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| bio | website | en.wikipedia.org/wiki/… |
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| visits | member for | 11 months |
| seen | 10 hours ago | |
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A Sufi prayer of love
O love, O pure deep love, be here, be now, be all.
Dissolve me into your stainless endless radiance,
Make me your servant, your breath, your core.
:- by sufi mystic Rumi
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May 12 |
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Some Dirac notation explanations $\dagger$ is transpose + complex conjugate. |
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May 9 |
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Irreducible Representations Of Lorentz Group This situation should be analyzed more carefully. But since $Q$'s (in supersymmetric extension of Poincare algebra) don't commute with general Lorentz transformations so I guess you are right. Choice of such an L(p) will not be possible in this case. But you can choose L(p) which takes |k,..> to |p,..> where |p,..> is some linear combination of eigenstates of Q and J's. |
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May 9 |
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Irreducible Representations Of Lorentz Group But even in case of Poincare algebra $J_3$ can be diagonalized in $V_p$ for those $p$'s which are related to $k$ by a boost along z direction. |
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May 9 |
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Irreducible Representations Of Lorentz Group $J$ and $P$ do not commute. But yes, if algebra $G_k$ were such that some element $Q$ of it commuted with $P$ then you could find some linear combination $|p,n>$ of $|p,\sigma>$'s such that $|p,n>$ be eigenstate of $Q$. This situation can not be realized in case of Poincare algebra. However, little group method also applies to some other algebras (namely supersymmetric extensions of Poincare algebra) where a situation similar to this holds. There we have elements in $G_k$ which commute with $P$. |
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May 9 |
revised |
Will adding heat to a material increase or decrease entropy? added 836 characters in body |
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May 8 |
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Irreducible Representations Of Lorentz Group Physical reality of a Hilbert space doesn't depend upon the basis you choose to work with in it. Anyway, in our case for every $p$ there is a group $G_p$ which keeps $V_p$ fixed. You will find e.g. a "boosted $J_3$" in $G_p$ which will get diagonalized in $V_p$ with eigenbasis $|p,\sigma>$, if $|k,\sigma>$ was eigenbasis of $J_3$ in $V_k$. Thus $\sigma$ appearing in $|p,\sigma>$ can be thought of as spin measured in that boosted frame which is obtained from the inertial frame in which you found spin eigenvalue of $|k,\sigma>$ to be $\sigma$, by applying the boost that takes you from $k$ to $p$ |
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May 7 |
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Irreducible Representations Of Lorentz Group As I said $V_p$ has nothing in common with $V_k$ except for the dimension. And since its dimension is same as that of $V_k$ so I can choose any arbitrary basis of $V_p$ and label it with $\sigma$; But this doesn't mean that $|p,\sigma>$ is eigenvalue of (say) $J_3$. In fact $G_k$ was defined such that its elements fix momentum $k$; so in particular there is no guarantee that elements of $G_k$ will also fix some $p$ different from $k$. In general they will not. So elements of $G_k$ (in general) may not have any eigenvectors in $V_p$ for $p$ different from $k$. |
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May 7 |
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Irreducible Representations Of Lorentz Group No. In basis $|k,\sigma>$, label $\sigma $ can be taken as eigenvalue of (say) $J_3$; but for $p$ different from $k$, $\sigma$ appearing in basis $|p,\sigma>$ is not in general spin eigenvalue or anything like that. Initially action of $G_k$ is only defined on $V_k$. $V_p$'s are completely different vector spaces which have nothing in common with $V_k$ except for the dimension. To know how $G_k$ acts on $V_p$ (and hence what are eigenvectors of (say) spin in $V_p$) one should follow the definition of action of Lorentz operators that we have given later. |
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May 7 |
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Irreducible Representations Of Lorentz Group This answer is actually reverse of Weinberg's approach. Weinberg begins with a Hilbert space H that is assumed to be irreducible representations of Poincare algebra; and then finds a basis of it using little group method. Here we begin from a finite dimensional representation of little group and construct a Hilbert space representation of Poincare group using it. In particular, while in Weinberg (1) is a definition of basis element $|p,\sigma>$ in our case it defines action of $U(L_p)$. These two approaches are completely equivalent. |
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May 7 |
revised |
Irreducible Representations Of Lorentz Group added 52 characters in body |
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May 7 |
answered | Irreducible Representations Of Lorentz Group |
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May 6 |
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Why there are constant numbers in the universe? The fact you mentioned about circle is actually quite amazing. On the one hand you can draw a circle on your copy and check that ratio of circumference to the radius is constant. On the other hand you can begin with assumptions of set theory and develop real numbers, real plane and calculus from it purely on the base of logical reasoning; and then you find that mathematical circle is the same as physical circle that we observe in this world. Actually the similarity between the physical circle and the mathematical (flat) circle has to do with the fact that curvature of our space is quite small. |
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May 3 |
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A three string tree diagram evaluated in CFT is different from string field theory evaluation "3 different worldsheets which are then glued together to form a circle" Could you please clarify this statement? How could 2d surfaces be glued to form a circle? |
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May 2 |
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Research Paper for relativistic mechanics You may specify your email in your profile. If I get the papers I will send you. |
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May 2 |
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The electric potential and the electric field So even though gravitational field can be taken almost constant near the surface of earth, the potential varies. The situation in case of electric field is same. Here role of gravitational field is played by electric field, and role of mass is played by electric charge. |
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May 2 |
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The electric potential and the electric field Electric field is like force while potential is like energy. Electric potential difference between two points is the amount of work done by electric field in taking a particle of unit charge from one point to the other i.e. $Edx=-d\phi$ (use of minus sign is by convention). Constant electric field doesn't imply constant potential. Compare it with the case when some object falls from a height h. During its fall gravity does work on it (thus increasing its speed), and the total work done (divided by the mass of object) is the potential difference between the ground and the initial position. |
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May 1 |
awarded | Civic Duty |
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Apr 30 |
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Casuality between ordinary people's language and physisct Yes, we can say that; but we don't really understand the law which decides the flow of time itself. See e.g. this wiki article. |
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Apr 30 |
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Casuality between ordinary people's language and physisct Jasmine you are getting downvotes may be because when it comes to time and causality a physicists' understanding is not much advanced than of an ordinary person. Existence of an arrow of time is taken as an assumption in relativity, in quantum mechanics, in field theory,... |
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Apr 30 |
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Vortex in D dimensions soliton Thanks for the nice reference :) |
