The TLorentzRotation class describes Lorentz transformations including Lorentz boosts and rotations (see TRotation)

         | xx  xy  xz  xt |
         |                |
         | yx  yy  yz  yt |
lambda = |                |
         | zx  zy  zz  zt |
         |                |
         | tx  ty  tz  tt |

Declaration

By default it is initialized to the identity matrix, but it may also be intialized by an other TLorentzRotation, by a pure TRotation or by a boost:

TLorentzRotation l; // l is initialized as identity TLorentzRotation m(l); // m = l TRotation r; TLorentzRotation lr(r); TLorentzRotation lb1(bx,by,bz); TVector3 b; TLorentzRotation lb2(b);

The Matrix for a Lorentz boosts is:

| 1+gamma'*bx*bx  gamma'*bx*by   gamma'*bx*bz  gamma*bx |
|  gamma'*by*bx  1+gamma'*by*by  gamma'*by*bz  gamma*by |
|  gamma'*bz*bx   gamma'*bz*by  1+gamma'*bz*bz gamma*bz |
|    gamma*bx       gamma*by       gamma*bz     gamma   |

with the boost vector b=(bx,by,bz) and gamma=1/Sqrt(1-beta*beta) and gamma'=(gamma-1)/beta*beta.

Access to the matrix components/Comparisons

Access to the matrix components is possible through the member functions XX(), XY() .. TT(), through the operator (int,int):

Double_t xx;
TLorentzRotation l;
xx = l.XX(); // gets the xx component
xx = l(0,0); // gets the xx component
if (l==m) {...} // test for equality
if (l !=m) {...} // test for inequality
if (l.IsIdentity()) {...} // test for identity

Transformations of a LorentzRotation

Compound transformations

There are four possibilities to find the product of two TLorentzRotation transformations:

TLorentzRotation a,b,c;
c = b*a;// product
c = a.MatrixMultiplication(b); // a is unchanged
a *= b;// Attention: a=a*b
c = a.Transform(b)// a=b*a then c=a

Lorentz boosts

Double_t bx, by, bz;
TVector3 v(bx,by,bz);
TLorentzRotation l;
l.Boost(v);
l.Boost(bx,by,bz);

Rotations

TVector3 axis;
l.RotateX(TMath::Pi()); // rotation around x-axis
l.Rotate(.5,axis);// rotation around specified vector

Inverse transformation

The matrix for the inverse transformation of a TLorentzRotation is as follows:

| xx  yx  zx -tx |
|                |
| xy  yy  zy -ty |
|                |
| xz  yz  zz -tz |
|                |
|-xt -yt -zt  tt |

To return the inverse transformation keeping the current unchanged use the member function Inverse(). Invert() inverts the current TLorentzRotation:

l1 = l2.Inverse(); // l1 is inverse of l2, l2 unchanged

l1 = l2.Invert(); // invert l2, then l1=l2

Transformation of a TLorentzVector

To apply TLorentzRotation to TLorentzVector you can use either the VectorMultiplication() member function or the * operator. You can also use the Transform() function and the *= operator of the TLorentzVector class.:

TLorentzVector v;
...
v=l.VectorMultiplication(v);
v = l * v;
v.Transform(l);
v *= l; // Attention v = l*v

Definition at line 20 of file TLorentzRotation.h.

Classes
class	TLorentzRotationRow

Public Member Functions
	TLorentzRotation ()

	TLorentzRotation (const TRotation &)

	TLorentzRotation (const TLorentzRotation &)

	TLorentzRotation (Double_t, Double_t, Double_t)

	TLorentzRotation (const TVector3 &)

TLorentzRotation &	Boost (Double_t, Double_t, Double_t)

TLorentzRotation &	Boost (const TVector3 &)

TLorentzRotation	Inverse () const

TLorentzRotation &	Invert ()

Bool_t	IsIdentity () const

TLorentzRotation	MatrixMultiplication (const TLorentzRotation &) const

Bool_t	operator!= (const TLorentzRotation &) const

Double_t	operator() (int, int) const

TLorentzVector	operator* (const TLorentzVector &) const

TLorentzRotation	operator* (const TLorentzRotation &) const

TLorentzRotation &	operator*= (const TLorentzRotation &)

TLorentzRotation &	operator= (const TLorentzRotation &)

