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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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: ...
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509 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The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
16
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505 views

O(N) sigma model at large N

I would like to better understand the main principles of large-N expansion in quantum field theory. To this end I decided to consider simple toy-model with lagrangian (from Wikipedia) $ \mathcal{L} = ...
16
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1k views

Gauge redundancies and global symmetries

It is often said that local (gauge) transformation is only redundancy of description of spin one massless particles, to make the number degrees of freedom from three to two. It is often said that ...
14
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393 views

TQFTs and Feynman motives

Questions Is a topological quantum field theory metrizable? or else a tqft coming from a subfactor? For a given metric, are there always renormalization and Feynman diagrams? Is there always a Feynman ...
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352 views

Relation among anomaly, unitarity bound and renormalizability

There is something I'm not sure about that has come up in a comment to other question: Why do we not have spin greater than 2? It's a good question--- the violation of renormalizability is linked ...
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250 views

How to apply the Faddeev-Popov method to a simple integral

Some time ago I was reviewing my knowledge on QFT and I came across the question of Faddeev-Popov ghosts. At the time I was studying thеse matters, I used the book of Faddeev and Slavnov, but the ...
13
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206 views

Intuitive sketch of the correspondence of a string theory to its limiting quantum field theory

I'm looking for an intuitive sketch of how one shows the correspondence of string theory to a certain QFT. My best guess is that one calculates the scattering amplitudes in the string theory as a ...
12
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167 views

Monopoles and the magnetic Higgs mechanism

In a paper of 't Hooft about the rôle of magnetic monopoles for a model of quark confinement, I don't understand the following sentence (end af paragraph 14) [...] in order for monopoles to ...
12
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526 views

Renormalization group evolution equations and ill-posed problems

There is a class of observables in QFT (event shapes, parton density functions, light-cone distribution amplitudes) whose the renormalization-group (RG) evolution takes the form of an ...
11
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344 views

Apparent failure of SUSY nonrenormalization theorem

I am having trouble reconciling two pieces of information. Consider supersymmetric QED, i.e. a supersymmetric U(1) gauge theory with two chiral superfields of opposite charges, $h$ and $\hat{h}$. The ...
11
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446 views

Noether currents for the BRST tranformation of Yang-Mills fields

The Lagrangian of the Yang-Mills fields is given by $$ \mathcal{L}=-\frac{1}{4}(F^a_{\mu\nu})^2+\bar{\psi}(i\gamma^{\mu} D_{\mu}-m)\psi-\frac{1}{2\xi}(\partial\cdot A^a)^2+ ...
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121 views

time-dependent Hartree-Fock for two-component bosons

How does the ansatz for the time-dependent Hartree-Fock wavefunction look like in the second quantization if we have two-component boson system and in one case the Hamiltonian commutes with number of ...
10
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139 views

experimental bounds on microcausality violation

In "The Great Soviet Encyclopedia", 3rd Edition from 1970-1979, (evidently an old book), some V. I. Grigor’ev has a well-written little note on microcausality. Towards the end he states an ...
9
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93 views

Stimulated Emission in QED

The explanations of stimulated emission which I have found all describe the phenomenon in terms of non-relativistic quantum mechanics. How might you describe it in a field theory such as QED? In ...
9
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384 views

Capturing (perturbatively) non-equilibrium field theory effects using “elementary” methods

I am considering a system of two interacting scalar fields: $\psi$, and $\phi$. The Lagrangian is given by: \begin{equation} ...
9
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381 views

Duality between Euclidean time and finite temperature, QFT and quantum gravity, and AdS/CFT

The thoughts below have occurred to me, several years ago (since 200x), again and again, since I learn quantum field theory(QFT) and statistical mechanics, and later AdS/CFT. It is about the duality ...
9
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195 views

Faddeev Popov Gauge Fixing in Electromagnetism

Reading section 9.4 in Peskin, I am wondering about the following: The functional integral on $A_{\mu}$ diverges for pure-gauge configurations, because for those configurations, the action is zero. ...
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182 views

