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 particle physics. Don’t combine with the [quantum-mechanics] tag.

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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 ...
AccidentalFourierTransform's user avatar
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2 answers
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Gauge-fixing of an arbitrary field: off-shell & on-shell degrees of freedom

How to count the number of degrees of freedom of an arbitrary field (vector or tensor)? In other words, what is the mathematical procedure of gauge fixing?
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Boosts are non-unitary!

Unlike rotations, the boost transformations are non-unitary. Therefore, the boost generators are not Hermitian. When boosts induce transformations in the Hilbert space, will those transformation be ...
SRS's user avatar
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Localized field quanta?

After the canonical quantization of the Klein-Gordon field (for example), we interpret the quantum of excitations of the fields with definite energy and momentum as particles. But our mental image of ...
SRS's user avatar
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8 answers
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Is gravity just electromagnetic attraction?

Recently, I was pondering over the thought that is most of the elementary particles have intrinsic magnetism, then can gravity be just a weaker form of electromagnetic attraction? But decided the ...
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Interacting Fields in QFT

I am trying to work through Peskin and Schröder and am a little stuck in Chapter 4 [section 4.2 p. 83 below eq. (4.13)], when he first treats interacting fields. The subject is the quartic interaction ...
QuantumStudent's user avatar
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1 answer
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Lorentz Algebra Representation and QFT

I just have a trouble making a full analogy between Lorentz Algebra Representation in Quantum Field Theory (QFT) and SU(2) representation in Quantum Mechanics (QM). To make my point, I will write few ...
Quantization's user avatar
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Why don't virtual particles violate conservation of mass/energy?

If virtual particles sometimes add more mass/energy to a system then was inputed or comes out in the output, how do they not violate conservation of mass/energy.
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Gauge fixing and equations of motion

Consider an action that is gauge invariant. Do we obtain the same information from the following: Find the equations of motion, and then fix the gauge? Fix the gauge in the action, and then find the ...
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Virtual Particles real? Virtual particles create a universe? [closed]

I am reading the book of Lawrence Krauss "A universe out of nothing", where he explained that the vacuum is not empty. It is a boiling brew of virtual particles that come out of their existence. And ...
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What are quantum fields mathematically?

I'm confused as to how quantum fields are defined mathematically, and I've seen from questions on this site and Wikipedia articles that classical fields are just functions that output a field value ...
Oliver Gregory's user avatar
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Suggested reading for quantum field theory in curved spacetime

I want to learn some QFT in curved spacetime. What papers/books/reviews can you suggest to learn this area? Are there any good books or other reference material which can help in learning about QFT ...
27 votes
1 answer
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Systematic way to draw all inequivalent Feynman diagrams

I am wondering whether there is some systematical approach to find Feynman diagrams for S-matrix (or to be more precise for $S-1$ since I am interested in scattering amplitude). For example in $\phi^3$...
I-L-P's user avatar
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Is there any theorem that suggests that QM+SR has to be an operator theory?

UPDATE To make my question more precise, I'll define what I mean by an operator theory: An operator theory is a theory in which the dynamical objects are operators, i.e., the equations of motion are ...
AccidentalFourierTransform's user avatar
24 votes
1 answer
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Classical Fermion and Grassmann number

In the theory of relativistic wave equations, we derive the Dirac equation and Klein-Gordon equation by using representation theory of Poincare algebra. For example, in this paper http://arxiv.org/...
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Spin - where does it come from?

I study physics and am attending a course on quantum field theory. It is hard for me to draw connections from there to the old conventional theories. In quantum field theory spin originates from the ...
physicsGuy's user avatar
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A question about causality and Quantum Field Theory from improper Lorentz transformation

Related post Causality and Quantum Field Theory In Peskin and Schroeder's QFT p28, the authors tried to show causality is preserved in scalar field theory. Consider commutator $$ [ \phi(x), \phi(y) ]...
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Derivative interaction: $\mathcal{H}_\mathrm{int}\neq - \mathcal{L}_\mathrm{int}$. Question about Feynman Rules

As we known, if there is time derivative interaction in $\mathcal L_\mathrm{int}$, then $\mathcal{H}_\mathrm{int}\neq -\mathcal{L}_\mathrm{int}$. For example, Scalar QED, $$ \begin{aligned} \mathcal{...
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13 votes
2 answers
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What is precisely the energy scale of a process?

