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A constraint condition can reduce the DOF of the system if it can be used to express a coordinate in terms of the others. This can always be done in case of holonomic constraints which are basically just algebraic functions of the coordinates and time. This means that you just have to manipulate the constraint equation in such a way that one of the ...

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2nd law of thermodynamics has many almost equivalent formulations. The traditional ones always assume closed system, isolation is not needed - heat and work transfer are assumed to be allowed. One formulation: When thermodynamic system goes from equilibrium state 1 to equilibrium state 2, the entropies of these states obey the relation $$S(2) - S(1) \geq ... 0 ANS: It is basically the same. All of them are anomalies for chiral fermion in even dimensional spacetime, like 1+1D, 3+1D, etc. Or, in odd dimensional space. ABJ anomaly is named after the discovers: Adler-Bell-Jackiw. - Chiral anomaly is named after and implies that the chiral current is not conserved. Chiral, means the left and the ... 0 In the context of Relativty, the adjective "coincident" characterizes all that which belongs together ("at once") to only one event without any temporal or spatial or light-like separation; i.e. indications (of any participant at this one event) or occurences (as far as they are understood to be contained within this one event). In contrast, the adjective ... 1 The "adjustable constant" in that statement is the total energy E, and they mean it's "adjustable" in that the behavior of the system is completely independent of E - this is known in physics as a symmetry, in that they system doesn't change if it has a different total amount of energy. In this case, the way to "adjust" the amount of energy would be ... 0 Positron is as "elementary" as the electron, in the current theory. Period. I took the word "elementary" in quote marks because if you hit a charged particle, it gets "broken apart" into the following pieces: the same charge and lots of neutral photons. It looks like the "target" is not that "elementary", but has "internal degrees of freedom", and sometimes ... 1 Positron IS an elementary particle, the anti-particle to the electron as you already know. But we do not get a "free positron" as a "free electron". They are usually generated through pair-production and get annihilated fast, or through radioactive decay (beta-decay) in weak interactions or in particle accelerators, and are present in cosmic rays too. A ... 1 The equation you are quoting gives the power of a lens in terms of its geometry and refractive index. Simply rearranging the terms (dividing by n) gives you an expression for \frac{1}{f} which is known as the power of the lens and is expressed in diopters. For the usual situation of a lens in air, we can put n=1 which leaves you with an even simpler ... 1 Dunno what book you're quoting, but you should realize that the index of refraction of air is n = 1+ \epsilon  (where I'm using the mathematics standard of \epsilon being a tiny number). Thus the power in air is 1/F 2 As I recall, covariant refers to how an object transforms when you boost to another inertial frame. An example would be the relativistic 4-momentum P^{\mu}. Invariant refers to quantities which are unchanged under boosts to different frames. For example the product P^{\mu}P_{\mu}=m has the same numerical value in any frame. Sometimes a relativistic ... 1 "Coincident" is defined in the Google online dictionary as (1) "occurring together in space OR time" (emphasis mine), and (2) "in agreement or harmony". "Simultaneous" is defined in the same dictionary as "occurring, operating, or done at the same time". (This begs the question: "Whose time?") Unfortunately, this dictionary lists "coincident" as a synonym ... 1 Regarding your assertions: Events \varepsilon_{AJ} and \varepsilon_{BK} were simultaneous in the inertial frame of participants A, B, M. This is a perfectly reasonable statement and it is the sort of language used in everyday physics. Participant M was the middle between J and K, in the inertial frame of participants A, B, M. ... 1 I would like to bring the ladder paradox here to explain simultaneity of events.A ladder (an inertial frame) is moving horizontally with a relatively high constant speed with respect to a garage (another inertial frame). The garage has an open door where the ladder can not actually enter if the ladder was at rest in the garage's frame but that is not ... 0 It's the net resultant that a force would react with on application of a certain change in momentum in the body, on which the force is applied. 1 A site is just a place or location with given coordinates e.g. (x_0,y_0,z_0) 0 Kinetics are focused on the rate and mechanism of chemical processes, so you are definitely right to say that you gain a lot of insight about mechanism from kinetics. Many kinetic theory make extensive use of statistical thermodynamics methods, and that's why you perceive a resemblance. However, keep in mind that in kinetics the system is not in ... 