Mandelstam Representation - Revision history

Vanwdani at 18:48, 15 May 2018

2018-05-15T18:48:21Z

Vanwdani at 22:26, 8 June 2017

2017-06-08T22:26:49Z

Vanwdani at 22:25, 8 June 2017

2017-06-08T22:25:09Z

Vanwdani: /* Mandelstam Representation */

2017-06-08T20:32:27Z

Mandelstam Representation

Vanwdani at 18:49, 7 June 2017

2017-06-07T18:49:05Z

Vanwdani: /* Mandelstam Representation */

2017-06-02T09:33:58Z

Mandelstam Representation

Vanwdani: /* Mandelstam Representation */

2017-06-01T19:28:20Z

Mandelstam Representation

Vanwdani: /* Mandelstam Representation */

2017-06-01T19:22:37Z

Mandelstam Representation

Vanwdani: Created page with "=Mandelstam Representation= 400 px $\Longrightarrow \left({\mathbf P_1^}+ {\mathbf P_2^{}}\right)^2=\left({\mathbf P_…"$

2017-05-31T20:43:22Z

Created page with "=Mandelstam Representation= <center> 400 px</center> <center><math>\Longrightarrow \left({\mathbf P_1^*}+ {\mathbf P_2^{*}}\right)^2=\left({\mathbf P_…"

New page

=Mandelstam Representation=

<center>[[File:Mandelstam.png | 400 px]]</center>

<center><math>\Longrightarrow \left({\mathbf P_1^*}+ {\mathbf P_2^{*}}\right)^2=\left({\mathbf P_1^{'*}}+ {\mathbf P_2^{'*}}\right)^2\equiv s</math></center>

<center><math>\Longrightarrow \left({\mathbf P_1^*}- {\mathbf P_1^{'*}}\right)^2=\left({\mathbf P_2^*}- {\mathbf P_2^{'*}}\right)^2\equiv t</math></center>

<center><math>\Longrightarrow \left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2=\left({\mathbf P_2^*}- {\mathbf P_1^{'*}}\right)^2\equiv s</math></center>

@@ Line 1: / Line 1: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[4-momenta|<math>\vartriangleleft </math>]]
@@ Line 31: / Line 31: @@
-<center><math>\textbf{\underline{Navigation}}</math>
+<center><math>\underline{\textbf{Navigation}}</math>
 [[4-momenta|<math>\vartriangleleft </math>]]

@@ Line 1: / Line 1: @@
 <center><math>\textbf{\underline{Navigation}}</math>
-[[New_4-momentum_quantities|<math>\vartriangleleft </math>]]
+[[4-momenta|<math>\vartriangleleft </math>]]
-[[VanWasshenova_Thesis#Weighted_Isotropic_Distribution_in_Lab_Frame|<math>\triangle </math>]]
+[[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[4-vectors|<math>\vartriangleright </math>]]
+[[S-Channel|<math>\vartriangleright </math>]]
 </center>
@@ Line 33: / Line 33: @@
 <center><math>\textbf{\underline{Navigation}}</math>
-[[New_4-momentum_quantities|<math>\vartriangleleft </math>]]
+[[4-momenta|<math>\vartriangleleft </math>]]
-[[VanWasshenova_Thesis#Weighted_Isotropic_Distribution_in_Lab_Frame|<math>\triangle </math>]]
+[[VanWasshenova_Thesis#Moller_Scattering|<math>\triangle </math>]]
-[[4-vectors|<math>\vartriangleright </math>]]
+[[S-Channel|<math>\vartriangleright </math>]]
 </center>

← Older revision		Revision as of 22:25, 8 June 2017
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−	~~==s Channel==~~

−	~~The s quantity is known as the square of the center of mass energy (invariant mass)~~
−	~~<center><math>s \equiv \left({\mathbf P_1^}+ {\mathbf P_2^{}}\right)^2=\left({\mathbf P_1^{'}}+ {\mathbf P_2^{'}}\right)^2</math></center>~~
−
−
−
−
−	~~<center><math>s \equiv \left({\mathbf P_1^}+ {\mathbf P_2^{}}\right)^2</math></center>~~
−
−
−	~~<center><math>s \equiv \mathbf P_1^{2}+2 \mathbf P_1^ \mathbf P_2^+ \mathbf P_2^{2}</math></center>~~
−
−
−	~~As shown earlier, the square of a 4-momentum is~~
−
−
−	~~<center><math>\mathbf P^{2} \equiv m^2</math></center>~~
−
−
−	~~<center><math>s \equiv m^{2}+2 \mathbf P_1^* \mathbf P_2^*+ m_2^{2}</math></center>~~
−
−
−	~~This gives~~
−
−	~~<center><math>s \equiv 2m^{2}+2 \mathbf P_1^* \mathbf P_2^*</math></center>~~
−
−
−	~~Similarly, the scalar product of two 4-momentums~~
−
−	~~<center><math>s \equiv 2m^2+2(E_1^E_2^-\vec p_1^* \vec p_2^*)</math></center>~~
−
−
−	~~In the center of mass frame of reference,~~
−
−	~~<center><math>E_1^=E_2^ \quad and \quad \vec p_1^=-\vec p_2^</math></center>~~
−
−
−	~~<center><math>s \equiv 2m^2+2(E_1^{2}+\vec p_1^{2} )</math></center>~~
−
−
−	~~Using the relativistic energy equation~~
−
−	~~<center><math>E^2 \equiv p^2+m^2</math></center>~~
−
−
−	~~<center><math>s \equiv 2m^2+2((m^2+p_1^{2})+p_1^{2})</math></center>~~
−
−
−	~~<center><math>s=4(m_{CM}^2+p_{CM}^2)</math></center>~~
−
−	~~==t Channel==~~
−	~~The t quantity is known as the square of the 4-momentum transfer~~
−
−	~~<center><math>t \equiv \left({\mathbf P_1^}- {\mathbf P_1^{'}}\right)^2=\left({\mathbf P_2^{}}+ {\mathbf P_2^{'}}\right)^2</math></center>~~
−
−	~~<center>[[File:400px-CMcopy.png]]</center>~~
−
−
−
−	~~<center><math>t \equiv \left({\mathbf P_1^}- {\mathbf P_1^{'}}\right)^2</math></center>~~
−
−
−	~~<center><math>t \equiv P_1^{2}-2P_1^P_1^{'}+P_1^{'2}</math></center>~~
−
−
−	~~<center><math>t \equiv 2m_1^2-2E_1^E_1^{'}+2p_1^p_1^{'}</math></center>~~
−
−
−	~~<center><math>t \equiv 2m_1^-2E_1^{2}+2p_1^{*2}cos\ \theta</math></center>~~
−
−
−	~~<center><math>t \equiv -2p_1^{*2}(1-cos\ \theta)</math></center>~~
−
−	~~==u Channel==~~