Coupling constants run with the energy scale $\mu$. But what is exactly this energy scale. My question is, if I have a physical process, how do I compute $\mu$?
Yossarian's user avatar
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11 votes
4 answers
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Nomenclature: Yang-Mills theory vs Gauge theory

If you're writing about a theory with Yang-Mills/Gauge fields for an arbitrary reductive gauge group coupled to arbitrary matter fields in some representation, is it best to call it a Yang-Mills ...
Simon's user avatar
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11 votes
1 answer
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Why is only the third component of weak isospin used as a conserved quantity?

Using Noether's theorem \begin{equation} \partial_0 \int d^3x \left(\frac{\partial L}{\partial(\partial_0\Psi)} \delta \Psi \right) = 0 \end{equation} we get three conserved quantites $Q_i$ from ...
jak's user avatar
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11 votes
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$(\frac{1}{2},\frac{1}{2})$ representation of $SU(2)\otimes SU(2)$

The representation $(\frac{1}{2},\frac{1}{2})$ of the Lorentz group correspond to a four- vector or a spin-one object. Right? Does it imply that any four-vector is identical to a spin-one object or ...
SRS's user avatar
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10 votes
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Why there is no unique "recipe" for quantization of a classical theory?

I have seen in Wikipedia that different quantization methods exist (see Wiki article with name "Quantization"). Moreover, Wikipedia stated that there is more than one way to quantize a classical ...
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8 votes
4 answers
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Proof of Connected Diagrams

If $Z[J]$ is the generating functional for the path-integral, could any prove (or more reasonably, refer me to a proof) that $$W[J]\equiv\frac{\hbar}{i}\log\left(Z[J]\right)$$ "generates" only ...
PPR's user avatar
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7 votes
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How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?

I came across the S. Coleman's seminal papers 'Fate of the false vacuum' (http://dx.doi.org/10.1103/PhysRevD.15.2929, http://dx.doi.org/10.1103/PhysRevD.16.1762) where he describes the tunneling ...
Wein Eld's user avatar
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3 votes
2 answers
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How does a photon mediate both electric attraction and repulsion?

The answer to this question probably lies in QFT, which I know just enough about to appreciate my current lack of understanding of the subject, if you follow me. About a year ago I asked our ...
user avatar
39 votes
6 answers
6k views

Formalizing Quantum Field Theory [duplicate]

I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or ...
35 votes
1 answer
2k views

What's the basic ontology of QFT?

I've been studying QFT for almost a year now but am still fairly unclear on the basic ontology of the theory. Here's what I'd consider the "basic ontology" of non-relativistic quantum mechanics: A ...
WillG's user avatar
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34 votes
1 answer
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Difference between 1PI effective action and Wilsonian effective action?

What is the simplest way to describe the difference between these two concepts, that often go by the same name?
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27 votes
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Does relativistic quantum mechanics (RQM) really violate causality?

The Hamiltonian $$H=\sqrt{p^2+m^2}$$ defines a one-particle quantum mechanics in the usual way. Let us call this theory RQM for short. Peskin and Schroeder claim that RQM violates causality because ...
Sam Gralla's user avatar
27 votes
3 answers
4k views

Does dilation/scale invariance imply conformal invariance?

Why does a quantum field theory invariant under dilations almost always also have to be invariant under proper conformal transformations? To show your favorite dilatation invariant theory is also ...
user avatar
26 votes
4 answers
7k views

Decay of massless particles

We don't normally consider the possibility that massless particles could undergo radioactive decay. There are elementary arguments that make it sound implausible. (A bunch of the following is ...
user avatar
26 votes
3 answers
9k views

What are the calculations for Vacuum Energy?

In wiki the Vacuum Energy in a cubic meter of free space ranges from $10^{-9}$ from the cosmological constant to $10^{113}$ due to calculations in Quantum Electrodynamics (QED) and Stochastic ...
metzgeer's user avatar
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26 votes
2 answers
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Why does the classical Noether charge become the quantum symmetry generator?

It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this ...
Edward Hughes's user avatar
20 votes
3 answers
5k views

Why cannot fermions have non-zero vacuum expectation value?

