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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Gauge symmetry is not a symmetry?
I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
39
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0answers
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Superfields and the Inconsistency of regularization by dimensional reduction
Question:
How can you show the inconsistency of regularization by dimensional reduction in the $\mathcal{N}=1$ superfield approach (without reducing to components)?
Background and some references:
...
36
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1answer
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Why do we not have spin greater than 2?
It is commonly asserted that no consistent, interacting quantum field theory can be constructed with fields that have spin greater than 2 (possibly with some allusion to renormalization). I've also ...
33
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18answers
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Quantum Field Theory from a mathematical point of view
I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view.
Are there any good books or other reference ...
25
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3answers
167 views
Continuum theory from lattice theory
I am looking for references on how to obtain continuum theories from lattice theories. There are basically a few questions that I am interested in, but any references are welcome. For example, you can ...
22
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3answers
1k views
Scattering of light by light: experimental status
Scattering of light by light does not occur in the solutions of Maxwell's equations (since they are linear and EM waves obey superposition), but it is a prediction of QED (the most significant Feynman ...
22
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6answers
2k views
Formalizing Quantum Field Theory
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 ...
22
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3answers
1k views
A No-Nonsense Introduction to Quantum Field Theory
I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page here. pdf here), a 24-page overview of the topic, very helpful for beginning study. It all got me over the hump ...
21
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9answers
2k views
Rigor in quantum field theory
Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
21
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13answers
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Suggested reading for renormalization (not only in QFT)
What papers/books/reviews can you suggest to learn what renormalization "really" is? Standard QFT textbooks are usually computation-heavy and provide little physical insight in this respect - after my ...
21
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9answers
2k views
Is a “third quantization” possible?
Classical mechanics: $t\mapsto \vec x(t)$, the world is described by particle trajectories $\vec x(t)$ or $x^\mu(\lambda)$, i.e. the Hilbert vector is the particle coordinate function $\vec x$ (or ...
21
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1answer
190 views
Vassiliev Higher Spin Theory and Supersymmetry
Recently there is renewed interest in the ideas of Vassiliev, Fradkin and others on generalizing gravity theories on deSitter or Anti-deSitter spaces to include higher spin fields (utilizing known ...
21
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2answers
167 views
Renormalization Group for non-equilibrium
For equilibrium/ground state systems, a (Wilson) renormalization group transformation
produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
18
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3answers
174 views
Geometric Langlands as a partially defined topological field theory
I have heard from several physicists that the Kapustin-Witten topological twist of $N=4$ 4-dimensional Yang-Mills theory ("the Geometric Langlands twist") is not expected to give
rise to fully defined ...
18
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2answers
131 views
Does 4D N = 3 supersymmetry exist?
Steven Weinberg's book "The Quantum Theory of Fields", volume 3, page 46 gives the following argument against N = 3 supersymmetry:
"For global N = 4 supersymmetry there is just one supermultiplet ... ...
18
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3answers
1k views
Why are von Neumann Algebras important in quantum physics?
At the moment I am studying operator algebras from a mathematical point of view. Up to now I have read and heard of many remarks and side notes that von Neumann algebras ($W^*$ algebras) are important ...
18
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2answers
160 views
Values of SM parameters at one certain scale
The general question is:
What are the values of Standard Model parameters (in the $\bar{MS}$ renormalization scheme) at some scale e.g. $m_{Z}$? As its parametrization in Yukawa matrices is not unique ...
17
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2answers
39 views
Significance of the hyperfinite $III_1$ factor for axiomatic quantum field theory
Using a form of the Haag-Kastler axioms for quantum field theory (see AQFT on the nLab for more details), it is possible in quite general contexts to prove that all local algebras are isomorphic to ...
17
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3answers
1k views
A pedestrian explanation of Renormalization Groups - from QED to classical field theories
shortly after the invention of quantum electrodynamics, one discovered that the theory had some very bad properties. It took twenty years to discover that certain infinities could be overcome by a ...
17
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7answers
624 views
Is there a symmetry associated to the conservation of information?
Conservation of information seems to be a deep physical principle.
For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory.
We may wonder if there is an underlying ...
17
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0answers
330 views
Sigma Models on Riemann Surfaces
I'm interested in knowing whether sigma models with an $n$-sheeted Riemann surface as the target space have been considered in the literature. To be explicit, these would have the action ...
16
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2answers
89 views
Can symmetry generators be used for quantization?
Take the Poincaré group for example. The conservation of rest-mass $m_0$ is generated by the invariance with respect to $p^2 = -\partial_\mu\partial^\mu$. Now if one simply claims
The state where ...
16
votes
3answers
143 views
Regularization of the Casimir effect
For starters, let me say that although the Casimir effect is standard textbook stuff, the only QFT textbook I have in reach is Weinberg and he doesn't discuss it. So the only source I currently have ...
16
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2answers
308 views
Kähler potential vs full effective potential
In evaluating the vacuum structure of quantum field theories you need to find the minima of the effective potential including perturbative and nonperturbative corrections where possible.
In ...
16
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3answers
93 views
Paper listing known Seiberg-dual pairs of N=1 gauge theories
Is there a nice list of known Seiberg-dual pairs somewhere? There are so many papers from the middle 1990s but I do not find comprehensive review. Could you suggest a reference?
Seiberg's original ...
16
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1answer
233 views
Why is there no theta-angle (topological term) for the weak interactions?
Why is there no analog for $\Theta_\text{QCD}$ for the weak interaction? Is this topological term generated? If not, why not? Is this related to the fact that $SU(2)_L$ is broken?
