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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Can quantum field theory be seen as an epistemic restriction on (quantum) causal structure

Suppose we take Vicary's quantum harmonic oscilator as a kind of "toy quantum field theory". Next, take the category of internal comonoids to not represent the background causal structure. We ...
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What does QFT “get right” that QM “gets wrong”?

Or, why is QFT "better" than QM? There may be many answers. For one example of an answer to a parallel question, GR is better than Newtonian gravity (NG) because it gets the perihelion advance of ...
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A question from Srednicki's QFT textbook

I have a question in Srednicki's QFT textbook. In order to compute the vacuum to vacuum transition amplitude given by : $$\left \langle 0|0 \right \rangle_{J}~=~\int \left [ d\varphi \right ]e^{i\int ...
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383 views

From quantization under external classical gauge field to a fully quantized theory

Let me take QED for example to clarify my question: The textbook-approach(at least for Peskin&Schroeder) to quantize ED is to first quantize EM field and Dirac field as free fields respectively, ...
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390 views

Why is ${\partial^i}{\partial_i\phi}$ = ${\partial^i {\phi}}{\partial_i{\phi}}$?

This notation can be found on page 254 of Victor Stenger's Comprehensible Cosmos and in David Tong's Lectures on QFT (Equation 2.4 http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf), and in EDIT: on ...
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228 views

How to define a field? [duplicate]

Possible Duplicate: What is a field, really? What are electromagnetic fields made of? What is a field ? What is magnetic field or other fields made of or what it is, How do u define it ...
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Why did Standard Model never sense a requirement to include gravitational quantum? [closed]

Standard Model is advanced (lorentz invariant) version of Quantum physics. It tried to include everything which came in the way while understanding quantum world. It even didn't bother to include ...
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693 views

Higgs field questions

The Wikipedia article about Higgs field poses some questions to me. The article says that the Higgs field is a "nonthermal" field, a field whose energy does not decrease as the universe expands, ...
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247 views

How can a pion have a mass, given it's a “field mediator” and created/destroyed continuously?

Maybe some of my assumptions here are basically wrong, but isn't it true that pion is the "mediator" for the strong force field. the quantum field theory basically says that there are no fields, ...
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447 views

How to calculate Rest Mass practically with Standard Model?

With relativistic physics, we can apply force to see resistance against acceleration. It'd give us relativistic mass and we have well established formula to get to the Rest Mass as long as we know the ...
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561 views

What is the ontological status of Faddeev Popov ghosts?

We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they ...
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Does Dark Matter interact with Higgs Field?

Dark matter does have gravitational mass as we know from its discovery. Does it have inertial mass?
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751 views

Does a spin-2 particle really return to its previous state after 180° rotation?

It is often claimed that spin-2 particles return to their previous state after $\pi$ rotation, just like spin-1/2 particles return after $4\pi$ rotation. But my calculation suggests otherwise. Let z ...
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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 ...
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569 views

Is the Higgs a quantum field or a particle?

The Higgs is not detected in the asymptotic data, so it is possible that there is no particle interpretation for the Higgs quantum field. Indeed, the Higgs potential is only positive definite if the ...
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What is the difference between pole and running mass?

For example, when we meassure Higgs boson mass to be 125 GeV, do we think about renormalized or pole mass? Should the mass of the Higgs change if it is produced at higher energies?
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1answer
179 views

Where can one learn about dispersion relations for S-matrices?

Most textbooks on quantum field theory never mention dispersion relations at all. Where can one learn about dispersion relations for S-matrices?
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371 views

Twistor notation in space-time (Part 1)

This is sort of a continuation of this and this previous discussions. In the first of my links one sees the surjective isometry between real or complex $(1,3)$ signature Minkowski space and the real ...
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210 views

What is Supersymmetry (SuSy)? [closed]

In particle physics, supersymmetry (often abbreviated SUSY) is a symmetry that relates elementary particles...etc. what is symmetry breaking? What is supersymmetry (SUSY)? What is spontaneous ...
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666 views

Winding number in the topology of magnetic monopoles

I am reading on magnetic monopoles from a variety of sources, eg. the Jeff Harvey lectures.. It talks about something called the winding $N$, which is used to calculate the magnetic flux. I searched ...
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Is there any correlation between the energy density fluctuations of two separate systems in a vacuum state?