4 The Weights and Measures Act (the origin of the Imperial Units) does not speak of temperature. It was intended to create a uniform system for trade. You don't sell temperature, in the way you sell a pint of milk or a yard of cloth. And frankly, when it was first conceived (before Magna Carta, which already stated: "There shall be but one Measure ... 2 According to the wiki page on Imperial and US customary units Fahrenheit is part of both the Imperial and US customary system. I can't think of any reason it wouldn't be included in the Imperial system. Note that in the wiki page on Imperial units it is mentioned that the weight's and measures act (which defined the Imperial system) explicitly used the ... 0 The effective potential is the potential of interaction you measure between two (or more) emergent physical objects when you forget (or "trace over" in the jargon) certain degrees of freedom of a more detailed model. If you take two pinned charges in vacuum for instance, they will interact with a "bare" Coulomb interaction in \sim 1/r. If you put these ... 1 As wiki says "The effective potential (also known as effective potential energy) is a mathematical expression combining multiple (perhaps opposing) effects into a single potential." Basically the concept of the effective potential simplifies the equations of motion and simplifies their analysis. 0 More on the perytons being caused by microwave ovens being opened while still operating. The microwave oven's magnetron is still generating the microwaves when the door is open before the timer has stopped the microwave. Article: http://phenomena.nationalgeographic.com/2015/04/10/rogue-microwave-ovens-are-the-culprits-behind-mysterious-radio-signals Study: ... 1 Four component formalism is the "right" formalism, but it has negative energy eigenstates corresponding to the antiparticles. Most chemists and solid state physics are not interested in the antiparticles, and such negative energy solution causes trouble for conventional variational methods, where you might end up falling to negative infinity energy. It is ... 0 Rolling friction result from for example small changes in the surface or in the wheel material (the rubber in a tire). The surface is not perfectly flat and rigid so there will be some small forces trying to stop the rotating motion: On the contrary, the static friction is not trying to stop the rotation of the wheel. Static and rolling friction are ... 0 Cicle is the smallest repatable segment between two points, where: 1. These point lies on one line and the line is parallel to direction of wave propagation. 2. These two points have the always same sign of slope. Thanks to Floris in help of derivation of the definition. 1 The below seems to be a candidate for the first use of the term 'Majorana fermion'. (I'm not sure if it satisfies your other criteria.) Salam, Abdus, and J. Strathdee. Super-symmetry and non-Abelian gauges. International Centre for Theoretical Physics, Trieste (Italy), 1974. 2 Using elementary graph theory identities one can show that the number of loops in a connected diagram is related to the number of external lines and the number of vertices of type i each of which has n_i lines attached to it, is related by$$ \sum \left(\frac{n_i}{2}-1\right) V_i -\tfrac{1}{2}E +1= L $$So you can see that for a fixed process (fixed ... 5 A paper came out this week pointing to them having a banal (if amusing) origin: they are from two 27 year old microwave ovens. When people get impatient and open the door before the timer runs down, a short burst from the ovens' magnetron is released, which appears as a peryton if the telescope is pointed in the right direction. Figure 7. shows the perytons ... 0 Let's check that parity is violated by the weak interaction lagrangian:$$\mathcal{L}(x) = \bar{\psi}(x) \gamma^\mu \frac{(1-\gamma^5)}{2} \psi(x) W_\mu(x)$$Saying that parity is violated means that the transformed lagrangian \mathcal{L}'(x) is not equal to the old lagrangian resulting from new coordinates \mathcal{L}(x') where x'^0 = x^0 and ... 2 The order of a quantity in general refers to the exponent of the quantity in an expression, ie$$x^3y^2$$would be 3rd order in x and 2nd order in y. According to the Feynman rules, each vertex in a Feynman diagrams contributes a factor of the coupling constant, so the order of each coupling constant is simply the number of vertices of that interaction. ... 0 Pressure-sensitive paints? Is that what you need? http://en.wikipedia.org/wiki/Pressure-sensitive_paint 0 I guess you have some typos in your question (or your lecture notes), since the two lines you give just differ by the index names (as already commented) . Starting from$$ R^n_{ikl;m} +R^n_{imk;l} +R^n_{ilm;k} =0 $$you can rewrite that with the symmetry relations R^n_{ikl}=- R^n_{ilk}=-R^i_{nkl} to$$ R^n_{ikl;m} - R^n_{ikm;l} +R^n_{ilm;k}=0. $$Now let ... 2 To contract a tensor is to set two of the indices equal and sum over them, so given a tensor A^i_j the contraction is A=A^i_i=A^1_1+A^2_2+A^3_3+A^4_4 The Bianchi identities you list have five indices. To contract them, you would set some pair equal and sum over them. Your second version is the same as the first, it just has the indices renamed. ... 