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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66 views

Observables labelling one-particle states in Quantum Field Theory

I'm studying introductory QFT using the first volume of Weinberg's series, and i'm having problems in understanding how single particle states of the free theory are labelled, i.e. what observables ...
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30 views

How to calculate the effective potential of two interacting scalar field in QFT?

for the potential: $V=\lambda_h(h^2-v^2)^2+\lambda_s(s^2-w^2)^2+\lambda_{hs}h^2s^2$, where h and s are two real scalar fields and v and w are the vacuum expectation values of the two fields. The ...
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37 views

Projecting out interactions with high-energy states

I have a single-particle Hamiltonian with a discrete energy spectrum $E_{n,k}$ with two degrees of freedom, $n=0,1,2,3...\infty$ and $k$ which has only a few possible values. $E_{n,k_1}$ and $E_{n,k_2}...
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34 views

Correlation function of partition functions

In this paper the authors study the correlation function of partition functions defined by $$\langle Z(\beta_1) \ldots Z(\beta_n) \rangle = \frac{1}{\mathcal{Z}}\int \mathrm{d}H \, \mathrm{e}^{-L \, \...
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81 views

Book reference: Quantum field theory from path integrals

a) What are some good references to learn quantum field theory from the approach of path integrals? Like books which start from path integral formulation of quantum mechanics and then do calculations ...
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1answer
50 views

Second quantisation for fermions

I am trying to build a model for reactions on a lattice in the Doi-Peliti formalism. Suppose there exists a lattice of $N$ sites indexed by $i$. Each site can be either occupied or unoccupied. ...
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1answer
44 views

Two definitions for normal ordering of $c_{k+q}^\dagger c_k$

Consider the fermionic operator $c_k, c^\dagger_k$, and where $k$ is discrete and unbounded. (Note: This situation frequently arises in bosonization.) Let the vacuum $|0\rangle$ be the state with all $...
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1answer
30 views

(Altland-Simons) Question about a seemingly additional term in the functional field integral

The following is the part of the book from Atland-Simons. My question is about the additional $-\overline{\psi}^{n+1}\psi_n$ in $(4,27)$ of the book. I understand that the term $\overline{\psi}^{n}\...
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40 views

What is the characteristic of a property?

Background: The following two observations are , in my understanding, pretty much accepted in quantum theory: Location is a property which is not preexisting but is established by measurement. It is ...
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70 views

Chern-Simons theory on a plane/sphere with a single charge insertion

Consider the pure Chern-Simons theory on the plane $\mathbb{R}^2$ with a single charge insertion in some representation $\rho$ of the group $G$. What does the Hilbert space look like? Is it null or ...
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1answer
45 views

How to get the imaginary part from the Källén-Lehmann propagator

During field theory course the Källén-Lehmann propagator was defined as follows: $$D_F(p^2) = \frac{i}{p^2-m^2+i\epsilon} + \int^{\infty}_{4m^2}ds\rho(s)*\frac{i}{p^2-s+i\epsilon} \tag{1}$$ ...
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20 views

Density fluctuation and derivative of the field operator $\partial_x \phi(x)$

In a literature about bosonization, one argues that $\partial_x \phi(x)$ represents the density fluctuation. Why can we think that the derivative is about the density fluctuation? My guess: For small ...
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1answer
44 views

Lorentz invariant but baryon number violating operators from a single fermion field?

In a theory of a single fermion, is it possible to write down a Lagrangian that violates the global U(1) symmetry (e.g. baryon number) but that is Lorenz invariant? I'm wondering because the only ...
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1answer
49 views

Decay rate of scalar Yukawa interaction

Considering the Lagrangian of two scalar fields in $d=4$: $$\mathcal{L}=\frac{1}{2}(\partial\phi)^2-\frac{1}{2}m^2\phi^2+\frac{1}{2}(\partial\chi)^2-\frac{1}{2}M^2\chi^2-g\phi^2\chi$$ Let's assume ...
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1answer
36 views

Self-energy in two scalar Yukawa interaction

Considering the Lagrangian of two scalar fields in $d=4$: $$\mathcal{L}=\frac{1}{2}(\partial\phi)^2-\frac{1}{2}m^2\phi^2+\frac{1}{2}(\partial\chi)^2-\frac{1}{2}M^2\chi^2-g\phi^2\chi$$ What would be ...
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71 views

How are anticommuting fields ($\eta \chi = -\chi \eta$) “forced upon us” by representation theory of $SO(d-1,1)$?

