Lorentz boost class with the (4D) transformation represented internally by a 4x4 orthosymplectic matrix.

A variable names bgamma appears in several places in this file.

See also BoostX, BoostY and BoostZ for classes representing specialized Lorentz boosts. Also, the 3-D rotation classes can be considered to be special Lorentz transformations which do not mix space and time components.

A few words of elaboration are needed to make its meaning clear. On page 69 of Misner, Thorne and Wheeler, (Exercise 2.7) the elements of the matrix for a general Lorentz boost are given as

\[ \Lambda^{j'}_k = \Lambda^{k'}_j = (\gamma - 1) n^j n^k + \delta^{jk} \]

where the n^i are unit vectors in the direction of the three spatial axes. Using the definitions, \( n^i = \beta_i/\beta \) , then, for example,

\[ \Lambda_{xy} = (\gamma - 1) n_x n_y = (\gamma - 1) \beta_x \beta_y/\beta^2 \]

By definition,

\[ \gamma^2 = 1/(1 - \beta^2) \]

so that

\[ \gamma^2 \beta^2 = \gamma^2 - 1 \]

or

\[ \beta^2 = (\gamma^2 - 1)/\gamma^2 \]

If we insert this into the expression for \( \Lambda_{xy} \), we get

\[ \Lambda_{xy} = (\gamma - 1) \gamma^2/(\gamma^2 - 1) \beta_x \beta_y \]

or, finally

\[ \Lambda_{xy} = \gamma^2/(\gamma+1) \beta_x \beta_y \]

The expression \( \gamma^2/(\gamma+1) \) is what we call bgamma in the code below.

Definition at line 46 of file Boost.h.

Public Types
enum	EBoostMatrixIndex { kXX = 0, kXY = 1, kXZ = 2, kXT = 3, kYY = 4, kYZ = 5, kYT = 6, kZZ = 7, kZT = 8, kTT = 9 }

enum	ELorentzRotationMatrixIndex { kLXX = 0, kLXY = 1, kLXZ = 2, kLXT = 3, kLYX = 4, kLYY = 5, kLYZ = 6, kLYT = 7, kLZX = 8, kLZY = 9, kLZZ = 10, kLZT = 11, kLTX = 12, kLTY = 13, kLTZ = 14, kLTT = 15 }

typedef double	Scalar

typedef DisplacementVector3D< Cartesian3D< double >, DefaultCoordinateSystemTag >	XYZVector
	The beta vector for this boost. More...

Public Member Functions
	Boost ()
	Default constructor (identity transformation) More...

	Boost (Scalar beta_x, Scalar beta_y, Scalar beta_z)
	Construct given a three Scalars beta_x, beta_y, and beta_z. More...

template<class Avector >
	Boost (const Avector &beta)
	Construct given a beta vector (which must have methods x(), y(), z()) More...

template<class IT >
	Boost (IT begin, IT end)
	Construct given a pair of pointers or iterators defining the beginning and end of an array of three Scalars to use as beta_x, _y, and _z. More...

	Boost (Boost const &b)
	copy constructor More...

	Boost (BoostX const &bx)
	Construct from an axial boost. More...

	Boost (BoostY const &by)

	Boost (BoostZ const &bz)

XYZVector	BetaVector () const

void	GetComponents (Scalar &beta_x, Scalar &beta_y, Scalar &beta_z) const
	Get components into beta_x, beta_y, and beta_z. More...

template<class IT >
void	GetComponents (IT begin, IT end) const
	Get given a pair of pointers or iterators defining the beginning and end of an array of three Scalars into which to place beta_x, beta_y, and beta_z. More...

template<class IT >
void	GetComponents (IT begin) const
	Get given a pointer or an iterator defining the beginning of an array into which to place beta_x, beta_y, and beta_z. More...

void	GetLorentzRotation (Scalar r[]) const
	Get elements of internal 4x4 symmetric representation, into a data array suitable for direct use as the components of a LorentzRotation Note – 16 Scalars will be written into the array; if the array is not that large, then this will lead to undefined behavior. More...

