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1

A gauge field transforms in the adjoint of the gauge group, but not in the adjoint (or any other) representation of the group of gauge transformations. In detail: Let $G$ be the gauge group, and $\mathcal{G} = \{g : \mathcal{M} \to \mathcal{G} \vert g \text{ smooth}\}$ the group of all gauge transformations. A gauge field $A$ is a connection form on a ...


0

Use the definition of work done over a period of time $t$ , and you have : $$ E_k = \int_0^{t} \vec{F} \vec{dx} = \int_0^{t} \vec{v} d (m\vec{v}) = \int_0^{v} d\bigg{(} \frac{mv^2}{2} \bigg{)} = \frac{mv^2}{2}$$


1

Both operations are equivalent, up to a local phase in the second mode. In particular, if you shift the second basis vector's phase by $i$, then you will turn $H$ into $A$. In a beam splitter this is perfectly natural, because the phases of the output modes are not particularly well defined, and you can always model the difference between the two operations ...


0

Yes, parity is really violated, even if neutrinos are massive. You seem to be confusing the relationship between parity, helicity, and chirality in the modern standard model with the physical symmetry operation of spatial inversion. Wu's experiment did not measure neutrino helicity. Wu and collaborators prepared a thin layer of a beta-emitting nucleus ...


0

"Downshear of the vortex"? And your link is just a google search for these words. -But as Vortex doesn't have too much shear stresses, it must mean this bottom flow which connects/feeds the low pressure vortex center with fluid. Please note that it doesn't make any difference if the fluid is going away from the bottom or from the top of the vortex. ...


0

The double slit experiment for electrons is mostly a Gedankenexperiment ... you can completely ignore it because there is nothing there for you to learn. Start with the Schroedinger equation for hydrogen and work your way trough atomic physics. – CuriousOne One can learn a lot from electron interaction with edges and the intensity pattern behind such ...


1

WetSavannaAnimal's answer covers the geometry of the slits necessary to produce a clear pattern. Which properties does it have to have to be a slit and prevent an electron from passing through? These factors decide what material to use for the barrier/boundary of the slits: it's electron-stopping power primarily, which depends on the energy of the ...


3

It means that when the neutrinos hit electrons, the electrons are moving preferentially in the same directions that the neutrinos were moving. So when we are building a water Cherenkov detector for solar neutrinos, the Cherenkov signal will be coming from the direction of the sun. This is very advantageous to suppress background and because of the daily and ...


6

To fill out Mew's comment further: A slit is a gap wide enough for the electron to pass through True, but for the purposes of a clear discussion of double slit interference, we need the following further quality: a slit should be such that there is much less than a wavelength difference between the pathlength of all paths through the putative "slit" to ...


1

The "unique" here is, IMO, not a good, evocative word. A better one would be preferred direction or privileged direction. Another way of looking at this is all directions are equivalent. A further confusing subtlety is that there is also something else that the author is assuming without telling you. There are no privileged directions for a problems with ...


3

The object for which you need to find the electric field is a uniformly charged sphere. Uniformly charged means that at every point on the sphere the charge density is same. Suppose someone blind-folded you and then he rotated the sphere in some arbitrary fashion about the origin(assuming your sphere has origin as the center). Then he takes off the blind ...


1

A vector is a scalar with direction. So Time can be a vector, but what it means depends on the context. In 1D it has only 2 directions, positive and negative with zero being positive. In 2D it can be an angle between ÷/-Pi radians. And so on. Time can be a single dimension attached to the familiar 3 Euclidian spacial dimensions and in this case it is ...


0

I agree with John in the comments above. In my knowledge, I haven't come across 'Perfect Dipole' as a defined physics term, but later it dawned upon me, in accordance with the context above, what differentiates a Physical Dipole from a $Perfect$ Dipole is, the Physical dipole consists of two equal and opposite charges $(+/-)Q$, separated by a finite, and ...


