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| In [[special relativity]], '''four-momentum''' is the generalization of the classical three-dimensional [[momentum]] to four-dimensional [[spacetime]]. Momentum is a vector in three dimensions; similarly four-momentum is a [[four-vector]] in [[spacetime]]. The [[contravariant vector|contravariant]] four-momentum of a particle with three-momentum '''p''' = (''p<sub>x</sub>'', ''p<sub>y</sub>'', ''p<sub>z</sub>'') and energy ''E'' is
| | The initially perfectly known type are the creams and ointments where we rub a medication onto the outside of the rectum. It intends to treat a hemorrhoid by relaxing the blood vessels. This relaxes the cells thus that it no longer continues to bulge. Once the tissues go down, the hemorrhoids might not flare up as much. This is fantastic for a little temporary relief, but the hemorrhoid will generally flare up again when using this method of primary treatment.<br><br>Later I did find out he had hemorrhoidectomy surgery. At the time I wondered when operation was the number one [http://hemorrhoidtreatmentfix.com/hemorrhoid-symptoms hemorrhoids symptoms] for him. I didn't learn anything about hemorrhoids back then.<br><br>When you need a bowel movement never stress. This puts extra stress on a hemorrhoids which will make them worse. We might think that we have to stress when we go to the toilet, nevertheless it happens to be the worse thing you are able to do. So try to take a little more time whenever we have to see the bathroom plus it might help we.<br><br>Step 6 - Try A Suppository. The cheapest thing inside this category is petroleum jelly. Many of the suppositories to be had over the counter are made from the same kind of ingredients. This signifies you can benefit from an inexpensive generic brand and get the same healing relief.<br><br>Then, don't stress out. I do have one answer which has assisted greatly. I would like to review a pretty safe and all-natural treatment that functions effectively in a few days. It is called the H Miracle system.<br><br>Since the biggest cause of hemorrhoids is strained bowel movements and difficult stools (chronic constipation), various individuals might discover lengthy term relief from hemorrhoids by acquiring a solutions that allows them to "go" more frequently plus easily. Chronic constipation is caused in remarkable piece because because a society you are a fast food country. We eat many processed food, and not nearly enough all-natural or fresh foods. I challenge we to take a look at the labels on a food for "nutritional fiber content" should you suffer from constipation. My guess is that there are on many foods we eat the nutritional fiber content to be low.<br><br>Piles may change each aspect of the lifetime, from how readily we take a seat plus curl as much as how much food you eat plus for many; it could feel like you can not do something to create your hemorrhoids disappear. While numerous folks could have the periodic flare up, a great deal of persons have piles that have progressed into a long-term condition. As an illustration, several modern mothers suffer from hemorrhoids from labour. The problem is the fact that based on the intensity, you will possibly end up suffering with this problem again, and again plus again. |
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| :<math>
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| \mathbf{P} = \begin{pmatrix}
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| P^0 \\ P^1 \\ P^2 \\ P^3
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| \end{pmatrix} =
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| \begin{pmatrix}
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| E/c \\ p_x \\ p_y \\ p_z
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| \end{pmatrix}
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| </math>
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| The four-momentum is useful in relativistic calculations because it is a Lorentz vector. This means that it is easy to keep track of how it transforms under [[Lorentz transformation]]s.
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| The above definition applies under the coordinate convention that ''x''<sup>0</sup> = ''ct''. Some authors use the convention ''x''<sup>0</sup> = ''t'' which yields a modified definition with ''P''<sup>0</sup> = ''E''/''c''<sup>2</sup>. It is also possible to define [[covariant vector|covariant]] four-momentum ''P''<sub>μ</sub> where the sign of the energy is reversed.