I would like to know if anticommuting fields (which physicists use as fermions) emerge naturally from the spin representation theory of $SO(d-1,1)$. Is the fact that spinor fields anticommute a ...
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1answer
94 views

Does technical naturalness hold only for global symmetries, or also gauge symmetries?

Suppose you have an action $S(\epsilon) = S_1 + S_2 + \epsilon\, S_\mathrm{int}$. Assume that $S_1$ is gauge invariant under the action of the group $G$ and $S_2$ is gauge invariant under the action ...
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1answer
82 views

Where the derivative corrections come from in Wilson renormalization?

I known that in the Wilson renormalization process fast modes are integrated out in order to define an effective action for the low modes field. Considering phi to the fourth theory it's easy to see ...
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68 views

Time reversal symmetry in Bilayer Graphene

In general the time reversal symmetry operation for spin half angular momentum requires $$H(-p)=\sigma_{y}H^{*}(p)\sigma_{y}.$$ The Hamiltonian of a bilayer Graphene is $$H(p)=\frac{1}{2m}(p^{2}_{x}-p^...
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2answers
46 views

Electron and positron pair production and annihilation

An electron and a positron arise from an energetic gamma photon. However during annihilation of an electron and positron, two gamma photons are released. Is this a violation of law of ...
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1answer
36 views

Deriving intensity of light as a function of frequency

Page 4 of the textbook Quantum Field Theory and the Standard Model by Schwartz says the following: The incompatibility of observations with the classical prediction led Planck to postulate that the ...
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3answers
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Why is quantum gravity non-renormalizable?

The book The Ideas Of Particle Physics contains a brief treatment of quantum gravity, in which the claim is asserted that if one attempts to construct a model of gravity along the same lines as QED, ...
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134 views

Importance of an extra total derivative term in Liouville theory

In this paper on boundary Liouville theory, the authors have introduced an extra term, $-\partial_{\sigma}^2\phi$, (the last term in the equation below) in defining the stress tensor of the Liouville ...
2
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1answer
93 views

Is the vacuum of a local ${\rm U(1)}$ gauge theory unique?

Consider a spontaneously broken scalar field theory with a global ${\rm U(1)}$ symmetry described by the Lagrangian $$\mathscr{L}=(\partial_\mu\phi^*)(\partial^\mu\phi)-\mathcal{V}(\phi),\\ \mathcal{V}...
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Coset construction for Goldstones in Weinberg Vol II

In section 19.6 of Weinberg Vol II, there is a discussion of the coset construction for effective actions of Goldstones arising from spontaneous symmetry breaking of internal symmetries. In this ...
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45 views

Exotic perturbative anomaly captured only by higher-loop Feynman graphs, but not by any 1-loop Feynman graph?

My question: Are there any perturbative anomaly captured by higher-loop but not by captured at the 1-loop Feynman graph (say, not enough)? We are familiar with the text book example of a ...
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1answer
53 views

One-loop corrections to vacuum polarization with a specific Lagrangian

I'm having some difficulties regarding this problem in QFT I'm doing to prepare for an exam. For the following problem I consider the theory described by the Lagrangian: $$\mathcal{L}=-\frac{1}{4}F_{\...
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1answer
54 views

Why using time-ordering causality? and what is Difference between Locality and Causality?

In QFT, the time-ordering causality is generally used. There are 4 ways to bypassing the pole called time-ordering, anti-time-ordering, retarded and advanced. But in many case only time-ordered ...
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2answers
84 views

Why only loop effects be quantum corrections when the full theory is quantum?

Feynman diagrams with one or more loops in an interacting QFT are diagrammatic representation of corrections to the Green's functions and amplitudes beyond the lowest order in perturbation theory (...
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1answer
103 views

What is the intuitive reason why matter and antimatter should be highly reactive?

Common knowledge has it that when an amount of matter and an amount of antimatter come anywhere near each other, they annihilate, leaving nothing but "pure energy". In more technical terms, maybe we ...
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1answer
59 views

Does the W boson necessarily change an anti-fermion's flavor to its anti-neutrino counterpart?

I'm writing the diagrams for the following process in Standard Model: $$\nu_e + e^+\rightarrow \mu^++\nu_\mu+\gamma$$ I want to know if the W boson changes the flavor of $\mu^+$, for instance, ...
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1answer
1k views

Does the CPT theorem hold for all spacetime dimensions?