Boost	Inverse () const
	Return inverse of a boost. More...

void	Invert ()
	Invert a Boost in place. More...

bool	operator!= (const Boost &rhs) const

LorentzVector< ROOT::Math::PxPyPzE4D< double > >	operator() (const LorentzVector< ROOT::Math::PxPyPzE4D< double > > &v) const
	Lorentz transformation operation on a Minkowski ('Cartesian') LorentzVector. More...

template<class CoordSystem >
LorentzVector< CoordSystem >	operator() (const LorentzVector< CoordSystem > &v) const
	Lorentz transformation operation on a LorentzVector in any coordinate system. More...

template<class Foreign4Vector >
Foreign4Vector	operator() (const Foreign4Vector &v) const
	Lorentz transformation operation on an arbitrary 4-vector v. More...

template<class A4Vector >
A4Vector	operator* (const A4Vector &v) const
	Overload operator * for boost on a vector. More...

Boost &	operator= (Boost const &rhs)
	Assignment operator. More...

Boost &	operator= (BoostX const &bx)
	Assign from an axial pure boost. More...

Boost &	operator= (BoostY const &by)

Boost &	operator= (BoostZ const &bz)

bool	operator== (const Boost &rhs) const
	Equality/inequality operators. More...

void	Rectify ()
	Re-adjust components to eliminate small deviations from a perfect orthosyplectic matrix. More...

void	SetComponents (Scalar beta_x, Scalar beta_y, Scalar beta_z)
	Set components from beta_x, beta_y, and beta_z. More...

template<class Avector >
void	SetComponents (const Avector &beta)
	Set components from a beta vector. More...

template<class IT >
void	SetComponents (IT begin, IT end)
	Set given a pair of pointers or iterators defining the beginning and end of an array of three Scalars to use as beta_x,beta _y, and beta_z. More...

Protected Member Functions
void	SetIdentity ()

Private Attributes
Scalar	fM [10]

#include <Math/GenVector/Boost.h>

Member Typedef Documentation

◆ Scalar

typedef double ROOT::Math::Boost::Scalar

Definition at line 50 of file Boost.h.

◆ XYZVector

typedef DisplacementVector3D<Cartesian3D<double>, DefaultCoordinateSystemTag > ROOT::Math::Boost::XYZVector

The beta vector for this boost.

Definition at line 205 of file Boost.h.

Member Enumeration Documentation

◆ EBoostMatrixIndex

enum ROOT::Math::Boost::EBoostMatrixIndex

Enumerator
kXX
kXY
kXZ
kXT
kYY
kYZ
kYT
kZZ
kZT
kTT

Definition at line 59 of file Boost.h.

◆ ELorentzRotationMatrixIndex

enum ROOT::Math::Boost::ELorentzRotationMatrixIndex

Enumerator
kLXX
kLXY
kLXZ
kLXT
kLYX
kLYY
kLYZ
kLYT
kLZX
kLZY
kLZZ
kLZT
kLTX
kLTY
kLTZ
kLTT

Definition at line 52 of file Boost.h.

Constructor & Destructor Documentation

◆ Boost() [1/8]

ROOT::Math::Boost::Boost ( )

inline

Default constructor (identity transformation)

Definition at line 71 of file Boost.h.

◆ Boost() [2/8]

ROOT::Math::Boost::Boost	(	Scalar	beta_x,
		Scalar	beta_y,
		Scalar	beta_z
	)

inline

Construct given a three Scalars beta_x, beta_y, and beta_z.

Definition at line 76 of file Boost.h.

◆ Boost() [3/8]

template<class Avector >

ROOT::Math::Boost::Boost ( const Avector & beta )

inlineexplicit

Construct given a beta vector (which must have methods x(), y(), z())

Definition at line 84 of file Boost.h.

