, it is hard to find any review on ...
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105 views

A question from A. Zee's book

On page 463, it writes in eq. (3) $$4H=\Sigma_\alpha(Q_\alpha Q^\dagger_\alpha+Q^\dagger_\alpha Q_\alpha).\tag 3$$ And then it writes that this is followed by eq.(4) as $$\langle S| H|S\rangle=\frac{...
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What is a method of finding minima of the one-loop effective potential?

Say you have a theory with an arbitrary number of real scalars, and you wants to find their Vevs in the global one-loop vacuum. How is this accomplished?
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63 views

How do we compute correlation function in the Schrodinger picture?

From concreteness' sake consider $\phi^4$ theory with a real scalar (even though the choice of the theory has nothing to do in principle with what I am going to ask). Consider thefollowing ...
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A few questions concerning one loop corrections to the action

When we perform a Legendre transform on the connected generate functional $W[J]$ we get the quantum action (or 1PI action) $ \Gamma[\phi] = W[J(\phi)] - \int\mathrm{d}^4x\,\phi J,\quad\phi(J)=\frac{\...
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51 views

Connection between “classical” Grassmann variables and Heisenberg Equation of motion

I have been reading di Francesco et al's textbook on Conformal Field theory, and am confused by a particular statement they make on pg 22. Let $\{\psi_i\}$ be a set of Grassmann variables. Starting ...
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29 views

Defining Thermodynamic beta in unit of second

If I define Thermodynamic beta in unit of second. Does this mean that: Boltzmann constant $k$ is unit-less? $T$ is in units of frequency (Hz) or Kelvin $K$? In this case, is defining Thermodynamic ...
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Gaussian Model scaling fields

last week one of my lectures mentioned the "scaling fields" for the 2D Gaussian Model, $\Phi = e^{\pm ip\phi}$ but did not give any further explanation what that means or where that comes from. ...
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57 views

Solving a step in the derivation of the anomalous magnetic moment of the electron

In the book An Introduction to Quantum Field Theory by Peskin and Schroeder there is a derivation of the anomalous magnetic moment of the electron. The Feynman diagram to be solved is this one: and ...
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27 views

Complex field with a chemical potential

This is probably a very basic question. I'm looking at the following Lagrangian with a single complex field $\phi$, $$\mathscr{L} = D_{\mu}\phi^*D^{\mu}\phi - m^2 \phi^* \phi - \lambda (\phi^* \phi)^...
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56 views

Reading a Paper on the Cosmological Constant Problem [closed]

My professor wants to give me (and another kid) a problem in quantum cosmology. To that end, he asked me to read through his recent paper that appeared in the Physical Review Letters. He said that I ...
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Wilsonian Renormalisation — Peskin & Schroder Sect. 12.1

I'm working my way through Peskin & Schroeder, but some of the details of the calculations done in their introduction to the renormalisation group are slipping past me. For concreteness, the ...
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Fine Structure and Fine Structure Constant - intuitive relation?

How does the fine structure and fine structure constant relate to each other, intuitively? I've seen $\alpha$ extrapolated as a term in energy calculations for fine structure, but is there a ...
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Doubts about the theta angle and the ground state energy density in Euclidean Yang-Mills theory

I am reading the following notes https://munsal.files.wordpress.com/2014/10/marino-lectures2014.pdf. On section 4.3 the euclidean Yang-Mills theory is considered. It is said that renormalizability and ...
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Equal amplitude for the processes P1: u g->W+ d and P2: d g->W- u? [closed]

My question is the following: We have two processes P1: ug->W+d and P2: dg->W-u. At tree level and in the limit of vanishing quark masses, which is the ratio between the averaged square amplitudes? ...
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What is the mathematical motivation for complexifying momenta in BCFW?