TLorentzRotation &	operator= (const TRotation &)

Bool_t	operator== (const TLorentzRotation &) const

TLorentzRotationRow	operator[] (int) const

TLorentzRotation &	Rotate (Double_t, const TVector3 &)

TLorentzRotation &	Rotate (Double_t, const TVector3 *)

TLorentzRotation &	RotateX (Double_t)

TLorentzRotation &	RotateY (Double_t)

TLorentzRotation &	RotateZ (Double_t)

TLorentzRotation &	Transform (const TLorentzRotation &)

TLorentzRotation &	Transform (const TRotation &)

Double_t	TT () const

Double_t	TX () const

Double_t	TY () const

Double_t	TZ () const

TLorentzVector	VectorMultiplication (const TLorentzVector &) const

Double_t	XT () const

Double_t	XX () const

Double_t	XY () const

Double_t	XZ () const

Double_t	YT () const

Double_t	YX () const

Double_t	YY () const

Double_t	YZ () const

Double_t	ZT () const

Double_t	ZX () const

Double_t	ZY () const

Double_t	ZZ () const

Protected Member Functions
	TLorentzRotation (Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t, Double_t)

void	SetBoost (Double_t, Double_t, Double_t)

Protected Attributes
Double_t	ftt

Double_t	ftx

Double_t	fty

Double_t	ftz

Double_t	fxt

Double_t	fxx

Double_t	fxy

Double_t	fxz

Double_t	fyt

Double_t	fyx

Double_t	fyy

Double_t	fyz

Double_t	fzt

Double_t	fzx

Double_t	fzy

Double_t	fzz

#include <TLorentzRotation.h>

Inheritance diagram for TLorentzRotation:

[legend]

Constructor & Destructor Documentation

◆ TLorentzRotation() [1/6]

TLorentzRotation::TLorentzRotation ( )

Definition at line 136 of file TLorentzRotation.cxx.

◆ TLorentzRotation() [2/6]

TLorentzRotation::TLorentzRotation ( const TRotation & r )

Definition at line 142 of file TLorentzRotation.cxx.

◆ TLorentzRotation() [3/6]

TLorentzRotation::TLorentzRotation ( const TLorentzRotation & r )

Definition at line 148 of file TLorentzRotation.cxx.

◆ TLorentzRotation() [4/6]

TLorentzRotation::TLorentzRotation	(	Double_t	bx,
		Double_t	by,
		Double_t	bz
	)

Definition at line 164 of file TLorentzRotation.cxx.

◆ TLorentzRotation() [5/6]

TLorentzRotation::TLorentzRotation ( const TVector3 & p )

Definition at line 172 of file TLorentzRotation.cxx.

◆ TLorentzRotation() [6/6]

TLorentzRotation::TLorentzRotation	(	Double_t	rxx,
		Double_t	rxy,
		Double_t	rxz,
		Double_t	rxt,
		Double_t	ryx,
		Double_t	ryy,
		Double_t	ryz,
		Double_t	ryt,
		Double_t	rzx,
		Double_t	rzy,
		Double_t	rzz,
		Double_t	rzt,
		Double_t	rtx,
		Double_t	rty,
		Double_t	rtz,
		Double_t	rtt
	)

protected

Definition at line 154 of file TLorentzRotation.cxx.

Member Function Documentation

◆ Boost() [1/2]

TLorentzRotation & TLorentzRotation::Boost	(	Double_t	bx,
		Double_t	by,
		Double_t	bz
	)

inline

Definition at line 278 of file TLorentzRotation.h.

◆ Boost() [2/2]

TLorentzRotation & TLorentzRotation::Boost ( const TVector3 & b )

inline

Definition at line 282 of file TLorentzRotation.h.

◆ Inverse()

TLorentzRotation TLorentzRotation::Inverse ( ) const

inline

Definition at line 267 of file TLorentzRotation.h.

◆ Invert()

TLorentzRotation & TLorentzRotation::Invert ( )

inline

Definition at line 274 of file TLorentzRotation.h.

◆ IsIdentity()

Bool_t TLorentzRotation::IsIdentity ( ) const

inline

Definition at line 231 of file TLorentzRotation.h.

◆ MatrixMultiplication()

TLorentzRotation TLorentzRotation::MatrixMultiplication ( const TLorentzRotation & b ) const

Definition at line 221 of file TLorentzRotation.cxx.