I think the title says it all. What I am curious to find out is if there are any observable changes in the fluctuations of zero-point energy in a vacuum state system that are the consequence of ...
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2answers
405 views

Do other particles besides scalars admit tachyonic solutions?

Do other particles besides scalars admit tachyonic solutions? For example fermions or gauge-boson tachyons? The picture in my head is that a tachyonic scalar simply rolls off some unstable potential ...
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2answers
734 views

M-theory no lagrangian?

Is there any formulated lagrangian (density) for M-theory? If not, why is there no lagrangian? If not, is this related to many vacua existing? Thnx.
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123 views

What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT?

What kinds of inconsistencies would one get if one starts with Lorentz noninvariant Lagrangian of QFT? The question is motivated by this preprint arXiv:1203.0609 by Murayama and Watanabe. Also, what ...
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191 views

Exercise QFT and CFT

Consider the action functional $S[z;t_1,t_2]=\int_{t_1}^{t^2}[g(z,\bar{z})\dot{z}\dot{\bar{z}}]^{\frac{1}{2}}dt$ with $z(t)$ a complex path with end points $z_i=z(t_i),\; i=1,2$. $g(z,\bar{z})$ is a ...
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How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer?

How do you simulate a quantum gauge theory in a gauge with negative norms on a quantum computer? There are some gauges with negative norms. It's true that if restricted to gauge invariant states, the ...
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1answer
225 views

Does there exist a nonrelativistic physical system in which the effective long-distance fields violate spin/statistics?

The nonrelativistic Schrodinger field allows spin independent of statistics, so that you can imagine a nonrelativistic Schrodinger scalar field with Fermionic statistics, or a Schrodinger spinor field ...
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887 views

The meaning of Goldstone boson equivalence theorem

The Goldstone boson equivalence theorem tells us that the amplitude for emission/absorption of a longitudinally polarized gauge boson is equal to the amplitude for emission/absorption of the ...
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1answer
243 views

Non-localities in Wilsonian effective action

Why terms non-analytical dependent on momenta in the effective action (in momentum space) are non-local? How to see this directly?
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285 views

Gauge symmetry description for $\phi^4$?

That is a follow-up to this question: Gauge symmetry is not a symmetry? Ok, gauge symmetry is not a symmetry, but ... ... a redundancy in our description, by introducing fake degrees of freedom ...
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4answers
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What is spontaneous symmetry breaking in QUANTUM GAUGE systems?

Wen's question What is spontaneous symmetry breaking in QUANTUM systems? is cute, but here's an even cuter question. What is spontaneous symmetry breaking in QUANTUM GAUGE systems? There are some ...
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1answer
524 views

How to find the Green's Functions for time-dependent inhomogeneous Klein-Gordon equation?

I'm trying to find the Green's functions for time-dependent inhomogeneous Klein-Gordon equation which is : \begin{align*}‎‎ \left[ -‎ ‎\nabla ‎^2 + ‎‎‎‎\frac{1}{c^2} ‎‎\dfrac{\partial ^2}{\partial ...
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1answer
263 views

Imaginary pertubation to a Hamiltonian: how is it the same as rotation to imaginary time?

I am struggling with the following affirmation found in Ryder's QFT book, page 177: instead of rotating the time axis as we have done, the ground state contribution may be isolated by adding a ...
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490 views

What tree-level Feynman diagrams are added to QED if magnetic monopoles exist?