Intuition behind mass corrections to massless fermions

I'm trying to understand the intuition behind the mass correction to massless fermions. To be concrete lets consider a theory with a massless Weyl fermion ($\psi $), as well as two massive particles, ...
9
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313 views

Gauge fields in Polyakov's treatment of renormalization for nonlinear sigma model

I am deriving the results of renormalization for nonlinear sigma model using Polyakov approach. I am closely following chapter 2 of Polyakov's book--- ``Gauge fields and strings''. Action for the ...
9
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489 views

Penrose's Zig-Zag Model and Conservation of Momentum

I was reading through Penrose's Road to Reality when I saw his interesting description of the Dirac electron (Chapter 25, Section 2). He points out that in the two-spinor formalism, Dirac's one ...
8
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1k views

Reflection positivity in general

In the Euclidean QFT obtained by "Wick-rotating" a unitary QFT, the correlation functions satisfy a property called reflection positivity, see e.g. this Wikipedia article for the case of a scalar ...
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344 views

Instantons and Borel Resummation

As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are ...
7
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138 views

What are the remaining obstacles to low-energy quantum gravity?

In a 2003 review Burgess outlined how the QFT perturbative methodology is being extended to gravity, and described some effective quantum gravity expansions that reproduce general relativity in the ...
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284 views

Do “typical” QFT's lack a lagrangian description?

Sometimes as a result of learning new things you realize that you are incredibly confused about something you thought you understood very well, and that perhaps your intuition needs to be revised. ...
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266 views

Integration & bremsstrahlung calculation

In this paper (relevant pdf section) that I'm reading, involving the calculation of bremsstrahlung in electron proton scattering (diagram below), the author calculates the integral over outgoing ...
7
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132 views

Electric charges on compact four-manifolds

Textbook wisdom in electromagnetism tells you that there is no total electric charge on a compact manifold. For example, consider space-time of the form $\mathbb{R} \times M_3$ where the first factor ...
7
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86 views

Candidates for holographic QFT of 4D Einstein gravity

If we are to believe that holographic principle holds over a wide number of dimensions, and gravitational theories, but specially, those that are relevant to our universe, then there must be some 3D ...
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118 views

Topology-dependent groud state degeneracy of $B \wedge F + B \wedge B$ and $B \wedge F + B \wedge B \wedge B$

There are some examples of topological BF theory with extra terms allow it still being topological. See this Ref. paper In 4d (3+1D), we have the trace of: $$ \int\frac{k}{2\pi}\text{Tr}[B \wedge F + ...
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346 views

How do we know for sure a theory is non-renormalizable?

In quantum field theory, we are looking for a Lagrangian that is, amongst other, renormalizable. But how do we determine whether or not a theory is renormalizable? Is this purely done by power ...
7
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152 views

Why is it hard to give a lattice definition of string theory?

In Polyakov's book, he explains that one possible way to compute the propagator for a point particle is to compute the lattice sum $\sum_{P_{x,x'}}\exp(-m_0L[P_{x,x'}])$, where the sum goes over all ...
7
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300 views

Dimensional regularization and IR divergences and scale invariance

I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant. Does dimensional regularization see "all" kinds of divergences? I mean - what ...
7
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257 views

Regulating the sum in Casimir Force

I am trying to evaluate the Casimir force using a Gaussian regulator (I know there are other much easier ways to do this, but I want to try this!) We then are reduced to evaluating the sum $$ ...
7
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154 views

gravitational convergence of light

light has a non-zero energy-stress tensor, so a flux of radiation will slightly affect curvature of spacetime Question: assume a flux of radiation in the $z$ direction, in flat Minkowski space it ...
7
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840 views

On the naturalness problem

I know that there are several questions about the naturalness (or hierarchy or fine-tunning) problem of scalars masses in physics.stackexcange.com, but I have not found answers to any of the following ...
7
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410 views

Descent equation and anomaly polynomial

I am just reading Ryu, Moore and Ludwig's paper on classifications of topological insulators and quantum anomaly. They are trying to relate the quantum anomaly as a signal of the presence of a ...
6
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70 views

Is it possible to do a path integral between two boundaries analytically on a quantum lattice?

