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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How does the Higgs mechanism work?

I'm not a particle physicist, but I did manage to get through the Feynman lectures without getting too lost. Is there a way to explain how the Higgs field works, in a way that people like me might ...
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4answers
5k views

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 ...
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Is anti-matter matter going backwards in time?

Or: can it be proved that anti-matter definitely is nót matter going backwards in time? From wikipedia: There is considerable speculation as to why the observable universe is apparently almost ...
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8answers
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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? ...
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What is a complete book for quantum field theory?

I am searching for a complete and comprehensive book for QFT. What is, in your opinion, a good one?
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669 views

Interaction potential in standard $\phi^4$ theory

In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by $$S=\int d^d\! x ...
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Are W & Z bosons virtual or not?

W and Z bosons are observed/discovered. But as force carrying bosons they should be virtual particles, unobservable? And also they require to have mass, but if they are virtual they may be off-shell, ...
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What are the various physical mechanisms for energy transfer to the photon during blackbody emission?

By conservation of energy, the solid is left in a lower energy state following emission of a photon. Clearly absorption and emission balance at thermal equilibrium, however, thermodynamic equilibrium ...
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How do I construct the $SU(2)$ representation of the Lorentz Group using $SU(2)\times SU(2)\sim SO(3,1)$ ?

This question is based on problem II.3.1 in Anthony Zee's book Quantum Field Theory in a Nutshell (I'm reading this for fun- it isn't a homework problem.) Show, by explicit calculation, that ...
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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, ...
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Diff(M) as a gauge group and local observables in theories with gravity

In a gauge theory like QED a gauge transformation transforms one mathematical representation of a physical system to another mathematical representation of the same system, where the two mathematical ...
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3answers
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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 ...
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7answers
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Can energy be taken out of the QFT vacuum?

There have been recent questions about the vacuum. In my simplified knowledge the vacuum is like a ground state energy level, and also that there might even exist other lower energy levels than the ...
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Why isn't Higgs coupling considered a fifth fundamental force?

When I first learned about the four fundamental forces of nature, I assumed that they were just the only four kind of interactions there were. But after learning a little field theory, there are many ...
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What equation describes the wavefunction of a single photon?

The Schrödinger equation describes the quantum mechanics of a single massive non-relativistic particle. The Dirac equation governs a single massive relativistic spin-½ particle. The photon is a ...
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1answer
1k views

Schrodinger equation from Klein-Gordon?

One can view QM as a 1+0 dimensional QFT, fields are only depending on time and so are only called operators, and I know a way to derive Schrodinger's equation from Klein-Gordon's one. Assuming a ...
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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 ...
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2answers
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Virtual photon description of B and E fields

I continue to find it amazing that something as “bulky” and macroscopic as a static magnetic or electric field is actually a manifestation of virtual photons. So putting on your QFT spectacles, look ...
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2answers
431 views

Lie Groups and group extensions?

Is $U(1)$ x $SU(2)$ x $SU(3)$ a vector space over a field? I saw an article here http://en.wikipedia.org/wiki/Group_extension that seemed to me that a similar concept to a field extension was ...
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8answers
932 views

Why do physicists believe that particles are pointlike?

String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories. So why is it that it's popular ...
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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 ...
13
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5answers
1k views

Reading list in topological QFT

I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm ...
21
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2answers
2k views

Classical and quantum anomalies

I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or point-views: Anomalies are due to the fact that quantum field ...
19
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5answers
3k views

Why not using Lagrangian, instead of Hamiltonian, in non relativistic QM?

When we studied classical mechanics on the undergraduate level, on the level of Taylor, we covered Hamiltonian as well as Lagrangian mechanics. Now when we studied QM, on the level of Griffiths, we ...
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1answer
671 views

Why path integral approach may suffer from operator ordering problem?

In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path. What did ...
20
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3answers
545 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 ...
31
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3answers
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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 ...
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Can the photoelectric effect be explained without photons?

Lamb 1969 states, A misconception which most physicists acquire in their formative years is that the photoelectric effect requires the quantization of the electromagnetic field for its ...
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4answers
737 views

Is the world $C^\infty$?

