4-momenta - Revision history

Vanwdani at 18:47, 15 May 2018

2018-05-15T18:47:19Z

2017-07-10T04:07:54Z

2017-06-23T18:07:20Z

4-momenta

2017-06-16T01:00:43Z

4-momenta

2017-06-08T22:16:12Z

2017-06-08T22:14:22Z

4-momenta

2017-06-08T22:04:03Z

4-momenta

2017-06-08T20:28:11Z

2017-06-08T20:27:09Z

2017-06-08T20:25:48Z

4-momenta

@@ Line 1: / Line 1: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[4-vectors|<math>\vartriangleleft </math>]]
@@ Line 100: / Line 100: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[4-vectors|<math>\vartriangleleft </math>]]

@@ Line 3: / Line 3: @@
 [[4-vectors|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[Mandelstam_Representation|<math>\vartriangleright </math>]]
+[[Frame_of_Reference_Transformation|<math>\vartriangleright </math>]]
 </center>
@@ Line 104: / Line 104: @@
 [[4-vectors|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[Mandelstam_Representation|<math>\vartriangleright </math>]]
+[[Frame_of_Reference_Transformation|<math>\vartriangleright </math>]]
 </center>

@@ Line 70: / Line 70: @@
 Using
-<center><math>\mathbf (\mathbf P_1 +\mathbf P_2)^2=m^2</math></center>
+<center><math>\mathbf P^2=m^2</math></center>
 This gives

@@ Line 10: / Line 10: @@
-As was previously shown for the space-time 4-vector, a similar 4-vector can be composed of momentum.  Using index notation, the energy and momentum components can be combined  into a single "4-vector" <math>\mathbf{p^{\mu}},\ \mu=0,\ 1,\ 2,\ 3</math>, that has units of momentum(i.e. E/c is a distance).
+As was previously shown for the space-time 4-vector, a similar 4-vector can be composed of momentum.  Using index notation, the energy and momentum components can be combined  into a single "4-vector" <math>\mathbf{p^{\mu}},\ \mu=0,\ 1,\ 2,\ 3</math>, that has units of momentum(i.e. E/c is a distance with c=1).
 <center><math>\mathbf{P} \equiv
@@ Line 20: / Line 20: @@
 \end{bmatrix}=
 \begin{bmatrix}
-E/c \\
+E \\
 p_x \\
 p_y \\
@@ Line 39: / Line 39: @@
-<center><math>\mathbf P \cdot \mathbf P = \frac{E^2}{c^2}-\vec p\ ^2</math></center>
+<center><math>\mathbf P \cdot \mathbf P = E^2-\vec p\ ^2</math></center>
@@ Line 48: / Line 48: @@
-<center><math>\mathbf P \cdot \mathbf P = \frac{E^2}{c^2}-E^2+m^2</math></center>
+<center><math>\mathbf P \cdot \mathbf P = E^2-E^2+m^2</math></center>

@@ Line 3: / Line 3: @@
 [[4-vectors|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[4-vectors|<math>\vartriangleright </math>]]
+[[Mandelstam_Representation|<math>\vartriangleright </math>]]
 </center>
@@ Line 104: / Line 104: @@
 [[4-vectors|<math>\vartriangleleft </math>]]
 [[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[4-vectors|<math>\vartriangleright </math>]]
+[[Mandelstam_Representation|<math>\vartriangleright </math>]]
 </center>

@@ Line 72: / Line 72: @@
 <center><math>\mathbf (\mathbf P_1 +\mathbf P_2)^2=m^2</math></center>
 <center><math>\mathbf (\mathbf P_1 +\mathbf P_2)^2 \equiv m_1^2+2 \mathbf P_1 \mathbf P_2+m_2^2</math></center>
 <center><math>\mathbf R_1 \cdot \mathbf R_2 = x_{0_1}x_{0_2}-(x_{1_1}x_{1_2}+x_{2_1}x_{2_2}+x_{3_1}x_{3_2})</math></center>
@@ Line 81: / Line 83: @@
-<center><math>\mathbf P_1 \cdot \mathbf P_2 = p_{0_1}p_{0_2}-(p_{1_1}p_{1_2}+p_{2_1}p_{2_2}+p_{3_1}p_{3_2})</math></center>
+<center><math>\Rightarrow \mathbf P_1 \cdot \mathbf P_2 = p_{0_1}p_{0_2}-(p_{1_1}p_{1_2}+p_{2_1}p_{2_2}+p_{3_1}p_{3_2})</math></center>
 <center><math>\mathbf P_1 \cdot \mathbf P_2 = E_{1}E_{2}-(\vec p_1 \vec p_2)</math></center>

← Older revision		Revision as of 22:04, 8 June 2017
Line 75:		Line 75:
	<center><math>\mathbf (\mathbf P_1 +\mathbf P_2)^2 \equiv m_1^2+2 \mathbf P_1 \mathbf P_2+m_2^2</math></center>		<center><math>\mathbf (\mathbf P_1 +\mathbf P_2)^2 \equiv m_1^2+2 \mathbf P_1 \mathbf P_2+m_2^2</math></center>

		+
		+
		+	<center><math>\mathbf R_1 \cdot \mathbf R_2 = x_{0_1}x_{0_2}-(x_{1_1}x_{1_2}+x_{2_1}x_{2_2}+x_{3_1}x_{3_2})</math></center>
		+
		+
		+
		+	<center><math>\mathbf P_1 \cdot \mathbf P_2 = p_{0_1}p_{0_2}-(p_{1_1}p_{1_2}+p_{2_1}p_{2_2}+p_{3_1}p_{3_2})</math></center>
		+
		+
		+	<center><math>\mathbf P_1 \cdot \mathbf P_2 = E_{1}E_{2}-(\vec p_1 \vec p_2)</math></center>

← Older revision		Revision as of 20:25, 8 June 2017
Line 1:		Line 1:
		+	<center><math>\textbf{\underline{Navigation}}</math>
		+
		+	[[Uniform_distribution_in_Energy_and_Theta_LUND_files\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Weighted_Isotropic_Distribution_in_Lab_Frame\|<math>\triangle </math>]]
		+	[[4-vectors\|<math>\vartriangleright </math>]]
		+
		+	</center>
		+
	=4-momenta=		=4-momenta=

Line 66:		Line 74:

	<center><math>\mathbf (\mathbf P_1 +\mathbf P_2)^2 \equiv m_1^2+2 \mathbf P_1 \mathbf P_2+m_2^2</math></center>		<center><math>\mathbf (\mathbf P_1 +\mathbf P_2)^2 \equiv m_1^2+2 \mathbf P_1 \mathbf P_2+m_2^2</math></center>
		+
		+
		+
		+	----
		+
		+
		+	<center><math>\textbf{\underline{Navigation}}</math>
		+
		+	[[Uniform_distribution_in_Energy_and_Theta_LUND_files\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Weighted_Isotropic_Distribution_in_Lab_Frame\|<math>\triangle </math>]]
		+	[[4-vectors\|<math>\vartriangleright </math>]]
		+
		+	</center>