◆ Boost() [4/8]

template<class IT >

ROOT::Math::Boost::Boost	(	IT	begin,
		IT	end
	)

inline

Construct given a pair of pointers or iterators defining the beginning and end of an array of three Scalars to use as beta_x, _y, and _z.

Definition at line 91 of file Boost.h.

◆ Boost() [5/8]

ROOT::Math::Boost::Boost ( Boost const & b )

inline

copy constructor

Definition at line 96 of file Boost.h.

◆ Boost() [6/8]

ROOT::Math::Boost::Boost ( BoostX const & bx )

inlineexplicit

Construct from an axial boost.

Definition at line 104 of file Boost.h.

◆ Boost() [7/8]

ROOT::Math::Boost::Boost ( BoostY const & by )

inlineexplicit

Definition at line 105 of file Boost.h.

◆ Boost() [8/8]

ROOT::Math::Boost::Boost ( BoostZ const & bz )

inlineexplicit

Definition at line 106 of file Boost.h.

Member Function Documentation

◆ BetaVector()

DisplacementVector3D< Cartesian3D< Boost::Scalar > > ROOT::Math::Boost::BetaVector ( ) const

Definition at line 108 of file Boost.cxx.

◆ GetComponents() [1/3]

void ROOT::Math::Boost::GetComponents	(	Scalar &	beta_x,
		Scalar &	beta_y,
		Scalar &	beta_z
	)		const

Get components into beta_x, beta_y, and beta_z.

Definition at line 99 of file Boost.cxx.

◆ GetComponents() [2/3]

template<class IT >

void ROOT::Math::Boost::GetComponents	(	IT	begin,
		IT	end
	)		const

inline

Get given a pair of pointers or iterators defining the beginning and end of an array of three Scalars into which to place beta_x, beta_y, and beta_z.

Definition at line 180 of file Boost.h.

◆ GetComponents() [3/3]

template<class IT >

void ROOT::Math::Boost::GetComponents ( IT begin ) const

inline

Get given a pointer or an iterator defining the beginning of an array into which to place beta_x, beta_y, and beta_z.

Definition at line 194 of file Boost.h.

◆ GetLorentzRotation()

void ROOT::Math::Boost::GetLorentzRotation ( Scalar r[] ) const

Get elements of internal 4x4 symmetric representation, into a data array suitable for direct use as the components of a LorentzRotation Note – 16 Scalars will be written into the array; if the array is not that large, then this will lead to undefined behavior.

Definition at line 115 of file Boost.cxx.

◆ Inverse()

Boost ROOT::Math::Boost::Inverse ( ) const

Return inverse of a boost.

Definition at line 163 of file Boost.cxx.

◆ Invert()

void ROOT::Math::Boost::Invert ( )

Invert a Boost in place.

Definition at line 156 of file Boost.cxx.

◆ operator!=()

bool ROOT::Math::Boost::operator!= ( const Boost & rhs ) const

inline

Definition at line 280 of file Boost.h.

◆ operator()() [1/3]

LorentzVector< PxPyPzE4D< double > > ROOT::Math::Boost::operator() ( const LorentzVector< ROOT::Math::PxPyPzE4D< double > > & v ) const

Lorentz transformation operation on a Minkowski ('Cartesian') LorentzVector.

Definition at line 143 of file Boost.cxx.

◆ operator()() [2/3]

template<class CoordSystem >

LorentzVector<CoordSystem> ROOT::Math::Boost::operator() ( const LorentzVector< CoordSystem > & v ) const

inline

Lorentz transformation operation on a LorentzVector in any coordinate system.

Definition at line 232 of file Boost.h.

◆ operator()() [3/3]

template<class Foreign4Vector >

Foreign4Vector ROOT::Math::Boost::operator() ( const Foreign4Vector & v ) const

inline

Lorentz transformation operation on an arbitrary 4-vector v.