One of the first steps in obtaining the on-shell BCFW recursion relations is complexifying the momenta of the external particles. Now complexifying things is not unprecedented (the dispersion program ...
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OPE coefficents and commutation relations, and OPE with stress tensor

Basic question about conformal field theory: In a conformal field theory in $d\geq 3$ dimensions, what is the relation between commutation relations and OPE coefficients? In particular, because ...
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2answers
92 views

The “harmonic paradigm” in physics

Disclaimer: I know this is a vague question, so if this is not the appropriate thread, please direct me to the correct one. On page 5 of Anthony Zee's Quantum Field Theory in a Nutshell he speaks of ...
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1answer
69 views

Question on Step in Lancaster's “Quantum Field Theory for the Gifted Amateur”

I'm having trouble understanding a single step in Lancaster's book. In Chapter 16, the propagator is derived and proved to be the Green's function of the Schrodinger equation. The derivation is pretty ...
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2answers
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Quantum Operators: An Identity

I came across the following neat property: For an operator $\hat{A}$ which is a linear combination of creation and annihilation operators, we have: $$ \langle e^{\hat{A}} \rangle = e^{\langle \...
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How to go from a Higgs which transforms in the adjoint representation to a 2x2 matrix?

I have a triplet transforming in the adjoint map of the lie albegra of su(2) but I don´t know how to include it in to a Lagrangian where I have two lepton doublets. It should be a 2x2 matrix but I don´...
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1answer
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Lattice QFT: Non-homogenous lattice spacing

I am interested why we fix the lattice spacing, $a$ to be homogenous in all dimensions. After a Wick rotation, $a=i \epsilon$ where $\epsilon=t_{i+1} - t_{i}$ and with euclidean time given by $\tau = ...
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2answers
94 views

Running coupling outside QFT

I'm reading about the running coupling in QCD. I understand the vacuum polarization and its consequences. Also I've read that you can find the same phenomenon on the strong interaction, giving us the ...
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1answer
60 views

Questions from Srednicki's Introduction to Interacting Field Theory using the LSZ Formula

I have been reading through the chapter on the LSZ Reduction Formula from Srednicki's Quantum Field Theory, and I have a few questions about which I'm sort of confused. The questions are referenced ...
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Decay rate revisited

According to Peskin&Schroeder (pp. 107), we have $$ d\Gamma=\frac{1}{2m_A}\left(\prod_f\frac{d^3p_f}{(2\pi)^3}\frac{1}{2E_f}\right)|\mathcal{M}(m_A)\rightarrow {p_f}|^2(2\pi)^4\delta^{(4)}(p_A\...
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1answer
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Two definitions of topological terms in field theory

I've seen two distinct definitions for "topological" terms in the context of quantum field theory. Topological terms don't depend on the metric $g_{\mu\nu}$. This makes sense since topology is '...
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1answer
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High $p_T$ and high $Q^2$ in deep inelastic hadronic collisions

When reading about high energy collisions (for example proton-proton collisions at LHC), I always find the relation $Q\sim p_T$, which, for me, is hard to demonstrate. Moreover, I found statements ...
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Re: Quantization of a Fermi field

Consider the quantization conditions for a complex Fermi field $\Psi=\Phi_1+i\Phi_2$: $$\{\Psi(x),\Psi(y)\}=\{\Psi^\dagger(x)\Psi^\dagger(y)\}=0,~~~~ \{\Psi^\dagger(x),\Psi(y)\}=\delta(x-y)$$ Compare ...
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Writing the Yang-Mills topological charge using differential forms

I have a very pedestrian knowledge of differential forms and I am having some trouble in a derivation. The topological charge $Q$ in Yang-Mills theories is supposed to be $$ Q=\int{}q(x)d^4x $$ where $...
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At most $N$ gapless charge/spin modes in a system of $N$ coupled 1D chains?

Leon Balents and Matthew P. A. Fisher claimed the following without any further explanation ($N$ is the number of chains) For a system of $N$ coupled 1D chains, the number of gapless charge modes ...