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| == Minkowski norm ==
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| Calculating the [[Minkowski space#Structure|Minkowski norm]] of the four-momentum gives a [[Lorentz invariant]] quantity equal (up to factors of the [[speed of light]] ''c'') to the square of the particle's [[proper mass]]:
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| :<math>-\|\mathbf{P}\|^2 = - P^\mu P_\mu = - \eta_{\mu\nu} P^\mu P^\nu = {E^2 \over c^2} - |\mathbf p|^2 = m^2c^2 </math>
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| where we use the convention that
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| :<math>\eta_{\mu\nu} = \begin{pmatrix}
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| -1 & 0 & 0 & 0\\ | |
| 0 & 1 & 0 & 0\\
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| 0 & 0 & 1 & 0\\
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| 0 & 0 & 0 & 1
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| \end{pmatrix}</math>
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| is the metric tensor of [[special relativity]]. The magnitude ||'''P'''||<sup>2</sup> is Lorentz invariant, meaning its value is not changed by Lorentz transformations/boosting into different frames of reference.
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| == Relation to four-velocity ==
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| For a massive particle, the four-momentum is given by the particle's [[invariant mass]] ''m'' multiplied by the particle's [[four-velocity]]:
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| :<math>P^\mu = m \, U^\mu\!</math>
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| where the four-velocity is
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| :<math>
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| \begin{pmatrix}
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| U^0 \\ U^1 \\ U^2 \\ U^3
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| \end{pmatrix} =
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| \begin{pmatrix}
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| \gamma c \\ \gamma v_x \\ \gamma v_y \\ \gamma v_z
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| \end{pmatrix}
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| </math>
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| and
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| :<math>\gamma = \frac{1}{\sqrt{1-\left(\frac{v}{c}\right)^2}}</math>
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| is the [[Lorentz factor]], ''c'' is the [[speed of light]].
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| == Conservation of four-momentum ==
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| The conservation of the four-momentum yields two conservation laws for "classical" quantities:
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| # The total [[energy]] ''E'' = ''P''<sup>0</sup>''c'' is conserved.
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| # The classical three-[[momentum]] '''p''' is conserved.
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| Note that the invariant mass of a system of particles may be more than the sum of the particles' rest masses, since [[kinetic energy]] in the system center-of-mass frame and [[potential energy]] from forces between the particles contribute to the invariant mass. As an example, two particles with four-momenta (−5 GeV/''c'', 4 GeV/''c'', 0, 0) and (−5 GeV/''c'', −4 GeV/''c'', 0, 0) each have (rest) mass 3 GeV/''c''<sup>2</sup> separately, but their total mass (the system mass) is 10 GeV/''c''<sup>2</sup>. If these particles were to collide and stick, the mass of the composite object would be 10 GeV/''c''<sup>2</sup>.
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| One practical application from [[particle physics]] of the conservation of the [[invariant mass]] involves combining the four-momenta '''P'''(''A'') and '''P'''(''B'') of two daughter particles produced in the decay of a heavier particle with four-momentum '''P'''(''C'') to find the mass of the heavier particle. Conservation of four-momentum gives ''P''(''C'')<sup>μ</sup> = ''P''(''A'')<sup>μ</sup> + ''P''(''B'')<sup>μ</sup>, while the mass ''M'' of the heavier particle is given by −||'''P'''(''C'')||<sup>2</sup> = ''M''<sup>2</sup>''c''<sup>2</sup>. By measuring the energies and three-momenta of the daughter particles, one can reconstruct the invariant mass of the two-particle system, which must be equal to M. This technique is used, e.g., in experimental searches for [[Z' boson]]s at high-energy particle [[collider]]s, where the Z' boson would show up as a bump in the invariant mass spectrum of [[electron]]-[[positron]] or [[muon]]-antimuon pairs.