Preconditions: v must implement methods x(), y(), z(), and t() and the arbitrary vector type must have a constructor taking (x,y,z,t)

Definition at line 245 of file Boost.h.

◆ operator*()

template<class A4Vector >

A4Vector ROOT::Math::Boost::operator* ( const A4Vector & v ) const

inline

Overload operator * for boost on a vector.

Definition at line 256 of file Boost.h.

◆ operator=() [1/4]

Boost& ROOT::Math::Boost::operator= ( Boost const & rhs )

inline

Assignment operator.

Definition at line 114 of file Boost.h.

◆ operator=() [2/4]

Boost& ROOT::Math::Boost::operator= ( BoostX const & bx )

inline

Assign from an axial pure boost.

Definition at line 125 of file Boost.h.

◆ operator=() [3/4]

Boost& ROOT::Math::Boost::operator= ( BoostY const & by )

inline

Definition at line 127 of file Boost.h.

◆ operator=() [4/4]

Boost& ROOT::Math::Boost::operator= ( BoostZ const & bz )

inline

Definition at line 129 of file Boost.h.

◆ operator==()

bool ROOT::Math::Boost::operator== ( const Boost & rhs ) const

inline

Equality/inequality operators.

Definition at line 274 of file Boost.h.

◆ Rectify()

void ROOT::Math::Boost::Rectify ( )

Re-adjust components to eliminate small deviations from a perfect orthosyplectic matrix.

Definition at line 123 of file Boost.cxx.

◆ SetComponents() [1/3]

void ROOT::Math::Boost::SetComponents	(	Scalar	beta_x,
		Scalar	beta_y,
		Scalar	beta_z
	)

Set components from beta_x, beta_y, and beta_z.

Definition at line 76 of file Boost.cxx.

◆ SetComponents() [2/3]

template<class Avector >

void ROOT::Math::Boost::SetComponents ( const Avector & beta )

inline

Set components from a beta vector.

Definition at line 156 of file Boost.h.

◆ SetComponents() [3/3]

template<class IT >

void ROOT::Math::Boost::SetComponents	(	IT	begin,
		IT	end
	)

inline

Set given a pair of pointers or iterators defining the beginning and end of an array of three Scalars to use as beta_x,beta _y, and beta_z.

Definition at line 165 of file Boost.h.

◆ SetIdentity()

void ROOT::Math::Boost::SetIdentity ( )

protected

Definition at line 67 of file Boost.cxx.

Member Data Documentation

◆ fM

Scalar ROOT::Math::Boost::fM[10]

private

Definition at line 290 of file Boost.h.

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

math/genvector/inc/Math/GenVector/Boost.h
math/genvector/src/Boost.cxx

Public Types

Public Member Functions

Protected Member Functions

Private Attributes

Member Typedef Documentation

◆ Scalar

◆ XYZVector

Member Enumeration Documentation

◆ EBoostMatrixIndex

◆ ELorentzRotationMatrixIndex

Constructor & Destructor Documentation

◆ Boost() [1/8]

◆ Boost() [2/8]

◆ Boost() [3/8]

◆ Boost() [4/8]

◆ Boost() [5/8]

◆ Boost() [6/8]

◆ Boost() [7/8]

◆ Boost() [8/8]

Member Function Documentation

◆ BetaVector()

◆ GetComponents() [1/3]

◆ GetComponents() [2/3]

◆ GetComponents() [3/3]

◆ GetLorentzRotation()

◆ Inverse()

◆ Invert()

◆ operator!=()

◆ operator()() [1/3]

◆ operator()() [2/3]

◆ operator()() [3/3]

◆ operator*()

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ operator==()

◆ Rectify()

◆ SetComponents() [1/3]

◆ SetComponents() [2/3]

◆ SetComponents() [3/3]

◆ SetIdentity()

Member Data Documentation

◆ fM