1

Based on a quick read of the Wikipedia article on the kinetic theory of gases, it looks like you would need statistical mechanics to derive any of the results in the kinetic theory of gases. For example, the Maxwell distribution of velocities is typically derived using the canonical ensemble. However, the equilibrium velocity distribution is not a dynamical ...


0

In the computer language FORTH the turtle can go anywhere in the plane, going always 'ahead' X units and turning left or right by a Y angle units. The turtle ignores the notion of negative and yet it moves i.e. in any referential the space coordinates vary in time , and it has a velocity. The Question and several of the Answers do not know the difference ...


0

A process is something that goes on, has duration. A change has no necessary relation to time. It is a statement of difference between the initial and the final state of the process.


2

This is simply about words. A process can cause a change. For example: A (reversible) adiabatic process can cause a (reversible) temperature change.


0

I will only consider one dimensional motion(motion along a single axis).The main objective of terms like position and velocity is to describe the motion of an object easily. We define velocity to be the rate of change of position .By convention we choose a fixed point (along the axis of motion) and call it origin and define an object's position on that line ...


6

From the math point of view, you cannot have “negative velocity” in itself, only “negative velocity in a given direction”. The velocity is a 3-dimension vector, there is no such thing as a positive or negative 3D vector. However, if you consider the velocity in direction $\mathrm{x}$, where $\hat{\mathbf{e}}_{\mathrm{x}}$ is some ...


1

I think one of the main reasons that you have velocity is to isolate a particular direction of movement from your forward speed. If you travel North north east, you can extract the speed at which you move eastwards by calculating your eastwards velocity (possibly 1/3 of your speed travelling NNE). Negative velocities probably arrived as a consequence of ...


55

Velocity is a vector. Speed is its magnitude. Position is a vector. Length (or distance) is its magnitude. A vector points in a direction in space. A negative vector (or more precisely "the negative of a vector") simply points the opposite way. If I drive from my home to my workplace (and then defining my positive direction in that way), then my velocity ...


0

I am trying to go to a bit basic level. The formula work=Force*Displacement works only if the force is constant and not changing its direction or magnitude. When an object moves in circle,the force continuously changes its direction. So to calculate it we have to use integral of F with dl,assuming that force remains constant for a very short displacement dl. ...


0

Work is defined as the line integral $\int \mathbf{F} \cdot \mathbf{d\ell}$. The force on an object can be a function of position or time, and could represent external forces placed on the system. Net and total work refer to the same concept, the sum of all work done on an object. For your example, you cannot simply say work is 0 because the object returns ...


3

Well, if you're wondering if people won't know what it is, or if you should be calling it something fancier: no. This and closely related notions are common language among physicists, much like "mass" and "force" are common language. A "right-handed triple" is a collection of three vectors in a particular order such that they obey the right-hand rule. A ...


0

I believe your professor's trying to tell you that the general solution will be a sum of three terms, and he could have just as easily used $f_{ij}$, $g_{ij}$ and $h_{ij}$ for the three superscript terms. Edit: In other words, you're Matrix $\rho$ can be expressed as a sum of matrices $\rho^{(1)}$, $\rho^{(2)}$, which is proportional to $e^{i\Omega t}$ and ...


2

In 1969 Adler [https://inspirehep.net/record/55000] and, Bell & Jackiw [https://inspirehep.net/record/54998] showed that in the UV divergent triangle Feynman diagram made up of one axial and two vector currents, only the vector current is conserved, whereas the conservation law of the axial current is broken. Hence the names ABJ or chiral anomaly. ...


1

Newton devised a very good law of gravity (until Einstein came along) where the force between the two bodies is scaled by a very small number usually written as a capital G. It's a general law that applies to any two bodies. But if you plug in the mass of the earth, the mass of a test ball, and the distance between the center of earth and the test ball, then ...