◆ operator!=()

Bool_t TLorentzRotation::operator!= ( const TLorentzRotation & r ) const

inline

Definition at line 223 of file TLorentzRotation.h.

◆ operator()()

Double_t TLorentzRotation::operator()	(	int	i,
		int	j
	)		const

Definition at line 177 of file TLorentzRotation.cxx.

◆ operator*() [1/2]

TLorentzVector TLorentzRotation::operator* ( const TLorentzVector & p ) const

inline

Definition at line 247 of file TLorentzRotation.h.

◆ operator*() [2/2]

TLorentzRotation TLorentzRotation::operator* ( const TLorentzRotation & m ) const

inline

Definition at line 251 of file TLorentzRotation.h.

◆ operator*=()

TLorentzRotation & TLorentzRotation::operator*= ( const TLorentzRotation & m )

inline

Definition at line 255 of file TLorentzRotation.h.

◆ operator=() [1/2]

TLorentzRotation & TLorentzRotation::operator= ( const TLorentzRotation & r )

inline

Definition at line 171 of file TLorentzRotation.h.

◆ operator=() [2/2]

TLorentzRotation & TLorentzRotation::operator= ( const TRotation & r )

inline

Definition at line 188 of file TLorentzRotation.h.

◆ operator==()

Bool_t TLorentzRotation::operator== ( const TLorentzRotation & r ) const

inline

Definition at line 206 of file TLorentzRotation.h.

◆ operator[]()

TLorentzRotation::TLorentzRotationRow TLorentzRotation::operator[] ( int i ) const

inline

Definition at line 167 of file TLorentzRotation.h.

◆ Rotate() [1/2]

TLorentzRotation & TLorentzRotation::Rotate	(	Double_t	angle,
		const TVector3 &	axis
	)

inline

Definition at line 298 of file TLorentzRotation.h.

◆ Rotate() [2/2]

TLorentzRotation & TLorentzRotation::Rotate	(	Double_t	angle,
		const TVector3 *	axis
	)

inline

Definition at line 302 of file TLorentzRotation.h.

◆ RotateX()

TLorentzRotation & TLorentzRotation::RotateX ( Double_t angle )

inline

Definition at line 286 of file TLorentzRotation.h.

◆ RotateY()

TLorentzRotation & TLorentzRotation::RotateY ( Double_t angle )

inline

Definition at line 290 of file TLorentzRotation.h.

◆ RotateZ()

TLorentzRotation & TLorentzRotation::RotateZ ( Double_t angle )

inline

Definition at line 294 of file TLorentzRotation.h.

◆ SetBoost()

void TLorentzRotation::SetBoost	(	Double_t	bx,
		Double_t	by,
		Double_t	bz
	)

protected

Definition at line 204 of file TLorentzRotation.cxx.

◆ Transform() [1/2]

TLorentzRotation & TLorentzRotation::Transform ( const TLorentzRotation & m )

inline

Definition at line 259 of file TLorentzRotation.h.

◆ Transform() [2/2]

TLorentzRotation & TLorentzRotation::Transform ( const TRotation & m )

inline

Definition at line 263 of file TLorentzRotation.h.

◆ TT()

Double_t TLorentzRotation::TT ( ) const

inline

Definition at line 158 of file TLorentzRotation.h.

◆ TX()

Double_t TLorentzRotation::TX ( ) const

inline

Definition at line 155 of file TLorentzRotation.h.

◆ TY()

Double_t TLorentzRotation::TY ( ) const

inline

Definition at line 156 of file TLorentzRotation.h.

◆ TZ()

Double_t TLorentzRotation::TZ ( ) const

inline

Definition at line 157 of file TLorentzRotation.h.

◆ VectorMultiplication()

TLorentzVector TLorentzRotation::VectorMultiplication ( const TLorentzVector & p ) const

inline

Definition at line 240 of file TLorentzRotation.h.

◆ XT()

Double_t TLorentzRotation::XT ( ) const

inline

Definition at line 146 of file TLorentzRotation.h.

◆ XX()

Double_t TLorentzRotation::XX ( ) const

inline

Definition at line 143 of file TLorentzRotation.h.

◆ XY()

Double_t TLorentzRotation::XY ( ) const

inline

Definition at line 144 of file TLorentzRotation.h.

