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].

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What exactly is a Feynman propagator?

Let $p,q$ be two points. On pg 671 of "Road to Reality", Penrose says that integrating the amplitudes of all paths between $p$ and $q$ would be infinite. Hence, we need the concept of a Feynman ...
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35 views

Spin-statistics theorem [on hold]

I am an undergrad physics student I was curious about the validity of the Pauli exclusion principle and found that spin statistics theorem gives the prrof of this principle . What background do I need ...
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Two inconsistent expression of density operator $\rho(x)$ in Giamarchi's book

I am currently reading Giamarchi's "Quantum Physics in One Dimension". From (2.28) one easily obtain $$ \rho(x)=\rho_R(x)+\rho_L(x)=-\frac{1}{\pi}\nabla\phi(x).$$ (Actually (2.55) exactly states this ...
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Understanding the statement “orbifold theories are QFTs with finite gauge group”

I'd like to understand the equivalence of orbifold theories in string theory and (2D worldsheet) QFTs with finite gauge group, using the path integral. Suppose my action is $$S= \frac{1}{2\pi \alpha'...
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Analytic Elements Haag-Araki theory

Why the elements of a local von Neumann algebra cannot be analytic elements of the timelike translation?
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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 ...
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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)\...
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(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 $$O_{SU}(r)=\Psi^\dagger(r)\Psi^\dagger(r+a)$$ ...
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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 ...
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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 ...
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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^...
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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 ...
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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 ...
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2answers
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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 ...
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55 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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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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)...
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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 ...
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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 ...
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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 ...
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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{...
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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....
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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 ...
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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\...
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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 ...
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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. ...
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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 ...
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107 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 \...
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1answer
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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 $$...
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Formation of fields with momentum operator

Ok. Weinberg says that in their QFT book Vol 1 on pages 238 and 239 that we can construct any bosonic (A,A) field from scalar ((0,0)) field if we form operator of 2A partial derivatives (momentum ...
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Gravitational contribution to the action for Coleman-de Luccia instanton?

In the Coleman-de Luccia calculation of the transition rate from one de Sitter minimum to another, the action for the scalar field $\phi(\xi)$ and Euclidean radius $\rho(\xi)$ is $S_E = 2\pi^2 \int \...
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1answer
63 views

What's the point of dimensional regularization?

I'm studying regularization of divergent integrals in QFT from Here: Roberto Soldati - Field Theory 2. Intermediate Quantum Field Theory (A Next-to-Basic Course for Primary Education) I think I'm ...
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Physical degree of freedom and gauge fixing?

I'm confused with the gauge fixing in the Higgs mechanism. So if we have an action like $$S=\int |D\phi|-\frac{1}{4}F^2 -V(\phi) ~ ,\tag{1}$$ then expand around some non-trivial vacuum, then we have ...
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Holography and field theory

If the holographic principle is right, and there is a FINITE but very big degrees of freedom per Planck area, would it imply that in that regime we should give up local field theory and addopt some ...
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Calculation of 3-point function given a generating funcional $Z[J]$

With: $$\ln Z[J]= \int dt \frac{J^2(t)}{2} f(t) + C \int dt \frac{J^3(t)}{3!}$$ I am asked to calculate the 3-point funcion. Attempted solution: The 3-point funcion is given by $\frac{ \delta^3 }{\...
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Why is the beta function in RG usually defined as a “logarithmic” derivative?

What is the motivation behind defining the beta function as the logarithmic derivative of the coupling constant with respect to scale and not just the regular derivative?
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Is vacuum energy transient or permanent?

Vacuum energy is based on Heisenberg's energy–time uncertainty principle which says that $\Delta E$ can exist for $\Delta t$. This $\Delta E$ can produce electron positron pair for $\Delta t$ by ...
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1answer
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How does the $p+p + e^-\rightarrow D + \gamma\gamma+ \nu$ reaction proceed in the sun?

In this video on nuclear fusion the explanation of the reaction $p+p\rightarrow D + \nu + \gamma\gamma$ is that the two protons collide, form a weakly bound state, and then sometimes decay into the ...
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Perturbing about the Renormalized Field Theory: What justifies perturbing if the counter-terms are large? [duplicate]

I have a very basic question about Renormalization in Quantum Field Theory. Consider the following passage (about $\phi^4$ theory) from Zee's Quantum Field Theory in a Nutshell (from Chapter III.3): ...
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Where does decay widths in mass mixing matrix come from?

For some time ago I've seen people use complex mass mixing matrix including decay width of the particles. It kind of makes sense, but I could never fully justify it. I would be grateful if you could ...
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Meaning of eq.(4.64) in Peskin & Schroeder?

In an introduction to the scattering matrix in the relativistic QFT setting, the book tries to generalize the non-relativistic Breit-Wigner formula (4.63): $$ f(E)\propto\frac1{E-E_0+i\Gamma/2}. $$ ...
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1answer
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Why can we use the equation of motion to calculate the amplitude in “Quantum Field Theory”?

I am reading the chapter on electron-proton scattering from "Quantum Field Theory in a Nutshell". The author calculates the amplitude of the electron-proton scattering (up to the second order). The ...
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106 views

On scheme dependence in QFT renormalization

I searched for the answer to my question quite a while and it seems nobody ever asked similar questions or it is written explicitly in any textbooks. The question is, If physical parameters of any ...
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1answer
49 views

Mass parameters in the spontaneous symmetry breaking

In Ashok: Lectures on Quantum Field Theory Sec. 7.5 p.279 he discusses the mass parameters for the potential $$ V = -\frac{m^2}{2}(\sigma^2+\xi^2) + \frac{\lambda}{16}(\sigma^2 + \xi^2)^2. $$ My (...
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1answer
49 views

How Gupta-Bleuler condition implies $(a_p^3-a_p^0)| \phi \rangle=0$?

Gupta-Bleuler condition is $$\partial^\mu A_\mu^+ | \phi \rangle=0\tag{6.54}$$ where $$A_\mu^+= \int\frac{d^3\mathbf p}{(2\pi)^3 \sqrt{2|\mathbf p|}} \sum_{\lambda=0}^3 \epsilon^\lambda_\mu a_p^\...
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Contradiction between aymptotically free particles in QFT and unlocalization

When studying different interactions in any QFT, one always assumes that the IN and OUT states are asymptotically free particles with definite momenta. For example, one assumes that an electron and a ...