16
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2answers
259 views
Edge theory of FQHE - Unable to produce Green's function from anticommutation relations and equation of motion?
I'm studying the edge theory of the fractional quantum Hall effect (FQHE) and I've stumbled on a peculiar contradiction concerning the bosonization procedure which I am unable to resolve. Help!
In ...
16
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1answer
81 views
Asymptoticity of Pertubative Expansion of QFT
It seems to be lore that the perturbative expansion of quantum field theories is generally asymptotic. I have seen two arguments.
i)There is the Dyson instability argument as in QED, that is showing ...
15
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6answers
203 views
Which QFTs were rigorously constructed?
Which QFTs have mathematically rigorous constructions a la AQFT? I understand there are many such constructions in 2D, in particular 2D CFT has been extensively studied mathematically. But even in 2D ...
15
votes
6answers
2k views
Why should the Standard Model be renormalizable?
Effective theories like Little Higgs models or Nambu-Jona-Lasinio model are non-renormalizable and there is no problem with it, since an effective theory does not need to be renormalizable. These ...
15
votes
7answers
1k views
Is the wave-particle duality a real duality?
I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. I most recently heard this in this video. However, I wonder; is this actually a duality? ...
15
votes
3answers
840 views
How general is the Lagrangian quantization approach to field theory?
It is an usual practice that any quantum field theory starts with a suitable Lagrangian density. It has been proved enormously successful. I understand, it automatically ensures valuable symmetries of ...
15
votes
4answers
168 views
What is a simple intuitive way to see the relation between imaginary time (periodic) and temperature relation?
I guess I never had a proper physical intuition on, for example, the "KMS condition". I have an undergraduate student who studies calculation of Hawking temperature using the Euclidean path integral ...
15
votes
1answer
131 views
Models of higher Chern-Simons type
It has long been clear that (the action functional of) Chern-Simons theory has various higher analogs and variations of interest. This includes of course traditional higher dimensional Chern-Simons ...
15
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4answers
494 views
Elegant approaches to quantum field theory
I have been reading Quantum Mechanics: A Modern Development by L. Ballentine. I like the way everything is deduced starting from symmetry principles. I was wondering if anyone familiar with the book ...
15
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0answers
106 views
Systematic approach to deriving equations of collective field theory to any order
The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
15
votes
3answers
918 views
Is decoherence even possible in anti de Sitter space?
Is decoherence even possible in anti de Sitter space? The spatial conformal boundary acts as a repulsive wall, thus turning anti de Sitter space into an eternally closed quantum system. Superpositions ...
14
votes
4answers
610 views
What is anti-matter?
Matter-- I guess I know what it is ;) somehow, at least intuitively. So, I can feel it in terms of the weight when picking something up. It may be explained by gravity which is itself is defined by ...
14
votes
2answers
274 views
BPS states : Mathematical definition
First of all, let me congratulate the theoretical physics community for this site. I am a mathematics student with very little background in phyiscs. The question I want to ask is:
What is the proper ...
14
votes
1answer
319 views
If the ground states of interacting QFTs are so complicated, how did Nature find them?
My question was inspired by trying to understand the paper Quantum Algorithms for Quantum Field Theories, by Jordan, Lee, and Preskill. The main result of that paper is that scattering experiments in ...
14
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1answer
63 views
Instantons and Non Perturbative Amplitudes in Gravity
In perturbative QFT in flat spacetime the perturbation expansion typically does not converge, and estimates of the large order behaviour of perturbative amplitudes reveals ambiguity of the ...
14
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3answers
796 views
Why does dilation invariance often imply proper 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 ...
13
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5answers
131 views
Other processes than formal power series expansions in quantum field theory calculations
I am not sure if this question is too naive for this site, but here it goes. In QFT calculations, it seems that everything is rooted in formal power series expansions, i.e. , what dynamical systems ...
13
votes
6answers
253 views
Is there a theorem that says that QFT reduces to QM in a suitable limit? A theorem similar to Ehrenfest's theorem?
Is there a theorem that says that QFT reduces to QM in a suitable limit?
Of course, it should be, as QFT is relativisitc quantum mechanics.
But, is there a more manifest one? such as Ehrenfest's ...
13
votes
3answers
535 views
Quantum Field Theory Variants
I am a math guy, so sorry for the naivety. When I peruse the wikipedia I see many "variants" of quantum field theory...conformal quantum field theory, topological quantum field theory, ...
13
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3answers
64 views
Status of local gauge invariance in axiomatic quantum field theory
In his recent review...
Sergio Doplicher, The principle of locality: Effectiveness, fate, and challenges, J. Math. Phys. 51, 015218 (2010), doi
...Sergio Doplicher mentions an important open ...
13
votes
2answers
65 views
Calculating correlation functions of exponentials of fields
In their book Condensed Matter Field Theory, Altland and Simons often use the following formula for calculating thermal expectation values of exponentials of a real field $\theta$:
$$ \langle ...
13
votes
2answers
160 views
Applications of the Feynman-Vernon Influence Functional
I am looking for a reference where the Feynman-Vernon influence functional was defined and used in the context of relativistic quantum field theory. This functional is one method to describe ...
13
votes
3answers
1k views
Good reading on the Keldysh formalism
I'd like some suggestions for good reading materials on the Keldysh formalism in a condmat context. I'm familiar with the imaginary time, coherent state, path integral formalism, but lately I've been ...
13
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3answers
759 views
Would a spin-2 particle necessarily have to be a graviton?
I'm reading often that a possible reason to explain why the Nobel committee is coping out from making the physics Nobel related to the higgs could be among other things the fact that the spin of the ...