2 Static comes from the same root as stasis, meaning stop, immovable, To create static electricity, you have to rub two different materials. At the moment you rub them, the electrons already moved Note the word "create", creation is not static, and yes there are transient fields and currents during creation of a static field. The static describes the ... 1 UV stands for Ultraviolet and it is referring to a special kind of divergences in quantum field theory. In NLO loop diagrams, we often encounter divergences (infinite integrals) when we investigate what happens at k \to \infty, where k is the internal momentum of a virtual particle in Feynman diagrams. These are precisely the divergences we call "UV ... 0 UV = Ultra-Violet = High energy = Small length-scale. 0 This is just a wild guess, but could it be the position vector of the element? 1 I think the magnon is a special case of the spin wave. Whereas spinon refers to the general quasiparticle that carries all spin of an electron, magnon refers to the limiting case of spin wave quantized in such a manner that it becomes part of an anti-magnetic cloud of quasiparticles. However, this may not be the complete story! Some usage of the terms: ... 0 In this context, it is a change of variables. The variable in the original Lagrangian is q, and Goldstein is asking you to use another variable s, which is related to the original q via the "transformation":$$s = \exp(\gamma t) \ q$$and later on, make sense of it (with the later questions). Point transformation in this context refers merely to this ... 1 i searched for the exact same problem recently after a debate with one of my colleagues. In my opinion, you already gave the answer to your question yourself. A source dipole is the flow field resulting from a sink and a source brought together. In a sink, all streamlines point radially inward to the singularity at the origin, in a source, all point ... 0 \hat{I}_D(k)={{g^2}\over4}\int_0^1d\alpha\int_0^\infty d\sigma\int\sigma\mathrm{e}^{-[q^2+\alpha(1-\alpha)k^2+m^2]\sigma}\vec{a}q. Just a wild guess. [Oh, you asked for two formulae. Sorry.] Either that, or it is \int_0^\infty\mathrm{e}^{-a\alpha}\sigma d\sigma=a^{-2}. 4 I got a translation of the article from the German Wikipedia. Here's an excerpt: Perytons are in radio astronomy short radio signals having a length of a few milliseconds, which probably terrestrial are origin. The Perytons are named after mythical creatures . In radio astronomy, terrestrial are noise is always a problem. A well-known noise signal ... 1 This paper describes them. http://www.ursi.org/proceedings/procGA11/ursi/GP2-41.pdf They were apparently given a new name because their origin was uncertain. 0 If the observer is not in free-fall, the metric-tensor g_{\mu,\nu}(s) at the observer's position, expressed in local coordinates around the observer, will not be \eta_{\mu,\nu}. Your first assumption about the path (\gamma) is wrong. I guess what you are aiming at is the notion of the space of coordinates around a point, which is indeed a flat space ... 2 When you say If something goes outside, then it will decrease inside! what you assume is exactly a conservation law. It may seem trivial, but it is not necessarily. Consider the population of a city, for example. At one point in time, you measure how many people are within the city borders; let's call this number N_0. Then, you observe all city ... 2 When we say something is conserved or that there is a conservation law for a given thing, we mean that the quantity of it does not change. You neither lose nor gain any of that thing. More specifically, conservation can come in two flavours. Something can be globally conserved. This means that the total amount of that something in the universe does not ... 1 It has a very simple yet important meaning.It simply means that the quantity that you are observing will always stay the same,even if that means that it gets transferred to another form or convert to another medium.You can not simply create more "stuff" of that quantity and you can not destroy it.It can not be created from nothing and it can not just be ... 3 Let M be your spacetime, a smooth manifold equipped with (pseudo) Riemannian metric (for example \mathbb{R}^{(1,3)} for special relativity). The set of reference frames is the frame bundle over M, usually denoted FM. Explicitly a frame at point p in M can be viewed as an ordered orthonormal basis (with respect to the the inner product defined ... 2 The kinetic term of the Lagrangian is proportional to$$g_{ij}v^iv^j$$where the vs are the generalised velocities. Writing them as the time derivative of the generalised coordinates, i.e. v^i\dot q^i, taking the square root, and multiplying by a small time lapse \epsilon you get$$\sqrt{g_{ij}\dot q^i\dot q^j}\epsilon, which is a first order ...

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The name T-duality stands for Target-space duality, see e.g. this preprint.

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It comes from S matrix theory, long before quarks were imagined, S,T and U characterize the type of exchange in the Feynman diagrams entering the S matrix calculation, and they are called Mandelstam variables. s channel-------------------------- t channel------------------------u channel duality meant that the sums could be done either in S ...

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