@@ Line 23: / Line 23: @@
 <center><math>\Longrightarrow \left({\mathbf P_1^*}- {\mathbf P_2^{'*}}\right)^2=\left({\mathbf P_2^*}- {\mathbf P_1^{'*}}\right)^2\equiv u</math></center>
 The s quantity is known as the square of the center of mass energy (invariant mass)
 The t quantity is known as the square of the 4-momentum transfer

← Older revision		Revision as of 18:49, 7 June 2017
Line 1:		Line 1:
		+	<center><math>\textbf{\underline{Navigation}}</math>
		+
		+	[[New_4-momentum_quantities\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Weighted_Isotropic_Distribution_in_Lab_Frame\|<math>\triangle </math>]]
		+	[[4-vectors\|<math>\vartriangleright </math>]]
		+
		+	</center>
		+
	=Mandelstam Representation=		=Mandelstam Representation=

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	The t quantity is known as the square of the 4-momentum transfer		The t quantity is known as the square of the 4-momentum transfer
		+
		+
		+
		+	----
		+
		+
		+	<center><math>\textbf{\underline{Navigation}}</math>
		+
		+	[[New_4-momentum_quantities\|<math>\vartriangleleft </math>]]
		+	[[VanWasshenova_Thesis#Weighted_Isotropic_Distribution_in_Lab_Frame\|<math>\triangle </math>]]
		+	[[4-vectors\|<math>\vartriangleright </math>]]
		+
		+	</center>

← Older revision		Revision as of 09:33, 2 June 2017
Line 13:		Line 13:


−	<center><math>\Longrightarrow \left({\mathbf P_1^}- {\mathbf P_2^{'}}\right)^2=\left({\mathbf P_2^}- {\mathbf P_1^{'}}\right)^2\equiv s</math></center>	+	<center><math>\Longrightarrow \left({\mathbf P_1^}- {\mathbf P_2^{'}}\right)^2=\left({\mathbf P_2^}- {\mathbf P_1^{'}}\right)^2\equiv u</math></center>

← Older revision		Revision as of 19:28, 1 June 2017
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	<center><math>\Longrightarrow \left({\mathbf P_1^}- {\mathbf P_2^{'}}\right)^2=\left({\mathbf P_2^}- {\mathbf P_1^{'}}\right)^2\equiv s</math></center>		<center><math>\Longrightarrow \left({\mathbf P_1^}- {\mathbf P_2^{'}}\right)^2=\left({\mathbf P_2^}- {\mathbf P_1^{'}}\right)^2\equiv s</math></center>
		+
		+
		+	The s quantity is known as the square of the center of mass energy (invariant mass)
		+
		+
		+	The t quantity is known as the square of the 4-momentum transfer

← Older revision		Revision as of 19:22, 1 June 2017
Line 1:		Line 1:
	=Mandelstam Representation=		=Mandelstam Representation=
		+

	<center>[[File:Mandelstam.png \| 400 px]]</center>		<center>[[File:Mandelstam.png \| 400 px]]</center>

Mandelstam Representation - Revision history

Vanwdani at 18:48, 15 May 2018

Vanwdani at 22:26, 8 June 2017

Vanwdani at 22:25, 8 June 2017

Vanwdani: /* Mandelstam Representation */

Vanwdani at 18:49, 7 June 2017

Vanwdani: /* Mandelstam Representation */

Vanwdani: /* Mandelstam Representation */

Vanwdani: /* Mandelstam Representation */

Vanwdani: Created page with "=Mandelstam Representation= 400 px \Longrightarrow \left({\mathbf P_1^*}+ {\mathbf P_2^{*}}\right)^2=\left({\mathbf P_…"

Vanwdani: Created page with "=Mandelstam Representation= 400 px $\Longrightarrow \left({\mathbf P_1^}+ {\mathbf P_2^{}}\right)^2=\left({\mathbf P_…"$