# Tag Info

14

IMHO, the notation $\int_a^b\mathrm{d}x\,f(x)$ is much cleaner than $\int_a^b f(x)\,\mathrm{d}x$, because the integration variable ($x$) and its associated integral range $(\int_a^b$) are kept together. This is particularly important in lengthy and multi-dimensional integrals. Consider  \Upsilon_{pq}(k)= \int_0^\infty\mathrm{d}x ...

12

It's not just QFT literature. Physicists, especially adult research physicists, find this notation sensible and popular – even though it may be more popular among particle physicists than elsewhere. Formally, $dx\,f(x)$ is a product of two factors and $\int$ is a form of a sum. Because product is commutative, it doesn't hurt when the order is interchanged. ...

8

Besides the reasons listed in Lubos Motl's answer, here is another reason for the $\int \!dx ~f(x)$ notation: By writing the integral sign $\int_a^b$ and $dx$ next to each other in multiple nested integrations, it becomes more easy to trace which limits belong to which integration. This becomes particularly handy when changing the orders of integration. ...

3

Photons undergo angular acceleration in very strong gravitational fields, gravitational lensing.. An acceleration can be defined in its change of direction, angular acceleration in radians/second^2, so the answer is positive, yes, light can be accelerated, but its speed will still be c, only the direction relative to the gravitational source changes.

3

In condensed matter "bulk" does not refer to the dimensionality of the problem but the location in the material. It refers to the volume of the crystal, as opposed to, e.g., surface effects. Many organic conductors behave as 1D systems, yet you can talk about bulk properties. Copper oxide superconductors have a 2D physics. However, often you will find ...

3

Elementary particle physics is an outgrowth of what was high energy physics, historically at the time. X-rays were high energy physics when first discovered, they are part of the tools of solid state physics now. Alpha particles and gamma rays were high energy physics at their time, they are nuclear physics now. Mesons discovered in cosmic rays started ...

3

As an alternative to Anna's nice historical discourse a heuristic that covers modern uses of the phrase would be that energies are "high" when the QCD can be treated as perturbative. That regime sets in considerably above the nucleon mass scale, say 10s of GeV. So LHC physics is in, JLAB physics is out (even with the 12 GeV upgrade).

3

In a hydrogen atom the kinetic energy is on the order of $8$ eV. From $T = \frac{p^2}{2m}$ we get that the typical momentum is about $3$ keV/c ($m = 511$ keV/$c^2$). On the other hand $\hbar/(2a_0)\approx 1.2$ keV/c where $a_0$ is the Bohr radius, which is about the size of a hydrogen atom. Since these quantities are of similar magnitude the Heisenberg ...

2

Sure, there are a lot of them ! In my opinion, a basic conceptual reason for this is that most of the time, models used to describe a given class of physical phenomena have at their boundaries "uncontrollable" phenomena (otherwise we could extend the model straightforwardly and include them). So it is often the case that when you try to take some limits, the ...

2

No-one knows what dark matter and dark energy are, so any comments on your question are necessarily speculative. Having said this, dark matter is generally considered to be just matter and the adjective dark is not meant to signify anything mysterious but merely that it doesn't interact with electromagnetic radiation or charge. The most popular suggestion ...

1

Classically, spinors are insignificant, and should not be expected to fulfill any physical role, since they are not proper representations of the rotation group $\mathrm{SO}(3)$ or the Lorentz group $\mathrm{SO}(1,3)$. The importance of spinors does not arise from any classically intuitive thinking about orientations. Instead, the reason why spinors appear ...

1

Spin-resolved current in the context of scanning probe methods means that due to a finite magnetisation of probe and sample the current consists of electrons of one spin in a larger quantity than of the other. Spin current usually refers to current that consists exclusively of electrons of one spin direction.

1

If you want to hard code a specific set of qubits you could measure the spin (pass it through an inhomogeneous magnetic field) of a spin 1/2 system and then if you get the wrong spin, flip it (tune a photon to a wavelength based on a given uniform magnetic field strength). If you want to read an output you could do the same thing, measure the spin of each ...

1

Sciences use mathematics only as a tool. In almost all such applications, mathematical problems (such as pointwise vs uniform convergence) are not inherent to the scientific problem at hand, but arise from the mathematical model and are indicative of its limitations. For example, when modelling a large collection of particles (be it in a solid (crystal) or ...

1

Triangles are the "strongest shape" only other things being equal, such as rigidity of sides. To the extent that the analogy works rigidity corresponds to the strength of forces between atoms in a lattice, and that depends on their type. So no, the strength of the lattice is not determined by geometry alone. For example, a triangular pattern would require ...

1

Above is a picture of a section of diamond crystal, the hardest naturally occuring material we know and to me that least, the triangle shape is not as evident in this section as it is in any man made structure. The other point that may be worth mentioning is that, as you probably know, a diamond is one giant molecule, whereas I don't think graphene ...

1

First off, quantum mechanics isn't "random". In QM, everything evolves perfectly deterministically, just in a somewhat strange way. Some people have the picture that a quantum mechanical universe looks just like a classical one, except that every once in a while crazy stuff randomly happens. Nope! It's not classical + randomness, it's a totally different ...

1

There is a reason physics starts with kinematics, description of motion and evolution is what it is about and once you throw in the causes you get dynamics, which is everything. It is not obvious that energy is secondary at all. And I dispute it. How can you tell you have something? Because it interacts in certain ways (dynamics) or it has the capacity to ...

1

So, can an area of space a few feet across (externally) be a light-year wide (internally) (TARDIS sort of thing)? Yes. It can and that's normal. If you made a region with less space inside than the surface area indicated that would require exotic matter. And with exotic matter you can make time machines. So ... Ironically you need something smaller on ...

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