In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory ...
Paul's user avatar
  • 351
20 votes
1 answer
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Identification of the state of particle types with representations of Poincare group

In the second chapter of the first volume of his books on QFT, Weinberg writes in the last paragraph of page 63: In general, it may be possible by using suitable linear combinations of the $\Psi_{p,...
user avatar
17 votes
4 answers
1k views

Is the term "quantum fluctuation" an aide to understanding? [closed]

I would like to ask if anyone has found a tight enough way to define the term "quantum fluctuation" so that it can become a useful rather than a misleading piece of physics terminology. Terminology ...
Andrew Steane's user avatar
17 votes
2 answers
4k views

Equivalence Theorem of the S-Matrix

as far as I know the equivalence theorem states, that the S-matrix is invariant under reparametrization of the field, so to say if I have an action $S(\phi)$ the canonical change of variable $\phi \to ...
gaugi's user avatar
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16 votes
1 answer
737 views

Can Poincare representations be embedded in non-standard Lorentz representations?

My impression for how Poincare and Lorentz representations are linked in $3+1$ dimensions is: Assuming positive mass for simplicity, irreducible representations of the Poincare group are indexed by ...
knzhou's user avatar
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3 answers
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Is it possible for more than two particles to be entangled in a quantum way?

So I know that two particles can be entangled in a quantum way, but is it possible that more than two particles be entangled in a quantum way? Most descriptions provide with two-particles cases, so I ...
user27515's user avatar
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14 votes
1 answer
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What is the value of a quantum field?

As far as I'm aware (please correct me if I'm wrong) quantum fields are simply operators, constructed from a linear combination of creation and annihilation operators, which are defined at every point ...
Siraj R Khan's user avatar
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12 votes
2 answers
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The derivation of the Belinfante-Rosenfeld tensor

It seems me that there is a "difference" (at least apparently) in how the Belinfante-Rosenfeld tensor is thought of in section 7.4 of Volume 1 of Weinberg's QFT book and in section 2.5.1 of ...
Student's user avatar
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11 votes
2 answers
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Does spontaneous emission actually emit in a random direction, or is it measured in a random direction?

When an excited state couples to the vacuum, it has an infinite number of directions of the quantized electromagnetic field to couple to. Does it evolve into a superposition of all those directions at ...
mactud's user avatar
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11 votes
2 answers
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Renormalized mass

I am reading Schwarz QFT and I reached the mass renormalization part. So he introduces, after renormalization, a physical mass, defined as the pole of the renormalized propagator, and a renormalized ...
Alex Marshall's user avatar
9 votes
1 answer
2k views

Feynman $i\varepsilon$-prescription in path integral by adding an imaginary part to time

It is known that the well-definiteness of the path integral leads to the Feynman's $i\varepsilon$-prescription for the field propagator. I've found many ways of showing this in the literature, but it ...
Guillermo Franco Abellán's user avatar
9 votes
3 answers
2k views

Is the fermion mass Lagrangian term imaginary instead of real?

This seems to be an absurd question, but bear with me. In quantum field theory, the Dirac fermion mass Lagrangian term reads $$ m\bar\psi \psi = m(\bar\psi_L \psi_R + \bar\psi_R \psi_L) = m(\psi_L^\...
MadMax's user avatar
  • 3,605
9 votes
1 answer
994 views

Lie algebra of axial charges

Starting from the lagrangian (linear sigma model without symmetry breaking, here $N$ is the nucleon doublet and $\tau_a$ are pauli matrices) $L=\bar Ni\gamma^\mu \partial_\mu N+ \frac{1}{2} \partial_\...
gian_25's user avatar
  • 93
8 votes
1 answer
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Quantum Zeno effect and unstable particles

Is it possible to increase indefinitely the lifetime of unstable particles by applying the quantum Zeno effect? Is there a bound from theoretical principles about the maximum extension one can get in ...
diffeomorphism's user avatar
4 votes
1 answer
3k views

Where does the delta of zero $\delta(0)$ come from?

It is common when evaluating the partition function for a $O(N)$ non-linear sigma model to enforce the confinement to the $N$-sphere with a delta functional, so that $$ Z ~=~ \int d[\pi] d[\sigma] ~ \...
ZachMcDargh's user avatar
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63 votes
4 answers
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How exact is the analogy between statistical mechanics and quantum field theory?

Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...
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