◆ XZ()

Double_t TLorentzRotation::XZ ( ) const

inline

Definition at line 145 of file TLorentzRotation.h.

◆ YT()

Double_t TLorentzRotation::YT ( ) const

inline

Definition at line 150 of file TLorentzRotation.h.

◆ YX()

Double_t TLorentzRotation::YX ( ) const

inline

Definition at line 147 of file TLorentzRotation.h.

◆ YY()

Double_t TLorentzRotation::YY ( ) const

inline

Definition at line 148 of file TLorentzRotation.h.

◆ YZ()

Double_t TLorentzRotation::YZ ( ) const

inline

Definition at line 149 of file TLorentzRotation.h.

◆ ZT()

Double_t TLorentzRotation::ZT ( ) const

inline

Definition at line 154 of file TLorentzRotation.h.

◆ ZX()

Double_t TLorentzRotation::ZX ( ) const

inline

Definition at line 151 of file TLorentzRotation.h.

◆ ZY()

Double_t TLorentzRotation::ZY ( ) const

inline

Definition at line 152 of file TLorentzRotation.h.

◆ ZZ()

Double_t TLorentzRotation::ZZ ( ) const

inline

Definition at line 153 of file TLorentzRotation.h.

Member Data Documentation

◆ ftt

Double_t TLorentzRotation::ftt

protected

Definition at line 122 of file TLorentzRotation.h.

◆ ftx

Double_t TLorentzRotation::ftx

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fty

Double_t TLorentzRotation::fty

protected

Definition at line 122 of file TLorentzRotation.h.

◆ ftz

Double_t TLorentzRotation::ftz

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fxt

Double_t TLorentzRotation::fxt

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fxx

Double_t TLorentzRotation::fxx

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fxy

Double_t TLorentzRotation::fxy

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fxz

Double_t TLorentzRotation::fxz

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fyt

Double_t TLorentzRotation::fyt

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fyx

Double_t TLorentzRotation::fyx

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fyy

Double_t TLorentzRotation::fyy

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fyz

Double_t TLorentzRotation::fyz

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fzt

Double_t TLorentzRotation::fzt

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fzx

Double_t TLorentzRotation::fzx

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fzy

Double_t TLorentzRotation::fzy

protected

Definition at line 122 of file TLorentzRotation.h.

◆ fzz

Double_t TLorentzRotation::fzz

protected

Definition at line 122 of file TLorentzRotation.h.

Libraries for TLorentzRotation:

[legend]

The documentation for this class was generated from the following files:

math/physics/inc/TLorentzRotation.h
math/physics/src/TLorentzRotation.cxx

Declaration

Access to the matrix components/Comparisons

Transformations of a LorentzRotation

Compound transformations

Lorentz boosts

Rotations

Inverse transformation

Transformation of a TLorentzVector

Classes

Public Member Functions

Protected Member Functions

Protected Attributes

Constructor & Destructor Documentation

◆ TLorentzRotation() [1/6]

◆ TLorentzRotation() [2/6]

◆ TLorentzRotation() [3/6]

◆ TLorentzRotation() [4/6]

◆ TLorentzRotation() [5/6]

◆ TLorentzRotation() [6/6]

Member Function Documentation

◆ Boost() [1/2]

◆ Boost() [2/2]

◆ Inverse()

◆ Invert()

◆ IsIdentity()

◆ MatrixMultiplication()

◆ operator!=()

◆ operator()()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator[]()

◆ Rotate() [1/2]

◆ Rotate() [2/2]

◆ RotateX()

◆ RotateY()

◆ RotateZ()

◆ SetBoost()

◆ Transform() [1/2]

◆ Transform() [2/2]

◆ TT()

◆ TX()

◆ TY()

◆ TZ()

◆ VectorMultiplication()

◆ XT()

◆ XX()

◆ XY()

◆ XZ()

◆ YT()

◆ YX()

◆ YY()

◆ YZ()

◆ ZT()

◆ ZX()

◆ ZY()

◆ ZZ()

Member Data Documentation

◆ ftt

◆ ftx

◆ fty

◆ ftz

◆ fxt

◆ fxx

◆ fxy

◆ fxz

◆ fyt

◆ fyx

◆ fyy

◆ fyz

◆ fzt

◆ fzx

◆ fzy

◆ fzz