I can't find any reference which mentions the dependence of the theorem on spacetime dimension, but it would be very interesting to know what if any it has!
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50 views

Understanding some lines from 't Hooft's paper on large-N QCD in 1+1d

In 't Hooft's paper "A two-dimensional model for mesons", the author shows that two-dimensional (1+1) QCD in the large-N limit interestingly gives a theory of mesons. 't Hooft calculates the "mesonic ...
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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 ...
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37 views

Anomalous dimension of double-trace operators

Is it true that if a single-trace operator, say, $O$ acquires an anomalous dimension $\gamma_o$, then the anomalous dimension of the double-trace operator $O^2$ is $2\gamma_o$? If no, can anyone ...
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1answer
56 views

Are the field equations describing quantum fields in a curved space time generally co-variant in the same sense as classical field equations?

I have seen in many references that the field equations for a quantum field in curved space time is mentioned to be 'manifestly co-variant'. The procedure that has been followed to arrive at these ...
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1answer
31 views

Does the amplitude of light increase the more it is squeezed? (Quantum Optics)

If I have a 2 mode squeezed state of light, emitted from some nonlinear parametric process, then the more it is squeezed, the larger the variance of one quadratures $X$, while the variance of the ...
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1answer
92 views

Is the $U(1)$ in the standard model identified with quantum-mechanical phase?

I think there's a tension between two claims I've read: The standard model is Yang-Mills theory with gauge group $SU(3) \times SU(2) \times U(1)$. Here the $U(1)$ factor is data on the same level as ...
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2answers
98 views

Gaussian path integral is equivalent to saddle-point?

If we have a path integral involving many fields, $$Z = \int \mathcal D \phi_1 \cdots \mathcal D \phi_n \exp(-S[\phi_1,\ldots, \phi_n]),$$ and $\phi_n$ occurs only quadratically-- i.e. the $\...
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1answer
71 views

Tadpole diagrams in 1-loop massive scalar amplitudes?

Consider a massive scalar diagram such as or The loop momentum enters and exits the tadpole vertex, so that in the first diagram the momentum in the propagator connecting the two vertices is zero ...
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2answers
91 views

Quantum corrections in path integral

I am working the following exercise: Calculate the generating functional $$Z[j]=\int \mathcal{D}\Phi \exp\left(\frac{i}{\hbar}S[\Phi,j]\right),\quad S[\Phi,j]=\int d^4x(\mathcal{L}(\Phi)+j\Phi),$$ $...
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51 views

Generators of the Poincaré group

I am specifically interested in constructing the generators of an Poincaré group for a 2+1 dimensional Euclidean field theory. But I am pretty new to the subject, so I would like to ask some basic ...
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3answers
104 views

Peskin and Schroeder Section 7.1 Mass Shift

I'm slowly reading my way through Peskin and Schroeder. Near the end of section 7.1 they compare the mass shift of the electron from QFT to the classical value, both of which are divergent but in ...
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1answer
89 views

Pion decay as a point-particle

The $\pi^-$ meson is a composite particle of $\bar{u}d$ quarks, but for many practical purposes it can be treated as a point particle with an effective interaction. The vertex responsible for the $\pi^...
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1answer
63 views

Why is the Jacobian factor for fermionic variables different from that for bosonic ones?

In Srednicki's textbook Quantum Field Theory, Section 77 discusses anomalies and the path integral for fermions. The path integral over the Dirac field is defined to be \begin{equation} Z(A) \equiv \...
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1answer
83 views

Normal ordering by contour integral in CFT

In chapter 6 of Di Francesco, they introduce the normal ordering $$ (AB)(w) = \oint_w \frac{ dz }{ 2\pi i (z-w) }A(z) B(w)\ .\tag{6.130}$$ So far so good. But then starting eq (6.139) $$ \oint_w \...
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1answer
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Why is zero-point energy idolized as a good source of energy? [closed]

I've really only seen it in like liquid helium and I don't understand how it can hold the potential portrayed in the incredible movie by the main villian
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1answer
100 views

In relativistic QFT, is it ever possible that the bare mass be finite and equal to the physical mass?

In renormalization, one follows the philosophy that the bare mass is unobservable and could be infinite, and the physical mass comes from the pole of the two-point function. Is it possible that in any ...
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1answer
42 views

Preparing vacuum state of the EM field

I have some heuristic idea of how to think about state preparation in quantum mechanics. It may be revolving around the idea of using filters, cooling/heating, Stern-Gerlach type setup, etc. However, ...
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1answer
91 views

Can I raise a quantum mechanical operator to another quantum mechanical operator?

The most complicated power operation for operators that I have seen is an operator (or a sum of operators) raised to a number. How can I handle an operator raised to another operator? Is this even ...