1

In the second law of Newton appears the acceleration $a$. It refers to a generic acceleration due to any phenomenon. $g$ has the same role of $a$, but it refers specifically to the acceleration of gravity (free fall particular case) on the Earth. Usually we approximate $g$ to be constant $\left(9.81\, \mathrm{m}/\mathrm{s}^2\right)$, but in the real case the ...


5

The Osher paper does define what a weak solution is. We seek a solution $w$ of $x$ and $t$ such that $$ \partial_t w + \partial_x f(w) = 0 $$ for a known function $f$ (the flux function), given initial conditions $$ w(x,0) = w_0(x) $$ for known $w_0$, for $-\infty < x < \infty$ and $0 < t < \infty$. A weak solution is a bounded measurable ...


1

The Hartree-Fock method treats the interaction between particles in a mean-field approximation. So the potential felt by particle i is given by the average over the wave functions of all the other particles. However - speaking semi-classically - you could imagine that particle j has a position as a function of time, and when it's on the "left" side of the ...


0

I think you are confused between gravitational CONSTANT g, and gravitational acceleration a which can be thought of as a VARIABLE. Gravitation acceleration g is around 9.81m/s^2 near sea level. But as you go higher the gravitational acceleration is no longer g, but another number, let's say a. a is a more generic gravitational acceleration that is not ...


2

This is to be read in conjunction with the answer by Lubos The particle data group has compiled a lot of crossections in this paper, whence I have copied a particular plot, fig 49.5. Squareroot(s) in GeV The blue part are the resonances that were found during the sixties , and are typical of other resonances in scattering ...


6

A resonance (in the particle physics or related physics sense) and an unstable particle is exactly the same thing. The object has some complex mass and the imaginary part determines the decay width (and decay rate). But these two terms describe different aspects of the same thing. "A particle" refers to the object, the particle species (in your URL's case, ...


4

I was taught that the Standard Model was a misnomer; that it ought to be called the Standard Theory. I'm inclined to agree, though theories and models are both indispensable in science. Ultimately, the purpose of a model is provide local understanding of a particular phenomena. A model: Typically considers only fields, objects or quantities relevant to a ...


5

A theory is a set of statements that is developed through a process of continued abstractions. A theory is aimed at a generalized statement aimed at explaining a phenomenon. A model, on the other hand, is a purposeful representation of reality. As you can see, both share common elements in their definitions. What differs one from the other (in my opinion) ...


0

Example of a hyperbolic system, the first order wave equation: $ {\partial \underline{U} \over \partial t} + \underline{A} {\partial \underline{U} \over \partial x} = 0$ The term hyperbolic means that: The eigenvalues of the $m \times m$ Jacobian matrix ($\underline A $) are all real There is a corresponding set of $m$ linearly independent eigenvectors ...


0

Completeness in mathematics is essentially a metric concept (that means that every Cauchy sequence in the metric space converges to an element of the space). Sometimes (but I think more on a physical standpoint, and I agree is a sort of repetition and not so common) it is used to characterize bases in vector spaces, in the sense that a basis is complete if ...


2

You need to be careful with the word span. A mathematician will say that the span of a set of vectors is the set of finite linear combinations, so you can only add linear combinations of finitely many at a time to get something in the span. So there are sets that are mutually orthogonal and all normalized but not enough to span the space with finite linear ...


3

As noted, many people use "complete" where perhaps they ought to say "complete and orthogonal and orthonormal" or the like. I'm not sure what I can tell you besides confirming that usage is not always ideal. I'll answer one question you brought up, but I'm worried I may have gotten confused myself by what kind of "complete" you meant: Is it even possible ...


2

The non-renormalization theorems mean that there is only wave-function renormaliziation for parameters in the superpotential. The important consequence is that there are no quadratic divergences for a mass in the superpotential - there are only logarithmic correction. The $\mu^2\phi^2$ operator is safe from large radiative corrections from, for example, ...



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