While it is quite common to use piecewise constant functions to describe reality, e.g. the optical properties of a layered system, or the Fermi–Dirac statistics at (the impossible to reach exactly) ...
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1answer
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Measured Higgs mass and vacuum stability

There is such a thing, called "stability bound" on mass of the Higgs boson. The basic idea (as I understand it) is that we take Higgs self-coupling, and calculate its renormalization running. And it ...
21
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3answers
3k views

Good reading on the Keldysh formalism

I'd like some suggestions for good reading materials on the Keldysh formalism in a condensed matter context. I'm familiar with the imaginary time, coherent state, and path integral formalisms, but ...
8
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1answer
594 views

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 ...
6
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1answer
986 views

What is the relationship between string net theory and string / M-theory?

I've just learned from this one of Prof. Wen's answers that there exists a theory called string net theory. Since I've never heard about this before it picks my curiosity, so I`d like to ask some ...
18
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2answers
722 views

Why treat complex scalar field and its complex conjugate as two different fields?

I am new to QFT, so I may have some of the terminology incorrect. Many QFT books provide an example of deriving equations of motion for various free theories. One example is for a complex scalar ...
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4answers
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Do all massless particles (e.g. photon, graviton, gluon) necessarily have the same speed $c$?

I suppose there was a discussion already on speed-of-gravity-and-speed-of-light. But I silly wonder whether all the massless mediators of four fundamental forces, i.e. Graviton: $g_{\mu\nu}$ ...
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Why on-shell vs. off-shell matters?

The definitions between on- and off-shell are given in Wikipedia. Why is it so important in QFT to distinguish these two notions ?
61
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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 ...
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11answers
5k views

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 ...
23
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2answers
885 views

Why do we expect our theories to be independent of cutoffs?

Final edit: I think I pretty much understand now (touch wood)! But there's one thing I don't get. What's the physical reason for expecting the correlation functions to be independent of the cutoff? ...
18
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Haag's theorem and practical QFT computations

There exists this famous Haag's theorem which basically states that the interaction picture in QFT cannot exist. Yet, everyone uses it to calculate almost everything in QFT and it works beautifully. ...
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4answers
5k views

Why don’t photons interact with the Higgs field?

Why don’t photons interact with the Higgs field and hence remain massless?
7
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1answer
128 views

geometric quantization of the moduli space of abelian Chern-Simons theory

I wish to understand the statement in this paper more precisely: (1). Any 3d Topological quantum field theories(TQFT) associates an inner-product vector space $H_{\Sigma}$ to a Riemann surface ...
12
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3answers
1k views

Hypercharge for $U(1)$ in $SU(2)\times U(1)$ model

I understand that the fundamental representation of $U(1)$ amounts to a multiplication by a phase factor, e.g. EM. I thought that when it is extended to higher dimensional representations, it would ...
3
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1answer
1k views

Why/How is this Wick's theorem?

Let $\phi$ be a scalar field and then I see the following expression for the square of the normal ordered version of $\phi^2(x)$. $$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 $$ ...
6
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4answers
776 views

Do strong and weak interactions have classical force fields as their limits?

Electromagnetic interaction has classical electromagnetism as its classical limit. Is it possible to similarly describe strong and weak interactions classically?
5
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2answers
768 views

Why are anticommutators needed in quantization of Dirac fields?

Why is the anticommutator actually needed in the canonical quantization of free Dirac field?
5
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4answers
3k views

Collision of two photons

Could someone explain me how will be look like collision of two photons? Will they behave like: Electromagnetic waves, they will interpher with each other and keep they wave nature Particles and ...
8
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2answers
3k views

What are zero modes?

What are zero modes in quantum field theory, and what are they used for? Or, where can I read about them? I was never able to find a good introduction on the subject. I am particularly interested in ...
7
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2answers
2k views

Definition of Casimir operator and its properties

I'm not sure which is the exact definition of a Casimir operator. In some texts it is defined as the product of generators of the form: $$X^2=\sum X_iX^i$$ But in other parts it is defined as an ...