I have been trying to perform some path integral between two boundaries for a massless scalar field $$\int_{\varphi(t_a, \vec{x})}^{\varphi(t_b, \vec{x})} \mathcal{D}\varphi(x)e^{iS[\varphi(x)]}$$ ...
6
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0answers
76 views

Understanding the $\phi^4$ phase diagram

I'm having trouble making sense of this phase diagram. The model is a $V(\phi)=g_2 \phi^2+g_4\phi^4$ scalar field theory. Here's what I think I understand: the capital letters represent different ...
6
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0answers
111 views

Canonical second quantization vs canonical quantization with multisymplectic form in AQFT

First of all, I'm a mathematician that knows less than the basics of QFT, so forgive me if this question is trivial. Please, keep in my mind that my background in physics is very poor. 1) The usual ...
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237 views

Peskin-Schroeder Problem 3.5, supersymmetric theories regarded as field theories on parameter space w/commuting & anticommuting coordinates?

I know how to do Problem 3.5 of Peskin-Schroeder. Let us organize the fields $\phi$, $\chi_\alpha$, $F$ of Problem 3.5 into a superfield$$\Phi(x + i\theta\sigma\overline{\theta}, \theta) = \phi(x) ...
6
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0answers
78 views

Distinguishing between left-handed and right-handed weak coupling from electron-neutrino scattering

This question comes from Schwartz's QFT book, exercise 13.6. In it we consider a coupling between fermions (neutrinos and electrons in this particular case) and the Z boson of the form $g_V \bar{\psi} ...
6
votes
0answers
276 views

Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
6
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0answers
125 views

Why don't we have logarithms or exponentials of the fields in the Lagrangians?

All tbe Lagrangian densities I have seen have always been polynomials of the fields. Is this a coincidence or is there a reason forbid, say, Lagrangians with logarithms or exponentials of the fields?
6
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108 views

What is the physical interpretation of the automorphism on bounded operators induced by an S matrix?

In a QFT, the S-matrix $S$ is a unitary operator, that fixes the vacuum and commutes with the unitary operators implementing the action of the Poincare group on an appropriate Hilbert space $H$. ...
6
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0answers
120 views

Intuition for Homological Mirror Symmetry

first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand ...
6
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0answers
185 views

Questions regarding $D=4 $ ${\cal N}=4$ supersymmetric Yang-Mills

I have some questions regarding the $D=4 $ ${\cal N}=4$ super-Yang-Mills theory (the one with a really long action which can be acquired by compactifying the 10-dimensional ${\cal N}=1$ theory). I ...
6
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0answers
108 views

Is it possible to have fermions in Schwarzschild spacetime?

To my understanding Geroch proved that on 4-dimensional non-compact manifold a necessary and sufficient condition for a manifold to have a notion of spinors is to be parallelizabe .1 (General ...
6
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287 views

Effective Field Theory (EFT) decoupling top

The decoupling theorem of Appelquist-Carazzone says that if you want to decouple a particle, the low energy resulting theory need to be renormalizable. You can't do that for the top, because you break ...
6
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110 views

target category of extended field theory

For a topological field theory to be a true “extension” of an Atiyah-Segal theory, the top two levels of its target (ie its $(n-1)^{\text{st}}$ loop space) must look like $\text{Vect}$. What other ...
6
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107 views

What is a superfluid in field theoretic terms?

I'm wondering how one precisely defines a superfluid in terms of the effective field theory description. In Nicolis's paper http://arxiv.org/abs/1108.2513 there seems to be an extremely simple ...