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| If an object's mass does not change, the Minkowski inner product of its four-momentum and corresponding [[four-acceleration]] ''A''<sup>μ</sup> is zero. The four-acceleration is proportional to the proper time derivative of the four-momentum divided by the particle's mass, so
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| :<math>P^{\mu} A_\mu = \eta_{\mu\nu} P^{\mu} A^\nu = \eta_{\mu\nu} P^\mu \frac{d}{d\tau} \frac{P^{\nu}}{m} = \frac{1}{2m} \frac{d}{d\tau} \|\mathbf{P}\|^2 = \frac{1}{2m} \frac{d}{d\tau} (-m^2c^2) = 0 .</math>
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| == Canonical momentum in the presence of an electromagnetic potential ==
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| For a [[charged particle]] of [[electric charge|charge]] ''q'', moving in an electromagnetic field given by the [[electromagnetic four-potential]]:
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| :<math>
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| \begin{pmatrix}
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| A^0 \\ A^1 \\ A^2 \\ A^3
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| \end{pmatrix} =
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| \begin{pmatrix}
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| \phi / c \\ A_x \\ A_y \\ A_z
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| \end{pmatrix}
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| </math>
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| where φ is the [[scalar potential]] and '''A''' = (''A<sub>x</sub>'', ''A<sub>y</sub>'', ''A<sub>z</sub>'') the [[vector potential]], the "canonical" momentum four-vector is
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| :<math> Q^\mu = P^\mu + q A^\mu. \!</math>
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| This allows the potential energy from the charged particle in an electrostatic potential and the [[Lorentz force]] on the charged particle moving in a magnetic field to be incorporated in a compact way, in [[relativistic quantum mechanics]].
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| ==See also==
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| *[[Four-force]]
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| *[[Pauli–Lubanski pseudovector]]
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| == References ==
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| *{{cite book|last=Goldstein|first=Herbert|title=Classical mechanics|year=1980|publisher=Addison–Wesley Pub. Co.|location=Reading, Mass.|isbn=0201029189|edition=2nd |ref=harv}}
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| *{{cite book|last=Landau|first=L.D.|title=The classical theory of fields|year=2000|publisher=Butterworth Heinemann|location=Oxford|isbn=9780750627689 |coauthors=E.M. Lifshitz |others=4th rev. English edition, reprinted with corrections; translated from the Russian by Morton Hamermesh|ref=harv}}
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| *{{cite book | author = Rindler, Wolfgang | title=Introduction to Special Relativity |edition=2nd| location= Oxford | publisher=Oxford University Press | year=1991 | isbn=0-19-853952-5 |ref=harv}}
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| [[Category:Minkowski spacetime]]
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| [[Category:Theory of relativity]]
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The initially perfectly known type are the creams and ointments where we rub a medication onto the outside of the rectum. It intends to treat a hemorrhoid by relaxing the blood vessels. This relaxes the cells thus that it no longer continues to bulge. Once the tissues go down, the hemorrhoids might not flare up as much. This is fantastic for a little temporary relief, but the hemorrhoid will generally flare up again when using this method of primary treatment.
Later I did find out he had hemorrhoidectomy surgery. At the time I wondered when operation was the number one hemorrhoids symptoms for him. I didn't learn anything about hemorrhoids back then.
When you need a bowel movement never stress. This puts extra stress on a hemorrhoids which will make them worse. We might think that we have to stress when we go to the toilet, nevertheless it happens to be the worse thing you are able to do. So try to take a little more time whenever we have to see the bathroom plus it might help we.
Step 6 - Try A Suppository. The cheapest thing inside this category is petroleum jelly. Many of the suppositories to be had over the counter are made from the same kind of ingredients. This signifies you can benefit from an inexpensive generic brand and get the same healing relief.
Then, don't stress out. I do have one answer which has assisted greatly. I would like to review a pretty safe and all-natural treatment that functions effectively in a few days. It is called the H Miracle system.
Since the biggest cause of hemorrhoids is strained bowel movements and difficult stools (chronic constipation), various individuals might discover lengthy term relief from hemorrhoids by acquiring a solutions that allows them to "go" more frequently plus easily. Chronic constipation is caused in remarkable piece because because a society you are a fast food country. We eat many processed food, and not nearly enough all-natural or fresh foods. I challenge we to take a look at the labels on a food for "nutritional fiber content" should you suffer from constipation. My guess is that there are on many foods we eat the nutritional fiber content to be low.
Piles may change each aspect of the lifetime, from how readily we take a seat plus curl as much as how much food you eat plus for many; it could feel like you can not do something to create your hemorrhoids disappear. While numerous folks could have the periodic flare up, a great deal of persons have piles that have progressed into a long-term condition. As an illustration, several modern mothers suffer from hemorrhoids from labour. The problem is the fact that based on the intensity, you will possibly end up suffering with this problem again, and again plus again.