Are the added diagrams the same as for the $e-\gamma$ interaction, but with "$e$" replaced by "monopole"? If so, is the force between two magnetic monopoles described by the same virtual ...
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1answer
241 views

Straightforward questions about calculating SUSY F-terms

So in the Lagrangian for a SUSY theory we have the F-terms, which I have seen written (e.g., in Stephen Martin's SUSY primer) as $F^*_i F^i$ where $F^i = \frac{\partial W}{\partial \phi^i}$. I ...
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1answer
569 views

Spontaneous symmetry breaking and 't Hooft and Polyakov monopoles

What is spontaneous symmetry breaking from a classical point of view. Could you give some examples, using classical systems.I am studying about the 't Hooft and Polyakov magnetic monopoles solutions, ...
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344 views

Commutator of scalar fields

So, in the calculation of $ D(t,r) = \left[ \phi(x) , \phi(y) \right] $, where $ t= x^0 - y^0,~ \vec{r} = \vec{x} - \vec{y} $ you need to calculate the following integral $$ D(t,r) = \frac{1}{2\pi^2 ...
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How does one calculate the quantum propagator for a massless photon

So I want to calculate the quantum massless photon propagator. To do this, I write $$ A_\mu(x) = \sum\limits_{i=1}^2 \int \frac{d^3p}{(2\pi)^3} \frac{1}{\sqrt{2\omega_p}} \left( \epsilon_\mu^i (p) ...
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222 views

How important are constrained Hamiltonian dynamics and BRST transformation as a formalism?

I am to study BRST transformations, for which I'm currently trying to understand constrained Hamiltonian dynamics to treat systems with singular Lagrangians. The crude recipe followed is Lagrangian -> ...
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Chiral anomalies à la Fujikawa: Why don't we just take another measure?

When deriving the chiral anomaly in the non perturbative approach for a theory of massless Dirac fermions, you start by showing that the path-integral measure is not invariant unter the chiral ...
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What is the importance of Vacua in Field Theory?

I understand that defining the Vacuum is important in Field Theory, why? Is this because it is the 'ground' state, before particles are added, so defines the 'background'? I assume its not important ...
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4answers
563 views

Is String Theory a Field Theory?

Is String Theory a Field or Quantum Mechanical Theory of the String rather than a Particle? I should know this having studied this for a term, but we jumped into the deep end, without really ...
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396 views

Non-relativistic spinors

Even in a non-relativistic theory Spinors can arise as irreducible representations of the rotation subgroup of the symmetries of the theory. Why do people then put so much emphasize on the role of ...
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is cosmic expansion related with IR divergencies?

This question is related to renormalization, but in the IR limit. It is assumed that unitarity does take care of IR divergencies in interacting theories like QED. But how would one interpret ...
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1answer
429 views

Why can i replace a gauge field by the current it couples to in the calculation of a greens function?

I am reading about anomalies in QFT at the moment and have a related question. Often people calculate the time ordered expectation value of some fields (in QED for example) by replacing the field ...
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1answer
243 views

Propagator of the Klein-Gorden equation

Does this integral converge? My question is related to this one: Free particle propagation amplitude calculation I am reading the book of Peskin and Schroesder. In the second page of their chapter ...
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513 views

Gauge-invariant field strength term in Yang-Mills Lagrangian

I am reading the chapter of non-abelian gauge invariance from Peskin and Schroeder. Why is the term $-\frac{1}{4}(L_{\mu\nu}^i)^{2} $ gauge invariant?
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Does the vacuum energy problem of quantum field theory only occur in the Hamiltonian approach, or also in the path integral approach and in AQFT?

In a standard QFT class, you're being indoctrinated that there is the "infinite vacuum energy density problem". (This is sometimes paraphrased as the "cosmological constant problem", which is in my ...
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Correlation function which has branch cut in momentum space

When correlation function has branch cut in momentum space, how to find correlation in coordinate space? For example $$ \tilde {G}(\omega) = \frac{2i}{\omega+(\omega^2-\nu^2)^{1/2}}$$ How to get the ...
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Semiclassical QED and long-range interaction

I'm interested in the (very) low energy limit of quantum electrodynamics. I've seen that taking this limit does not yield Maxwell equations, but a quantum corrected non-linear version of them. If ...